Research ArticleRoute Selection of Multimodal Transport Based on ChinaRailway Transportation

Hui Zhang 1234 Yao Li 1 Qingpeng Zhang 5 and Dingjun Chen 123

1School of Transportation and Logistics Southwest Jiaotong University Chengdu 610031 China2National and Local Joint Engineering Laboratory of Comprehensive Intelligent Transportation Southwest Jiaotong UniversityChengdu 610031 China3National Engineering Laboratory of Integrated Transportation Big Data Application Technology Chengdu 610031 China4State Laboratory of Rail Transit (Under Preparation) Beijing China5School of Data Science City University of Hong Kong Kowloon Tong Hong Kong

Correspondence should be addressed to Dingjun Chen chen-dingjun163com

Received 4 April 2021 Revised 25 May 2021 Accepted 30 June 2021 Published 12 July 2021

Academic Editor Chi-Hua Chen

Copyright copy 2021 Hui Zhang et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e advantage ofmultimodal transport is that it can deliver the goods to their destination in a reasonable combination of transportmodes while ensuring security and punctuality Multimodal transportation can effectively reduce logistics costs improve logisticsefficiency and reduce environmental pollution In the process of multimodal transportation due to the interference of naturalfactors (weather terrain etc) and some special human factors it may have different degrees of impact on the transportation timeand transportation safety of different transportation modes +erefore when choosing a transportation method it is necessary toconsider the transportation time and transportation safety under the interference However the current research on multimodaltransport has not considered the impact of external interference on transportation time and transportation safety Compared withother modes of transportation external interference has a relatively small impact on railway transportation Railways can safelydeliver goods to their destinations on time Under the background of Chinarsquos huge railway network and advanced heavy-dutytechnology this paper establishes a multimodal transport route selection model for considering railway as the core introducestime penalty cost and damage compensation cost and takes the lowest comprehensive transportation cost as the model objectiveunder the premise of considering transportation reliability and transportation safety Finally taking a multimodal transportnetwork in China as an example an improved ant colony algorithm is used to solve the model and the results verify the rationalityof the model

1 Introduction

Multimodal transport [1] is a mode of cargo transportationthrough the connection and transshipment of two or moretransportation modes (such as railway transportation watertransportation road transportation and air transportation)to complete the transportation process At present China isat an important stage of economic structural transformationand upgrading and the freight transportation market isfacing historical changes +e establishment of a new andefficient logistics channel based onmultimodal transport canconnect Chinarsquos inland economy and coastal economywhich is the key to the transformation and upgrading of

Chinarsquos economic structure +is shows that promoting thedevelopment of multimodal transport is of great signifi-cance According to statistics in 2017 Chinarsquos multimodalfreight volume was 1368 billion tons accounting for 29 ofthe total freight volume of the society According to theldquoNotice on Further Encouraging Multimodal TransportWorkrdquo by 18 departments including the Ministry ofTransport Chinarsquos multimodal transport freight volume willreach 302 billion tons in 2020 By then the scale of mul-timodal transport freight will account for 6 of the totalfreight volume the proportion is still low +e multimodaltransport freight volume accounts for a small proportion ofthe whole societyrsquos freight volume which is caused by the

HindawiJournal of Advanced TransportationVolume 2021 Article ID 9984659 12 pageshttpsdoiorg10115520219984659

incomplete construction of Chinarsquos current integratedtransportation system With the increasing market re-quirements more efficient more resource-efficient andmore intensive transportation services are required toachieve a rational division of labor and organic linkage ofvarious modes of transportation and to give full play to theoverall efficiency and effectiveness of the integrated trans-portation system However at present all kinds of trans-portation modes in the integrated transportation system areself-contained which are only physically connected throughhubs and the limited joint command is carry out under theemergency condition +ere are some problems such asimperfect mechanism market segmentation prominenttransport structural contradictions weak hub service ca-pacity poor operational coordination and low safety andservice level which make the great potential of integratedtransportation not fully released It affects the full play of theefficiency of various modes of transport and the publicrsquossense of gain (quoted the 13th Five-Year Plan of IntegratedTransport Services) which cannot meet the economic re-liable and efficient freight demand

Compared with other modes of transportation rail-way transportation is more economical and environ-mentally friendly and the advantages of transportationreliability and transportation security are more obviousAt the same time railway transportation as a participantof multimodal transportation has good transportationconditions Data show that in 2018 the national railwayscompleted 319 billion tons of cargo shipments a year-on-year increase of 93 which increased transportation by272 million tons With the formation of the ldquofour verticaland four horizontalsrdquo networks of high-speed railwaysand the promotion of the ldquoeight vertical and eight hori-zontalsrdquo high-speed rail network the operating mileage ofthe railway reached 131000 kilometers of which theoperating mileage of the high-speed railway was31000 kilometers It is concluded that China has a hugerailway network and the operating mileage of railwayscovers the entire country Although railways have a na-tionwide road network and huge transportation capacitythey have not been fully utilized In 2018 Chinarsquos highwayfreight volume was 39568 billion tons accounting for7679 of the countryrsquos total freight Chinarsquos railway freightvolume was 4022 billion tons accounting for 781 of thecountryrsquos total freight So making full use of railway ca-pacity has become a key goal for China to promote thedevelopment of multimodal transport In response to thissituation relevant Chinese departments have formulated aldquoroad to rail transportationrdquo policy and railway manage-ment is included in the Ministry of Transport +esepolicies make it possible for railways to play a backbonerole in the integrated transportation system So it is urgentto study the cooperative operation theory and key tech-nologies of the railway-based integrated transportationsystem +is paper will deeply study the optimization ofmultimodal transport path selection with railway trans-portation as the main body and realize the rational divisionof labor and coordinated development of various trans-portation modes

In multimodal transport network design Christine andSabine [2] conducted a scenario-based assessment of thefuture position of intermodal transport within Belgium-based case studies and discussed service network designmodels for consolidation-based freight transport systemsDemir et al [3] studied the design problem of green mul-timodal transport network with uncertain transportationtime [4ndash6] and established a stochastic optimization modelthat can generate robust transportation plans according todifferent objectives (cost time and carbon emissions)Wang and Meng [7] considered a discrete multimodaltransport network design problem and decided whether thenetwork planner needs to establish or extend a path tominimize operating costs Cheng and Jin [8] constructed themultimodal transportation route selection models withcongestion considered under different low-carbon policesDemir et al [3] introduced a green intermodal servicenetwork design problem with travel time uncertainty(GISND-TTU) for combined offline intermodal routingdecisions of multiple commodities In the path optimizationof multimodal transport many scholars have made in-depthresearch based on different aspects Fazayeli et al [9] studiedthe problem of multimodal transport path optimizationunder fuzzy demand established a mixed-integer fuzzymathematical model and solved it by genetic algorithms[10] Fotuhi studied the optimization problem of multi-modal transport path with uncertain network topology [11]Idri et al [12] introduced a search method for the shortestpath algorithm in parallel distributed architecture to solvethe path optimization problem of dynamic multimodaltransport network with time dependence [13 14] Liu et al[15] established a super transportation network to predictthe generalized cost of multimodal transportation whichprovides technical support for the comprehensive trans-portation planning Li constructed a route selection modelfor cargo multimodal transportation and used an improvedant colony algorithm to be solved Tian et al [16] exploredthe influence of multiple time windows on the route se-lection of fresh products and designed genetic algorithms tosolve it Zhu et al established an evaluation model ofcontainer multimodal transport based on BP neural networkand solved the optimal path Russo et al [17] research objectis a variable of the operating cycle of a rail transit terminalthe variable considered is the overall average time of theterminal operation cycle relative to the number of trucks andvehicles entering the terminal which solved the problem ofthe efficiency of public rail transport Abderrahman et al[18] proposed a robust optimization model for the trans-portation cost of multimodal freight and the uncertainty ofnetwork terminal capacity [19] Liu et al [20] in the contextof global containerized transportation of soybeans considersthe transportation and purchase costs of soybeans estab-lishes a multimodal transport network model and optimizesthe soybean transportation path [21] Verma et al [22]designed a dual-objective mixed-integer linear program-ming model for the problem of joint transportation pathselection for dangerous goods with minimum transportationcosts and risks of transportation and designed a model-solving algorithm based on taboo search Toumazi and

2 Journal of Advanced Transportation

Kwon [23] introduced the conditional value-at-risk (CVaR)theory and built a CVaR-based road transport route opti-mization model for dangerous goods under a time-varyingnetwork [16 24] +e optimal dangerous goods roadtransport can be selected based on the risk aversion ofdecision makersrsquo path Sun and Long [25] took into accountthe customerrsquos need for timeliness of transportation whenplanning the multimodal transport path [26] and obtainedthe optimal solution through Pareto optimality

At present the research on multimodal transport doesnot consider the influence of natural factors such asweather terrain and some special human factors on thetransport [15] In actual transportation these factors maylead to the delay [27] of transport time and even theoccurrence of dangerous accidents [28] and damage ofgoods At this time the cost and time of the original op-timal path will change and the optimal path will changeaccordingly [29 30] +e multimodal transport researchbased on railways mostly focuses on transportation policyand there are few research projects on path selection+erefore this paper establishes a multimodal transportroute selection model based on railway transportationintroduces time penalty cost and damage compensationcost considering the transportation reliability and trans-portation safety factors in the transportation processaiming at the minimum transportation cost and finds theoptimal path that is in line with reality

2 Construction of MultimodalTransport Model

21 Problem Description +e route selection problem ofmultimodal transportation mainly based on railway trans-portation can be described as follows In a multimodaltransport network G (V A) Vis the node set of networksG and Ais the path set of networks G +e shipper requiresthat a batch of goods be transported from the originationo isin A to the destination d isin A +e carrier needs to considerthe reliability and safety of the transportation routes betweenthe origination and destination so as to select the trans-portation route and mode that can reach the destinationwithin the time specified by the shipper and ensure that thegoods are intact

22 Variable Definitions +e notation of parameters andvariables is shown in Table 1

3 Objective Functions

+e goal of multimodal transport is to maximize thetransport efficiency and spend as little cost and time aspossible to make the goods arrive at the destination safelyMultimodal transport is the combined transport of multiplemodes of transport and transportation cost and trans-portation time for different modes of transport are different+erefore when calculating the model target it is necessaryto choose a transportation mode with lower transportationcost and shorter transportation time However in the actual

transportation process the transportation cost and trans-portation time of various transportation modes are not fixed+ey will change with the interference of natural factors andsome special human factors Different transportation modeshave different antijamming capabilities and transportationcosts and transportation time have different degrees of var-iation For example in foggy weather conditions variousmodes of transportation will be affected but rail trans-portation will be less affected and the transportation time willbe slightly extended the speed of road transportation will begreatly reduced and safety accidents may occur due to op-erational errors not only the safety of life is involved but alsothe transported goods will be damaged +e carrier will haveto compensate the shipper for losses and the transportationcost and transportation time will increase significantly

When the transportation cost and transportation timeare dynamically changing it will dynamically affect thechoice of transportation mode +erefore the model built inthis paper focuses on the change of transportation cost andtransportation time during transportation In this paper thedegree of change in transportation time is expressed astransportation reliability and the time penalty cost isestablished +e degree of change in transportation cost isexpressed as transportation safety and the damage com-pensation cost is established At the same time consideringthe global low-carbon environmental protection at thecurrent stage low-carbon transportation is the top priorityfor the country Multimodal operation is an emerging ef-ficient transportation mode It is also necessary to reducecarbon emissions as much as possible in response to nationalcalls +erefore this paper will start from the cost energyconservation time transport reliability and transport safetyto build a path optimization model with the minimumcomprehensive cost

minZ ω1 C1 + C2 + C3( 1113857 + ω2C4 + ω3C5 (1)

In the formula Z is the comprehensive transport costC1 C2 C3 C4 and C5 are transportation cost transit costcarbon emission cost time penalty cost and damagecompensation cost respectively and ω1 ω2 and ω3 are theweights of each cost in the objective function

31 Transportation Cost and Transit Cost +e cost of freighttransportation between adjacent nodes is the transportationcost and the cost of replacing the transportation modeinside the transferable node is the transit cost

minC1 1113944iisinM

1113944jisinM

1113944sisinS

Qcsijd

sijx

sij

minC2 1113944iisinM

1113944sisinS

1113944

sprimeisinS

Qcssprimei y

ssprimei

(2)

32 CarbonEmissionCost In order to develop a low-carboneconomy countries all over the world have studied energyconservation and emission reduction and proposed a carbontax scheme Carbon tax is a tax imposed on carbon emissions

Journal of Advanced Transportation 3

and is an important means of limiting carbon emissions+ecalculation formula of carbon tax is as follows

θ 1113944t

0Dt(1 + λ)

minust (3)

In the formula Dt is the damage value of thet-yearcaused by the unit carbon emissions and λ is the discountrate In fact the carbon tax is not levied as high as possible Ifthe carbon tax is higher it will restrict the economic de-velopment of the country If the carbon tax is too low it willnot play a good role in energy conservation and emissionreduction According to the research of experts and scholarsin China the proposal of the Ministry of environmentalprotection for carbon tax is 20 $ton +erefore in thispaper the carbon tax is assumed to be 20 $ton and 002 $kg +e carbon emission cost is the product of carbonemissions and carbon tax

minC3 θ times 1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij (4)

33 Transportation Reliability and Time Penalty CostTransport reliability herein refers to the on-time arrival ratefrom the starting point to the end point within a specifiedtime using either mode of transport In the actual trans-portation process various modes of transportation will beaffected by natural factors and some special human factorsresulting in delays in transportation such as traffic jamscaused by road conditions trains will stop and wait duringthe meeting and long ramps will have a great impact on therunning speed and so on Transportation delay will prolong

the transportation time and may exceed the delivery timelimit so if the model does not take into account thetransportation reliability factors the obtained optimal pathwill lose its significance in the actual transportation contextIn order to quantify the impact of transportation reliabilityon transportation time this paper defines the time delaycoefficient taking into account the complex influencingfactors between adjacent nodes and taking values within 0ndash1so that the transportation time of the section is extendedlinearly on the basis of the original transportation time asshown in Figure 1

In the diagram t represents the transportation timebetween two nodes without considering the delay and μ isthe time delay coefficient When μ 0 there is no time delayin the transportation process of goods and the actualtransportation time of goods is the initial transportationtime t When μ 1 there is time delay in the transportationprocess of goods and the actual transportation time is theinitial time t plus the delay time quantified as t When μ isbetween 0 and 1 the delay time of goods is related to thedelay coefficient defining that the delay time has a linearrelationship with the delay coefficient

A certain penalty is imposed for transportation schemesthat exceed the time limit In order to quantify the impact ofthe time limit of delivery on the transportation plan se-lection the time penalty function is introduced in this paperTaking into account the changes in the psychological state ofthe consignee while waiting for the delivery of the goods thispaper adopts the fuzzy convenience function to express anddefines 2 hours as a state change gradient in case of ex-ceeding the arrival time limit and assigns different degrees ofpunishment to different state gradients as shown inFigure 2

Table 1 Subscripts and parameters used in mathematical formulations

Symbol DescriptionM Network node set (all nodes including the start node and the end node)K Transportable node setS S s sprime 1113864 1113865 transportation mode collectionQ Total quantity of goods to be transported in the multimodal transport modelπ Unit value of goods that need to be transportedψs

ijAccident damage coefficient from node city i to node city j transport modesis used for transportation

dsij

Transportation mileage from node city i to node city j transport modesis used for transportationμs

ijTime delay coefficient from node city i to node city j transport modesis used for transportation

csij

Unit transportation cost from node city i to node cityj transport modesis used for transportationcssrsquoi

Unit transfer cost at the transferable node i the mode of transport is changed fromsto sprime

Tssprimei

Transit time at the transferable node i the mode of transport is changed from s to sprimeVS Average speed of transportation mode s

ES Carbon emission factor unit carbon emissions of transportation mode s

E Total carbon emissions allowed in the modelT +e maximum delivery time of the goods specified in the modelxs

ijDecision variables if transportation modesis selected from city i to node city j then the value is 1 otherwise the value is 0

yssprimei

Decision variables if the mode of transportation changes from s to sprime in node city i then the value is 1 otherwise the value is 0Cd Cd represents the calculated value of total carbon emissionsX +e total transportation time from o to D

qsij

From the city i to the city j the transportation volume of mode s is adoptedqs

hiFrom the city h to the city i the transportation volume of mode s is adopted

4 Journal of Advanced Transportation

X 1113944iisinM

1113944jisinM

1113944sisinS

1 + μsij1113872 1113873

dsij

VS

xsij + 1113944

iisinM1113944sisinS

1113944

sprimeisinS

Tssprimei y

ssprimei (5)

minC4

0 XleT

y1

2(X minus T) TleXleT + 2

y1 T + 2leXleT + 4

y2 T + 4leX

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

Formula (5) is the transportation time calculation for-mula for any transportation scheme the first part is the sumof transportation time and delay time and the second part isthe transit time of the transportable node Formula (6) is thetime penalty cost calculation formula when the trans-portation time is from T to T + 2 the penalty function is alinear increasing function when the time is from T + 2 toT + 4 the penalty function is a constant (y1) when thetransportation time exceeds T + 4 the penalty function is aconstant (y2)

34 Transportation Safety and Damage Compensation CostsTransport safety in this paper refers to the value loss rate ofgoods transported during transportation from the startingpoint to the end point +e influencing factors mainly in-clude road conditions and traffic management status vehicletechnical performance and warranty quality as well as thedriverrsquos operating skill level and responsibility If a safetyaccident occurs during transportation the transportationgoods will be damaged +e carrier shall compensate theconsignor for the corresponding loss according to the degree

of damage to the goods because the liability of the accident isthat the carrier has not planned the transportation route Ifthe safety factors in the transportation process are notconsidered when optimizing the route the final result islikely to lose more In order to facilitate the calculation thispaper assumes that the degree of damage to the goods isdetermined by the severity of the accident when a safetyaccident occurs during transportation +at is to say if theseverity of the accident is relatively low the goods may onlybe partially damaged rather than completely damaged Inorder to quantify the impact of the severity of the accident onthe damage of the goods this paper proposes and defines theaccident damage coefficient the value is within 0ndash1 and thechange from 0 to 1 indicates that the degree of damage of thegoods increases gradually and the amount of compensationrequired by the carrier increases gradually and the amountof compensation is based on the value of the goods

minC5 1113944iisinM

1113944jisinM

1113944sisinS

ψsijx

sijQπ (7)

4 Constraints

41 Transportation Process Constraint

1113944sisinS

xsij le 1 forall(i j) isinM (8)

1113944

ssprimeisinS

yssprimei le 1 foralli isin K (9)

xshi + x

sprimeij ge 2y

ssprimei forallh i j isinMforalls sprime isin S (10)

1113944sisinS

qshi 1113944

sisinSq

sij forall(h i j) isinM (11)

Constraint (8) makes sure that only one mode oftransport can be selected between any adjacent nodesConstraint (9) ensures that only one transit can occur in anytransit node Constraint (10) guarantees the continuity oftransportation mode during transit Constraint (11) is theflow equilibrium constraint of nodes in the network

42 Carbon Emission Constraint

1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij Cd (12)

CdleE (13)

Constraint (12) is the formula of total carbon emissionsand for this paper which is a known constant Constraint(13) ensures that the transportation plan meets the totalcarbon emission limit

5 Multiobjective Ant Colony Algorithm

+e ant colony algorithm is a simulation evolution algorithmproposed by DORIGO It is an effective means to solve the

T0

Time penaltycost (yuan)

y2

y1

T + 2 T + 4 Time (h)

Figure 2 Time penalty cost function

10

t

Time delaycoefficient (μ)

Figure 1 Time delay function

Journal of Advanced Transportation 5

multiobjective optimization problem in discrete spacehowever the basic ant colony algorithm has the problems ofslow running efficiency premature convergence and easy tofall into a local optimal solution +is paper combines thesolution requirements of the multimodal transport pathselection model In order to improve the effectiveness of thealgorithm the basic algorithm is improved accordingly

51 Node Transition Probability Although the objectivefunction of the model in this paper is the total cost value in

the transportation process the time penalty cost is deter-mined by the length of the transportation time +e modeltarget expectation cost and time are as small as possible so inthe improved ant colony algorithm a cost heuristic functionand a time heuristic function need to be set at the same timeIt will mainly rely on the influence of path pheromoneconcentration cost heuristic experience and time heuristicexperience when choosing to reach the node

Pkij(t)

ταij(t)ηβij(t)θλij(t)

1113936sisinallowedkταis(t)ηβis(t)θλis(t)

j isin allowedk

0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

ηij 1

1113936sisinSQcsij d

sijVS1113872 1113873x

sij + 1113936sisinSθQESd

sijx

sij + 1113936sisinSψ

sijx

sijQπ + 1113936sisinS1113936sprimeisinSQc

ssprimei y

ssprimei

(15)

θij 1

1113936sisinS dsijVS1113872 1113873x

sij + 1113936

sisinS1113936

sprimeisinST

ssprimei y

ssprimei (16)

Formula (14) is the node transition probability formulain the multiobjective ant colony algorithm where α is theinformation heuristic factor β is the cost expectationheuristic factor λ is the time expectation heuristic factorand τij is the pheromone concentration on path (i j)Formula (15) is a cost heuristic function whose value isinversely proportional to the sum of transportation costcarbon emission cost and damage compensation cost onpath 1 and transit cost of inode Formula (16) is a timeheuristic function whose value is inversely proportional tothe sum of transportation time on path (i j) and transittime of inode

52 Pheromone Update Rule +e principle of the positivefeedback mechanism of ant colony algorithm is based on thecontinuous update of pheromone so the pheromone updaterule is the key to solving the problem of speed and accuracyof ant colony algorithm +is paper considers the basic ideaof ant colony algorithm with elite strategy at the end of eachcycle additional pheromone enhancement is given to theoptimal solution found in this cycle in order to make theoptimal solution found so far more attractive to the ants inthe next cycle +e pheromone is updated according to thefollowing formula

τij(t + n) (1 minus ρ)τij(t) + Δτij(t t + n) + Δτlowastij(t t + n) (17)

Δτlowastij(t t + n) σ middot

q

Clowast If path (i j) is part of the optimal path in this cycle

0 otherwise

⎧⎪⎪⎨

⎪⎪⎩(18)

Formula (17) is the pheromone concentration on path(i j) at time t + n and ρ is the pheromone global vola-tilization coefficient Δτij(t t + n) is the amount ofpheromone increase on path (i j) from time t totime t + n Formula (18) is the amount of pheromoneincrease on path (i j) caused by elite ants from time t totime t + n q is the pheromone intensity σ is the numberof elite ants and Clowast is the optimal solution value found inthis cycle

Using the elite strategy can make the ant system find abetter solution through fewer cycles and the solution speedis faster However after using the elite strategy the at-tractiveness of the current optimal solution increases so thatthe search process is concentrated near the optimal solutionfound so far thereby preventing further searches for a bettersolution +e problem of premature convergence is morelikely to occur In order to maintain the selection pressurethis paper extends the concept of ranking in genetic

6 Journal of Advanced Transportation

algorithms to the elite mechanism and calculatesΔτij(t t + n)

by a weighted method After completing a cycle the ants aresorted according to the size of the target value found in thecycle and the antrsquos contribution to the pheromone update isconsidered to be inversely proportional to the target value ofthe path the ant passes +e contribution of the ant to thepheromone update is weighted according to the ranking ofthe ant (ξ) In order to ensure the speed of the solution whileexpanding the solution space it is considered that only thetop (m4) ants can contribute to the pheromone update andthe amount of pheromone obtained by the path it passes isproportional to the antrsquos ranking Δτij(t t + n) is calculatedas follows

Δτij(t t + n) 1113944

(m4)

μ1Δτξij(t t + n) (19)

Δτξij(t t + n)

Cav minus Cξ

Cav minus Clowast middot

q

Cξ if ant ξ passes the path (i j)

0 otherwise

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(20)

Formula (20) represents the contribution of the ant ξ tothe increase in the amount of pheromone on the path (i j) ξis the ranking of the ants Cav represents the average value ofthe target of this cycle and Cξ represents the target valuefound by the ant ξ

53 Pheromone Limit Interval Although the aforemen-tioned improved pheromone update rule can solve theproblems of solution speed and precocious convergence it iseasy to fall into the dilemma of local optimization and thealgorithm stops searching +erefore in this paper the ideaof MMAS is introduced in the process of pheromoneupdating +e upper and lower limits are imposed on thepheromone and the limiting interval of the pheromone is setto[τmin τmax] When performing pheromone updateaccording to the aforementioned pheromone update rulesthe following is obtained

(1) If τij(t)gt τmax occurs τij(t) τmax is required(2) If τij(t)lt τmin occurs τij(t) τmin is required

+is can effectively avoid that the amount of pheromoneon one path is much larger than the rest so that all ants areconcentrated on the same path resulting in a local optimalsituation

54 Algorithm Flowchart In summary the multiobjectiveant colony algorithm flowchart is as shown in Figure 3

6 Case Study

Take Chinarsquos multimodal transport network with 10 cities asan example it involves 10 cities the origination is Chengduand the destination is Shanghai as shown in Table 2 Sincethere are many inland cities in this multimodal transportnetwork and the water transport is poor we considered three

transport modes road railway and air in this case+e nodecities in the multimodal transport network are numberedsequentially and the schematic diagram of the multimodaltransport network of this case is made accordingly as shownin Figure 4

+is case involves three transportation modes We needto consider how to clearly express the antrsquos choice behaviorfor transportation mode when using the ant colony algo-rithm +erefore we have simply dealt with the multimodaltransport network Each transport node is expanded intomultiple virtual subnodes according to the number oftransport modes For example transfer node 3 is extended torailway node highway node and airport node In theprocessed network diagram there is a transport problemamong multiple subnodes of the same node But it is not theant to select the next arrival node that is to say there is nosequence between the subnodes which is the same levelparallel relationship +e network deformation diagram isshown in Figure 5

+e transportation mileage time delay coefficient andaccident damage coefficient of different transportationmodes among node cities are shown in Table 3 +e timedelay coefficient is given according to the road condition ofeach node city and the different characteristics of trans-portation mode +e accident damage coefficient is given bythe traffic management status of each node city and thetechnical performance of each transportation mode

+e requirements for freight volume transportationtime limit and unit value of goods by freight forwarders andthe requirements for carbon emission limit by governmentofficials are shown in Table 4

+e unit transit cost and unit transit time betweendifferent modes of transport are shown in Table 5

+e transportation cost average speed and carbonemission factors of each transportation mode are shown inTable 6

61 Resultsrsquo Analysis +e multiobjective ant colony algo-rithm is used to write the algorithm code on theMATLAB R2014a platform +e algorithm parameters areset as follows λ 3 α 1 β 3 q 2 ρ 09 the numberof ants is 100 and the number of iterations is 200y1 10000 y2 20000 Taking the weight of the objectivefunction as 13 as an example the optimal path of multi-modal transport is Chengdu to Chongqing to Wuhan toHefei to Nanjing and the total cost is 331750 To explore theresults of multimodal transport route optimization con-sidering different cost factors the weight of each objectivefunction is assigned in turn and the following conclusionsare drawn in this paper

62ObjectiveWeight SensitivityAnalysis In order to explorethe multimodal path optimization results when consideringdifferent cost factors this paper analyzes the sensitivity ofthe objective function weights as shown in Table 7 and drawsthe following conclusions

In Figure 6 Experiment (1 5) and (2 4) are compared itis found that when the weight of damage compensation cost

Journal of Advanced Transportation 7

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

Kwon [23] introduced the conditional value-at-risk (CVaR)theory and built a CVaR-based road transport route opti-mization model for dangerous goods under a time-varyingnetwork [16 24] +e optimal dangerous goods roadtransport can be selected based on the risk aversion ofdecision makersrsquo path Sun and Long [25] took into accountthe customerrsquos need for timeliness of transportation whenplanning the multimodal transport path [26] and obtainedthe optimal solution through Pareto optimality

At present the research on multimodal transport doesnot consider the influence of natural factors such asweather terrain and some special human factors on thetransport [15] In actual transportation these factors maylead to the delay [27] of transport time and even theoccurrence of dangerous accidents [28] and damage ofgoods At this time the cost and time of the original op-timal path will change and the optimal path will changeaccordingly [29 30] +e multimodal transport researchbased on railways mostly focuses on transportation policyand there are few research projects on path selection+erefore this paper establishes a multimodal transportroute selection model based on railway transportationintroduces time penalty cost and damage compensationcost considering the transportation reliability and trans-portation safety factors in the transportation processaiming at the minimum transportation cost and finds theoptimal path that is in line with reality

2 Construction of MultimodalTransport Model

21 Problem Description +e route selection problem ofmultimodal transportation mainly based on railway trans-portation can be described as follows In a multimodaltransport network G (V A) Vis the node set of networksG and Ais the path set of networks G +e shipper requiresthat a batch of goods be transported from the originationo isin A to the destination d isin A +e carrier needs to considerthe reliability and safety of the transportation routes betweenthe origination and destination so as to select the trans-portation route and mode that can reach the destinationwithin the time specified by the shipper and ensure that thegoods are intact

22 Variable Definitions +e notation of parameters andvariables is shown in Table 1

3 Objective Functions

+e goal of multimodal transport is to maximize thetransport efficiency and spend as little cost and time aspossible to make the goods arrive at the destination safelyMultimodal transport is the combined transport of multiplemodes of transport and transportation cost and trans-portation time for different modes of transport are different+erefore when calculating the model target it is necessaryto choose a transportation mode with lower transportationcost and shorter transportation time However in the actual

transportation process the transportation cost and trans-portation time of various transportation modes are not fixed+ey will change with the interference of natural factors andsome special human factors Different transportation modeshave different antijamming capabilities and transportationcosts and transportation time have different degrees of var-iation For example in foggy weather conditions variousmodes of transportation will be affected but rail trans-portation will be less affected and the transportation time willbe slightly extended the speed of road transportation will begreatly reduced and safety accidents may occur due to op-erational errors not only the safety of life is involved but alsothe transported goods will be damaged +e carrier will haveto compensate the shipper for losses and the transportationcost and transportation time will increase significantly

When the transportation cost and transportation timeare dynamically changing it will dynamically affect thechoice of transportation mode +erefore the model built inthis paper focuses on the change of transportation cost andtransportation time during transportation In this paper thedegree of change in transportation time is expressed astransportation reliability and the time penalty cost isestablished +e degree of change in transportation cost isexpressed as transportation safety and the damage com-pensation cost is established At the same time consideringthe global low-carbon environmental protection at thecurrent stage low-carbon transportation is the top priorityfor the country Multimodal operation is an emerging ef-ficient transportation mode It is also necessary to reducecarbon emissions as much as possible in response to nationalcalls +erefore this paper will start from the cost energyconservation time transport reliability and transport safetyto build a path optimization model with the minimumcomprehensive cost

minZ ω1 C1 + C2 + C3( 1113857 + ω2C4 + ω3C5 (1)

In the formula Z is the comprehensive transport costC1 C2 C3 C4 and C5 are transportation cost transit costcarbon emission cost time penalty cost and damagecompensation cost respectively and ω1 ω2 and ω3 are theweights of each cost in the objective function

31 Transportation Cost and Transit Cost +e cost of freighttransportation between adjacent nodes is the transportationcost and the cost of replacing the transportation modeinside the transferable node is the transit cost

minC1 1113944iisinM

1113944jisinM

1113944sisinS

Qcsijd

sijx

sij

minC2 1113944iisinM

1113944sisinS

1113944

sprimeisinS

Qcssprimei y

ssprimei

(2)

32 CarbonEmissionCost In order to develop a low-carboneconomy countries all over the world have studied energyconservation and emission reduction and proposed a carbontax scheme Carbon tax is a tax imposed on carbon emissions

Journal of Advanced Transportation 3

and is an important means of limiting carbon emissions+ecalculation formula of carbon tax is as follows

θ 1113944t

0Dt(1 + λ)

minust (3)

In the formula Dt is the damage value of thet-yearcaused by the unit carbon emissions and λ is the discountrate In fact the carbon tax is not levied as high as possible Ifthe carbon tax is higher it will restrict the economic de-velopment of the country If the carbon tax is too low it willnot play a good role in energy conservation and emissionreduction According to the research of experts and scholarsin China the proposal of the Ministry of environmentalprotection for carbon tax is 20 $ton +erefore in thispaper the carbon tax is assumed to be 20 $ton and 002 $kg +e carbon emission cost is the product of carbonemissions and carbon tax

minC3 θ times 1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij (4)

33 Transportation Reliability and Time Penalty CostTransport reliability herein refers to the on-time arrival ratefrom the starting point to the end point within a specifiedtime using either mode of transport In the actual trans-portation process various modes of transportation will beaffected by natural factors and some special human factorsresulting in delays in transportation such as traffic jamscaused by road conditions trains will stop and wait duringthe meeting and long ramps will have a great impact on therunning speed and so on Transportation delay will prolong

the transportation time and may exceed the delivery timelimit so if the model does not take into account thetransportation reliability factors the obtained optimal pathwill lose its significance in the actual transportation contextIn order to quantify the impact of transportation reliabilityon transportation time this paper defines the time delaycoefficient taking into account the complex influencingfactors between adjacent nodes and taking values within 0ndash1so that the transportation time of the section is extendedlinearly on the basis of the original transportation time asshown in Figure 1

In the diagram t represents the transportation timebetween two nodes without considering the delay and μ isthe time delay coefficient When μ 0 there is no time delayin the transportation process of goods and the actualtransportation time of goods is the initial transportationtime t When μ 1 there is time delay in the transportationprocess of goods and the actual transportation time is theinitial time t plus the delay time quantified as t When μ isbetween 0 and 1 the delay time of goods is related to thedelay coefficient defining that the delay time has a linearrelationship with the delay coefficient

A certain penalty is imposed for transportation schemesthat exceed the time limit In order to quantify the impact ofthe time limit of delivery on the transportation plan se-lection the time penalty function is introduced in this paperTaking into account the changes in the psychological state ofthe consignee while waiting for the delivery of the goods thispaper adopts the fuzzy convenience function to express anddefines 2 hours as a state change gradient in case of ex-ceeding the arrival time limit and assigns different degrees ofpunishment to different state gradients as shown inFigure 2

Table 1 Subscripts and parameters used in mathematical formulations

Symbol DescriptionM Network node set (all nodes including the start node and the end node)K Transportable node setS S s sprime 1113864 1113865 transportation mode collectionQ Total quantity of goods to be transported in the multimodal transport modelπ Unit value of goods that need to be transportedψs

ijAccident damage coefficient from node city i to node city j transport modesis used for transportation

dsij

Transportation mileage from node city i to node city j transport modesis used for transportationμs

ijTime delay coefficient from node city i to node city j transport modesis used for transportation

csij

Unit transportation cost from node city i to node cityj transport modesis used for transportationcssrsquoi

Unit transfer cost at the transferable node i the mode of transport is changed fromsto sprime

Tssprimei

Transit time at the transferable node i the mode of transport is changed from s to sprimeVS Average speed of transportation mode s

ES Carbon emission factor unit carbon emissions of transportation mode s

E Total carbon emissions allowed in the modelT +e maximum delivery time of the goods specified in the modelxs

ijDecision variables if transportation modesis selected from city i to node city j then the value is 1 otherwise the value is 0

yssprimei

Decision variables if the mode of transportation changes from s to sprime in node city i then the value is 1 otherwise the value is 0Cd Cd represents the calculated value of total carbon emissionsX +e total transportation time from o to D

qsij

From the city i to the city j the transportation volume of mode s is adoptedqs

hiFrom the city h to the city i the transportation volume of mode s is adopted

4 Journal of Advanced Transportation

X 1113944iisinM

1113944jisinM

1113944sisinS

1 + μsij1113872 1113873

dsij

VS

xsij + 1113944

iisinM1113944sisinS

1113944

sprimeisinS

Tssprimei y

ssprimei (5)

minC4

0 XleT

y1

2(X minus T) TleXleT + 2

y1 T + 2leXleT + 4

y2 T + 4leX

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

Formula (5) is the transportation time calculation for-mula for any transportation scheme the first part is the sumof transportation time and delay time and the second part isthe transit time of the transportable node Formula (6) is thetime penalty cost calculation formula when the trans-portation time is from T to T + 2 the penalty function is alinear increasing function when the time is from T + 2 toT + 4 the penalty function is a constant (y1) when thetransportation time exceeds T + 4 the penalty function is aconstant (y2)

34 Transportation Safety and Damage Compensation CostsTransport safety in this paper refers to the value loss rate ofgoods transported during transportation from the startingpoint to the end point +e influencing factors mainly in-clude road conditions and traffic management status vehicletechnical performance and warranty quality as well as thedriverrsquos operating skill level and responsibility If a safetyaccident occurs during transportation the transportationgoods will be damaged +e carrier shall compensate theconsignor for the corresponding loss according to the degree

of damage to the goods because the liability of the accident isthat the carrier has not planned the transportation route Ifthe safety factors in the transportation process are notconsidered when optimizing the route the final result islikely to lose more In order to facilitate the calculation thispaper assumes that the degree of damage to the goods isdetermined by the severity of the accident when a safetyaccident occurs during transportation +at is to say if theseverity of the accident is relatively low the goods may onlybe partially damaged rather than completely damaged Inorder to quantify the impact of the severity of the accident onthe damage of the goods this paper proposes and defines theaccident damage coefficient the value is within 0ndash1 and thechange from 0 to 1 indicates that the degree of damage of thegoods increases gradually and the amount of compensationrequired by the carrier increases gradually and the amountof compensation is based on the value of the goods

minC5 1113944iisinM

1113944jisinM

1113944sisinS

ψsijx

sijQπ (7)

4 Constraints

41 Transportation Process Constraint

1113944sisinS

xsij le 1 forall(i j) isinM (8)

1113944

ssprimeisinS

yssprimei le 1 foralli isin K (9)

xshi + x

sprimeij ge 2y

ssprimei forallh i j isinMforalls sprime isin S (10)

1113944sisinS

qshi 1113944

sisinSq

sij forall(h i j) isinM (11)

Constraint (8) makes sure that only one mode oftransport can be selected between any adjacent nodesConstraint (9) ensures that only one transit can occur in anytransit node Constraint (10) guarantees the continuity oftransportation mode during transit Constraint (11) is theflow equilibrium constraint of nodes in the network

42 Carbon Emission Constraint

1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij Cd (12)

CdleE (13)

Constraint (12) is the formula of total carbon emissionsand for this paper which is a known constant Constraint(13) ensures that the transportation plan meets the totalcarbon emission limit

5 Multiobjective Ant Colony Algorithm

+e ant colony algorithm is a simulation evolution algorithmproposed by DORIGO It is an effective means to solve the

T0

Time penaltycost (yuan)

y2

y1

T + 2 T + 4 Time (h)

Figure 2 Time penalty cost function

10

t

Time delaycoefficient (μ)

Figure 1 Time delay function

Journal of Advanced Transportation 5

multiobjective optimization problem in discrete spacehowever the basic ant colony algorithm has the problems ofslow running efficiency premature convergence and easy tofall into a local optimal solution +is paper combines thesolution requirements of the multimodal transport pathselection model In order to improve the effectiveness of thealgorithm the basic algorithm is improved accordingly

51 Node Transition Probability Although the objectivefunction of the model in this paper is the total cost value in

the transportation process the time penalty cost is deter-mined by the length of the transportation time +e modeltarget expectation cost and time are as small as possible so inthe improved ant colony algorithm a cost heuristic functionand a time heuristic function need to be set at the same timeIt will mainly rely on the influence of path pheromoneconcentration cost heuristic experience and time heuristicexperience when choosing to reach the node

Pkij(t)

ταij(t)ηβij(t)θλij(t)

1113936sisinallowedkταis(t)ηβis(t)θλis(t)

j isin allowedk

0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

ηij 1

1113936sisinSQcsij d

sijVS1113872 1113873x

sij + 1113936sisinSθQESd

sijx

sij + 1113936sisinSψ

sijx

sijQπ + 1113936sisinS1113936sprimeisinSQc

ssprimei y

ssprimei

(15)

θij 1

1113936sisinS dsijVS1113872 1113873x

sij + 1113936

sisinS1113936

sprimeisinST

ssprimei y

ssprimei (16)

Formula (14) is the node transition probability formulain the multiobjective ant colony algorithm where α is theinformation heuristic factor β is the cost expectationheuristic factor λ is the time expectation heuristic factorand τij is the pheromone concentration on path (i j)Formula (15) is a cost heuristic function whose value isinversely proportional to the sum of transportation costcarbon emission cost and damage compensation cost onpath 1 and transit cost of inode Formula (16) is a timeheuristic function whose value is inversely proportional tothe sum of transportation time on path (i j) and transittime of inode

52 Pheromone Update Rule +e principle of the positivefeedback mechanism of ant colony algorithm is based on thecontinuous update of pheromone so the pheromone updaterule is the key to solving the problem of speed and accuracyof ant colony algorithm +is paper considers the basic ideaof ant colony algorithm with elite strategy at the end of eachcycle additional pheromone enhancement is given to theoptimal solution found in this cycle in order to make theoptimal solution found so far more attractive to the ants inthe next cycle +e pheromone is updated according to thefollowing formula

τij(t + n) (1 minus ρ)τij(t) + Δτij(t t + n) + Δτlowastij(t t + n) (17)

Δτlowastij(t t + n) σ middot

q

Clowast If path (i j) is part of the optimal path in this cycle

0 otherwise

⎧⎪⎪⎨

⎪⎪⎩(18)

Formula (17) is the pheromone concentration on path(i j) at time t + n and ρ is the pheromone global vola-tilization coefficient Δτij(t t + n) is the amount ofpheromone increase on path (i j) from time t totime t + n Formula (18) is the amount of pheromoneincrease on path (i j) caused by elite ants from time t totime t + n q is the pheromone intensity σ is the numberof elite ants and Clowast is the optimal solution value found inthis cycle

Using the elite strategy can make the ant system find abetter solution through fewer cycles and the solution speedis faster However after using the elite strategy the at-tractiveness of the current optimal solution increases so thatthe search process is concentrated near the optimal solutionfound so far thereby preventing further searches for a bettersolution +e problem of premature convergence is morelikely to occur In order to maintain the selection pressurethis paper extends the concept of ranking in genetic

6 Journal of Advanced Transportation

algorithms to the elite mechanism and calculatesΔτij(t t + n)

by a weighted method After completing a cycle the ants aresorted according to the size of the target value found in thecycle and the antrsquos contribution to the pheromone update isconsidered to be inversely proportional to the target value ofthe path the ant passes +e contribution of the ant to thepheromone update is weighted according to the ranking ofthe ant (ξ) In order to ensure the speed of the solution whileexpanding the solution space it is considered that only thetop (m4) ants can contribute to the pheromone update andthe amount of pheromone obtained by the path it passes isproportional to the antrsquos ranking Δτij(t t + n) is calculatedas follows

Δτij(t t + n) 1113944

(m4)

μ1Δτξij(t t + n) (19)

Δτξij(t t + n)

Cav minus Cξ

Cav minus Clowast middot

q

Cξ if ant ξ passes the path (i j)

0 otherwise

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(20)

Formula (20) represents the contribution of the ant ξ tothe increase in the amount of pheromone on the path (i j) ξis the ranking of the ants Cav represents the average value ofthe target of this cycle and Cξ represents the target valuefound by the ant ξ

53 Pheromone Limit Interval Although the aforemen-tioned improved pheromone update rule can solve theproblems of solution speed and precocious convergence it iseasy to fall into the dilemma of local optimization and thealgorithm stops searching +erefore in this paper the ideaof MMAS is introduced in the process of pheromoneupdating +e upper and lower limits are imposed on thepheromone and the limiting interval of the pheromone is setto[τmin τmax] When performing pheromone updateaccording to the aforementioned pheromone update rulesthe following is obtained

(1) If τij(t)gt τmax occurs τij(t) τmax is required(2) If τij(t)lt τmin occurs τij(t) τmin is required

+is can effectively avoid that the amount of pheromoneon one path is much larger than the rest so that all ants areconcentrated on the same path resulting in a local optimalsituation

54 Algorithm Flowchart In summary the multiobjectiveant colony algorithm flowchart is as shown in Figure 3

6 Case Study

Take Chinarsquos multimodal transport network with 10 cities asan example it involves 10 cities the origination is Chengduand the destination is Shanghai as shown in Table 2 Sincethere are many inland cities in this multimodal transportnetwork and the water transport is poor we considered three

transport modes road railway and air in this case+e nodecities in the multimodal transport network are numberedsequentially and the schematic diagram of the multimodaltransport network of this case is made accordingly as shownin Figure 4

+is case involves three transportation modes We needto consider how to clearly express the antrsquos choice behaviorfor transportation mode when using the ant colony algo-rithm +erefore we have simply dealt with the multimodaltransport network Each transport node is expanded intomultiple virtual subnodes according to the number oftransport modes For example transfer node 3 is extended torailway node highway node and airport node In theprocessed network diagram there is a transport problemamong multiple subnodes of the same node But it is not theant to select the next arrival node that is to say there is nosequence between the subnodes which is the same levelparallel relationship +e network deformation diagram isshown in Figure 5

+e transportation mileage time delay coefficient andaccident damage coefficient of different transportationmodes among node cities are shown in Table 3 +e timedelay coefficient is given according to the road condition ofeach node city and the different characteristics of trans-portation mode +e accident damage coefficient is given bythe traffic management status of each node city and thetechnical performance of each transportation mode

+e requirements for freight volume transportationtime limit and unit value of goods by freight forwarders andthe requirements for carbon emission limit by governmentofficials are shown in Table 4

+e unit transit cost and unit transit time betweendifferent modes of transport are shown in Table 5

+e transportation cost average speed and carbonemission factors of each transportation mode are shown inTable 6

61 Resultsrsquo Analysis +e multiobjective ant colony algo-rithm is used to write the algorithm code on theMATLAB R2014a platform +e algorithm parameters areset as follows λ 3 α 1 β 3 q 2 ρ 09 the numberof ants is 100 and the number of iterations is 200y1 10000 y2 20000 Taking the weight of the objectivefunction as 13 as an example the optimal path of multi-modal transport is Chengdu to Chongqing to Wuhan toHefei to Nanjing and the total cost is 331750 To explore theresults of multimodal transport route optimization con-sidering different cost factors the weight of each objectivefunction is assigned in turn and the following conclusionsare drawn in this paper

62ObjectiveWeight SensitivityAnalysis In order to explorethe multimodal path optimization results when consideringdifferent cost factors this paper analyzes the sensitivity ofthe objective function weights as shown in Table 7 and drawsthe following conclusions

In Figure 6 Experiment (1 5) and (2 4) are compared itis found that when the weight of damage compensation cost

Journal of Advanced Transportation 7

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

and is an important means of limiting carbon emissions+ecalculation formula of carbon tax is as follows

θ 1113944t

0Dt(1 + λ)

minust (3)

In the formula Dt is the damage value of thet-yearcaused by the unit carbon emissions and λ is the discountrate In fact the carbon tax is not levied as high as possible Ifthe carbon tax is higher it will restrict the economic de-velopment of the country If the carbon tax is too low it willnot play a good role in energy conservation and emissionreduction According to the research of experts and scholarsin China the proposal of the Ministry of environmentalprotection for carbon tax is 20 $ton +erefore in thispaper the carbon tax is assumed to be 20 $ton and 002 $kg +e carbon emission cost is the product of carbonemissions and carbon tax

minC3 θ times 1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij (4)

33 Transportation Reliability and Time Penalty CostTransport reliability herein refers to the on-time arrival ratefrom the starting point to the end point within a specifiedtime using either mode of transport In the actual trans-portation process various modes of transportation will beaffected by natural factors and some special human factorsresulting in delays in transportation such as traffic jamscaused by road conditions trains will stop and wait duringthe meeting and long ramps will have a great impact on therunning speed and so on Transportation delay will prolong

the transportation time and may exceed the delivery timelimit so if the model does not take into account thetransportation reliability factors the obtained optimal pathwill lose its significance in the actual transportation contextIn order to quantify the impact of transportation reliabilityon transportation time this paper defines the time delaycoefficient taking into account the complex influencingfactors between adjacent nodes and taking values within 0ndash1so that the transportation time of the section is extendedlinearly on the basis of the original transportation time asshown in Figure 1

In the diagram t represents the transportation timebetween two nodes without considering the delay and μ isthe time delay coefficient When μ 0 there is no time delayin the transportation process of goods and the actualtransportation time of goods is the initial transportationtime t When μ 1 there is time delay in the transportationprocess of goods and the actual transportation time is theinitial time t plus the delay time quantified as t When μ isbetween 0 and 1 the delay time of goods is related to thedelay coefficient defining that the delay time has a linearrelationship with the delay coefficient

A certain penalty is imposed for transportation schemesthat exceed the time limit In order to quantify the impact ofthe time limit of delivery on the transportation plan se-lection the time penalty function is introduced in this paperTaking into account the changes in the psychological state ofthe consignee while waiting for the delivery of the goods thispaper adopts the fuzzy convenience function to express anddefines 2 hours as a state change gradient in case of ex-ceeding the arrival time limit and assigns different degrees ofpunishment to different state gradients as shown inFigure 2

Table 1 Subscripts and parameters used in mathematical formulations

Symbol DescriptionM Network node set (all nodes including the start node and the end node)K Transportable node setS S s sprime 1113864 1113865 transportation mode collectionQ Total quantity of goods to be transported in the multimodal transport modelπ Unit value of goods that need to be transportedψs

ijAccident damage coefficient from node city i to node city j transport modesis used for transportation

dsij

Transportation mileage from node city i to node city j transport modesis used for transportationμs

ijTime delay coefficient from node city i to node city j transport modesis used for transportation

csij

Unit transportation cost from node city i to node cityj transport modesis used for transportationcssrsquoi

Unit transfer cost at the transferable node i the mode of transport is changed fromsto sprime

Tssprimei

Transit time at the transferable node i the mode of transport is changed from s to sprimeVS Average speed of transportation mode s

ES Carbon emission factor unit carbon emissions of transportation mode s

E Total carbon emissions allowed in the modelT +e maximum delivery time of the goods specified in the modelxs

ijDecision variables if transportation modesis selected from city i to node city j then the value is 1 otherwise the value is 0

yssprimei

Decision variables if the mode of transportation changes from s to sprime in node city i then the value is 1 otherwise the value is 0Cd Cd represents the calculated value of total carbon emissionsX +e total transportation time from o to D

qsij

From the city i to the city j the transportation volume of mode s is adoptedqs

hiFrom the city h to the city i the transportation volume of mode s is adopted

4 Journal of Advanced Transportation

X 1113944iisinM

1113944jisinM

1113944sisinS

1 + μsij1113872 1113873

dsij

VS

xsij + 1113944

iisinM1113944sisinS

1113944

sprimeisinS

Tssprimei y

ssprimei (5)

minC4

0 XleT

y1

2(X minus T) TleXleT + 2

y1 T + 2leXleT + 4

y2 T + 4leX

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

Formula (5) is the transportation time calculation for-mula for any transportation scheme the first part is the sumof transportation time and delay time and the second part isthe transit time of the transportable node Formula (6) is thetime penalty cost calculation formula when the trans-portation time is from T to T + 2 the penalty function is alinear increasing function when the time is from T + 2 toT + 4 the penalty function is a constant (y1) when thetransportation time exceeds T + 4 the penalty function is aconstant (y2)

34 Transportation Safety and Damage Compensation CostsTransport safety in this paper refers to the value loss rate ofgoods transported during transportation from the startingpoint to the end point +e influencing factors mainly in-clude road conditions and traffic management status vehicletechnical performance and warranty quality as well as thedriverrsquos operating skill level and responsibility If a safetyaccident occurs during transportation the transportationgoods will be damaged +e carrier shall compensate theconsignor for the corresponding loss according to the degree

of damage to the goods because the liability of the accident isthat the carrier has not planned the transportation route Ifthe safety factors in the transportation process are notconsidered when optimizing the route the final result islikely to lose more In order to facilitate the calculation thispaper assumes that the degree of damage to the goods isdetermined by the severity of the accident when a safetyaccident occurs during transportation +at is to say if theseverity of the accident is relatively low the goods may onlybe partially damaged rather than completely damaged Inorder to quantify the impact of the severity of the accident onthe damage of the goods this paper proposes and defines theaccident damage coefficient the value is within 0ndash1 and thechange from 0 to 1 indicates that the degree of damage of thegoods increases gradually and the amount of compensationrequired by the carrier increases gradually and the amountof compensation is based on the value of the goods

minC5 1113944iisinM

1113944jisinM

1113944sisinS

ψsijx

sijQπ (7)

4 Constraints

41 Transportation Process Constraint

1113944sisinS

xsij le 1 forall(i j) isinM (8)

1113944

ssprimeisinS

yssprimei le 1 foralli isin K (9)

xshi + x

sprimeij ge 2y

ssprimei forallh i j isinMforalls sprime isin S (10)

1113944sisinS

qshi 1113944

sisinSq

sij forall(h i j) isinM (11)

Constraint (8) makes sure that only one mode oftransport can be selected between any adjacent nodesConstraint (9) ensures that only one transit can occur in anytransit node Constraint (10) guarantees the continuity oftransportation mode during transit Constraint (11) is theflow equilibrium constraint of nodes in the network

42 Carbon Emission Constraint

1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij Cd (12)

CdleE (13)

Constraint (12) is the formula of total carbon emissionsand for this paper which is a known constant Constraint(13) ensures that the transportation plan meets the totalcarbon emission limit

5 Multiobjective Ant Colony Algorithm

+e ant colony algorithm is a simulation evolution algorithmproposed by DORIGO It is an effective means to solve the

T0

Time penaltycost (yuan)

y2

y1

T + 2 T + 4 Time (h)

Figure 2 Time penalty cost function

10

t

Time delaycoefficient (μ)

Figure 1 Time delay function

Journal of Advanced Transportation 5

multiobjective optimization problem in discrete spacehowever the basic ant colony algorithm has the problems ofslow running efficiency premature convergence and easy tofall into a local optimal solution +is paper combines thesolution requirements of the multimodal transport pathselection model In order to improve the effectiveness of thealgorithm the basic algorithm is improved accordingly

51 Node Transition Probability Although the objectivefunction of the model in this paper is the total cost value in

the transportation process the time penalty cost is deter-mined by the length of the transportation time +e modeltarget expectation cost and time are as small as possible so inthe improved ant colony algorithm a cost heuristic functionand a time heuristic function need to be set at the same timeIt will mainly rely on the influence of path pheromoneconcentration cost heuristic experience and time heuristicexperience when choosing to reach the node

Pkij(t)

ταij(t)ηβij(t)θλij(t)

1113936sisinallowedkταis(t)ηβis(t)θλis(t)

j isin allowedk

0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

ηij 1

1113936sisinSQcsij d

sijVS1113872 1113873x

sij + 1113936sisinSθQESd

sijx

sij + 1113936sisinSψ

sijx

sijQπ + 1113936sisinS1113936sprimeisinSQc

ssprimei y

ssprimei

(15)

θij 1

1113936sisinS dsijVS1113872 1113873x

sij + 1113936

sisinS1113936

sprimeisinST

ssprimei y

ssprimei (16)

Formula (14) is the node transition probability formulain the multiobjective ant colony algorithm where α is theinformation heuristic factor β is the cost expectationheuristic factor λ is the time expectation heuristic factorand τij is the pheromone concentration on path (i j)Formula (15) is a cost heuristic function whose value isinversely proportional to the sum of transportation costcarbon emission cost and damage compensation cost onpath 1 and transit cost of inode Formula (16) is a timeheuristic function whose value is inversely proportional tothe sum of transportation time on path (i j) and transittime of inode

52 Pheromone Update Rule +e principle of the positivefeedback mechanism of ant colony algorithm is based on thecontinuous update of pheromone so the pheromone updaterule is the key to solving the problem of speed and accuracyof ant colony algorithm +is paper considers the basic ideaof ant colony algorithm with elite strategy at the end of eachcycle additional pheromone enhancement is given to theoptimal solution found in this cycle in order to make theoptimal solution found so far more attractive to the ants inthe next cycle +e pheromone is updated according to thefollowing formula

τij(t + n) (1 minus ρ)τij(t) + Δτij(t t + n) + Δτlowastij(t t + n) (17)

Δτlowastij(t t + n) σ middot

q

Clowast If path (i j) is part of the optimal path in this cycle

0 otherwise

⎧⎪⎪⎨

⎪⎪⎩(18)

Formula (17) is the pheromone concentration on path(i j) at time t + n and ρ is the pheromone global vola-tilization coefficient Δτij(t t + n) is the amount ofpheromone increase on path (i j) from time t totime t + n Formula (18) is the amount of pheromoneincrease on path (i j) caused by elite ants from time t totime t + n q is the pheromone intensity σ is the numberof elite ants and Clowast is the optimal solution value found inthis cycle

Using the elite strategy can make the ant system find abetter solution through fewer cycles and the solution speedis faster However after using the elite strategy the at-tractiveness of the current optimal solution increases so thatthe search process is concentrated near the optimal solutionfound so far thereby preventing further searches for a bettersolution +e problem of premature convergence is morelikely to occur In order to maintain the selection pressurethis paper extends the concept of ranking in genetic

6 Journal of Advanced Transportation

algorithms to the elite mechanism and calculatesΔτij(t t + n)

by a weighted method After completing a cycle the ants aresorted according to the size of the target value found in thecycle and the antrsquos contribution to the pheromone update isconsidered to be inversely proportional to the target value ofthe path the ant passes +e contribution of the ant to thepheromone update is weighted according to the ranking ofthe ant (ξ) In order to ensure the speed of the solution whileexpanding the solution space it is considered that only thetop (m4) ants can contribute to the pheromone update andthe amount of pheromone obtained by the path it passes isproportional to the antrsquos ranking Δτij(t t + n) is calculatedas follows

Δτij(t t + n) 1113944

(m4)

μ1Δτξij(t t + n) (19)

Δτξij(t t + n)

Cav minus Cξ

Cav minus Clowast middot

q

Cξ if ant ξ passes the path (i j)

0 otherwise

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(20)

Formula (20) represents the contribution of the ant ξ tothe increase in the amount of pheromone on the path (i j) ξis the ranking of the ants Cav represents the average value ofthe target of this cycle and Cξ represents the target valuefound by the ant ξ

53 Pheromone Limit Interval Although the aforemen-tioned improved pheromone update rule can solve theproblems of solution speed and precocious convergence it iseasy to fall into the dilemma of local optimization and thealgorithm stops searching +erefore in this paper the ideaof MMAS is introduced in the process of pheromoneupdating +e upper and lower limits are imposed on thepheromone and the limiting interval of the pheromone is setto[τmin τmax] When performing pheromone updateaccording to the aforementioned pheromone update rulesthe following is obtained

(1) If τij(t)gt τmax occurs τij(t) τmax is required(2) If τij(t)lt τmin occurs τij(t) τmin is required

+is can effectively avoid that the amount of pheromoneon one path is much larger than the rest so that all ants areconcentrated on the same path resulting in a local optimalsituation

54 Algorithm Flowchart In summary the multiobjectiveant colony algorithm flowchart is as shown in Figure 3

6 Case Study

Take Chinarsquos multimodal transport network with 10 cities asan example it involves 10 cities the origination is Chengduand the destination is Shanghai as shown in Table 2 Sincethere are many inland cities in this multimodal transportnetwork and the water transport is poor we considered three

transport modes road railway and air in this case+e nodecities in the multimodal transport network are numberedsequentially and the schematic diagram of the multimodaltransport network of this case is made accordingly as shownin Figure 4

+is case involves three transportation modes We needto consider how to clearly express the antrsquos choice behaviorfor transportation mode when using the ant colony algo-rithm +erefore we have simply dealt with the multimodaltransport network Each transport node is expanded intomultiple virtual subnodes according to the number oftransport modes For example transfer node 3 is extended torailway node highway node and airport node In theprocessed network diagram there is a transport problemamong multiple subnodes of the same node But it is not theant to select the next arrival node that is to say there is nosequence between the subnodes which is the same levelparallel relationship +e network deformation diagram isshown in Figure 5

+e transportation mileage time delay coefficient andaccident damage coefficient of different transportationmodes among node cities are shown in Table 3 +e timedelay coefficient is given according to the road condition ofeach node city and the different characteristics of trans-portation mode +e accident damage coefficient is given bythe traffic management status of each node city and thetechnical performance of each transportation mode

+e requirements for freight volume transportationtime limit and unit value of goods by freight forwarders andthe requirements for carbon emission limit by governmentofficials are shown in Table 4

+e unit transit cost and unit transit time betweendifferent modes of transport are shown in Table 5

+e transportation cost average speed and carbonemission factors of each transportation mode are shown inTable 6

61 Resultsrsquo Analysis +e multiobjective ant colony algo-rithm is used to write the algorithm code on theMATLAB R2014a platform +e algorithm parameters areset as follows λ 3 α 1 β 3 q 2 ρ 09 the numberof ants is 100 and the number of iterations is 200y1 10000 y2 20000 Taking the weight of the objectivefunction as 13 as an example the optimal path of multi-modal transport is Chengdu to Chongqing to Wuhan toHefei to Nanjing and the total cost is 331750 To explore theresults of multimodal transport route optimization con-sidering different cost factors the weight of each objectivefunction is assigned in turn and the following conclusionsare drawn in this paper

62ObjectiveWeight SensitivityAnalysis In order to explorethe multimodal path optimization results when consideringdifferent cost factors this paper analyzes the sensitivity ofthe objective function weights as shown in Table 7 and drawsthe following conclusions

In Figure 6 Experiment (1 5) and (2 4) are compared itis found that when the weight of damage compensation cost

Journal of Advanced Transportation 7

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

X 1113944iisinM

1113944jisinM

1113944sisinS

1 + μsij1113872 1113873

dsij

VS

xsij + 1113944

iisinM1113944sisinS

1113944

sprimeisinS

Tssprimei y

ssprimei (5)

minC4

0 XleT

y1

2(X minus T) TleXleT + 2

y1 T + 2leXleT + 4

y2 T + 4leX

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

Formula (5) is the transportation time calculation for-mula for any transportation scheme the first part is the sumof transportation time and delay time and the second part isthe transit time of the transportable node Formula (6) is thetime penalty cost calculation formula when the trans-portation time is from T to T + 2 the penalty function is alinear increasing function when the time is from T + 2 toT + 4 the penalty function is a constant (y1) when thetransportation time exceeds T + 4 the penalty function is aconstant (y2)

34 Transportation Safety and Damage Compensation CostsTransport safety in this paper refers to the value loss rate ofgoods transported during transportation from the startingpoint to the end point +e influencing factors mainly in-clude road conditions and traffic management status vehicletechnical performance and warranty quality as well as thedriverrsquos operating skill level and responsibility If a safetyaccident occurs during transportation the transportationgoods will be damaged +e carrier shall compensate theconsignor for the corresponding loss according to the degree

of damage to the goods because the liability of the accident isthat the carrier has not planned the transportation route Ifthe safety factors in the transportation process are notconsidered when optimizing the route the final result islikely to lose more In order to facilitate the calculation thispaper assumes that the degree of damage to the goods isdetermined by the severity of the accident when a safetyaccident occurs during transportation +at is to say if theseverity of the accident is relatively low the goods may onlybe partially damaged rather than completely damaged Inorder to quantify the impact of the severity of the accident onthe damage of the goods this paper proposes and defines theaccident damage coefficient the value is within 0ndash1 and thechange from 0 to 1 indicates that the degree of damage of thegoods increases gradually and the amount of compensationrequired by the carrier increases gradually and the amountof compensation is based on the value of the goods

minC5 1113944iisinM

1113944jisinM

1113944sisinS

ψsijx

sijQπ (7)

4 Constraints

41 Transportation Process Constraint

1113944sisinS

xsij le 1 forall(i j) isinM (8)

1113944

ssprimeisinS

yssprimei le 1 foralli isin K (9)

xshi + x

sprimeij ge 2y

ssprimei forallh i j isinMforalls sprime isin S (10)

1113944sisinS

qshi 1113944

sisinSq

sij forall(h i j) isinM (11)

Constraint (8) makes sure that only one mode oftransport can be selected between any adjacent nodesConstraint (9) ensures that only one transit can occur in anytransit node Constraint (10) guarantees the continuity oftransportation mode during transit Constraint (11) is theflow equilibrium constraint of nodes in the network

42 Carbon Emission Constraint

1113944iisinM

1113944jisinM

1113944sisinS

QESdsijx

sij Cd (12)

CdleE (13)

Constraint (12) is the formula of total carbon emissionsand for this paper which is a known constant Constraint(13) ensures that the transportation plan meets the totalcarbon emission limit

5 Multiobjective Ant Colony Algorithm

+e ant colony algorithm is a simulation evolution algorithmproposed by DORIGO It is an effective means to solve the

T0

Time penaltycost (yuan)

y2

y1

T + 2 T + 4 Time (h)

Figure 2 Time penalty cost function

10

t

Time delaycoefficient (μ)

Figure 1 Time delay function

Journal of Advanced Transportation 5

multiobjective optimization problem in discrete spacehowever the basic ant colony algorithm has the problems ofslow running efficiency premature convergence and easy tofall into a local optimal solution +is paper combines thesolution requirements of the multimodal transport pathselection model In order to improve the effectiveness of thealgorithm the basic algorithm is improved accordingly

51 Node Transition Probability Although the objectivefunction of the model in this paper is the total cost value in

the transportation process the time penalty cost is deter-mined by the length of the transportation time +e modeltarget expectation cost and time are as small as possible so inthe improved ant colony algorithm a cost heuristic functionand a time heuristic function need to be set at the same timeIt will mainly rely on the influence of path pheromoneconcentration cost heuristic experience and time heuristicexperience when choosing to reach the node

Pkij(t)

ταij(t)ηβij(t)θλij(t)

1113936sisinallowedkταis(t)ηβis(t)θλis(t)

j isin allowedk

0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

ηij 1

1113936sisinSQcsij d

sijVS1113872 1113873x

sij + 1113936sisinSθQESd

sijx

sij + 1113936sisinSψ

sijx

sijQπ + 1113936sisinS1113936sprimeisinSQc

ssprimei y

ssprimei

(15)

θij 1

1113936sisinS dsijVS1113872 1113873x

sij + 1113936

sisinS1113936

sprimeisinST

ssprimei y

ssprimei (16)

Formula (14) is the node transition probability formulain the multiobjective ant colony algorithm where α is theinformation heuristic factor β is the cost expectationheuristic factor λ is the time expectation heuristic factorand τij is the pheromone concentration on path (i j)Formula (15) is a cost heuristic function whose value isinversely proportional to the sum of transportation costcarbon emission cost and damage compensation cost onpath 1 and transit cost of inode Formula (16) is a timeheuristic function whose value is inversely proportional tothe sum of transportation time on path (i j) and transittime of inode

52 Pheromone Update Rule +e principle of the positivefeedback mechanism of ant colony algorithm is based on thecontinuous update of pheromone so the pheromone updaterule is the key to solving the problem of speed and accuracyof ant colony algorithm +is paper considers the basic ideaof ant colony algorithm with elite strategy at the end of eachcycle additional pheromone enhancement is given to theoptimal solution found in this cycle in order to make theoptimal solution found so far more attractive to the ants inthe next cycle +e pheromone is updated according to thefollowing formula

τij(t + n) (1 minus ρ)τij(t) + Δτij(t t + n) + Δτlowastij(t t + n) (17)

Δτlowastij(t t + n) σ middot

q

Clowast If path (i j) is part of the optimal path in this cycle

0 otherwise

⎧⎪⎪⎨

⎪⎪⎩(18)

Formula (17) is the pheromone concentration on path(i j) at time t + n and ρ is the pheromone global vola-tilization coefficient Δτij(t t + n) is the amount ofpheromone increase on path (i j) from time t totime t + n Formula (18) is the amount of pheromoneincrease on path (i j) caused by elite ants from time t totime t + n q is the pheromone intensity σ is the numberof elite ants and Clowast is the optimal solution value found inthis cycle

Using the elite strategy can make the ant system find abetter solution through fewer cycles and the solution speedis faster However after using the elite strategy the at-tractiveness of the current optimal solution increases so thatthe search process is concentrated near the optimal solutionfound so far thereby preventing further searches for a bettersolution +e problem of premature convergence is morelikely to occur In order to maintain the selection pressurethis paper extends the concept of ranking in genetic

6 Journal of Advanced Transportation

algorithms to the elite mechanism and calculatesΔτij(t t + n)

by a weighted method After completing a cycle the ants aresorted according to the size of the target value found in thecycle and the antrsquos contribution to the pheromone update isconsidered to be inversely proportional to the target value ofthe path the ant passes +e contribution of the ant to thepheromone update is weighted according to the ranking ofthe ant (ξ) In order to ensure the speed of the solution whileexpanding the solution space it is considered that only thetop (m4) ants can contribute to the pheromone update andthe amount of pheromone obtained by the path it passes isproportional to the antrsquos ranking Δτij(t t + n) is calculatedas follows

Δτij(t t + n) 1113944

(m4)

μ1Δτξij(t t + n) (19)

Δτξij(t t + n)

Cav minus Cξ

Cav minus Clowast middot

q

Cξ if ant ξ passes the path (i j)

0 otherwise

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(20)

Formula (20) represents the contribution of the ant ξ tothe increase in the amount of pheromone on the path (i j) ξis the ranking of the ants Cav represents the average value ofthe target of this cycle and Cξ represents the target valuefound by the ant ξ

53 Pheromone Limit Interval Although the aforemen-tioned improved pheromone update rule can solve theproblems of solution speed and precocious convergence it iseasy to fall into the dilemma of local optimization and thealgorithm stops searching +erefore in this paper the ideaof MMAS is introduced in the process of pheromoneupdating +e upper and lower limits are imposed on thepheromone and the limiting interval of the pheromone is setto[τmin τmax] When performing pheromone updateaccording to the aforementioned pheromone update rulesthe following is obtained

(1) If τij(t)gt τmax occurs τij(t) τmax is required(2) If τij(t)lt τmin occurs τij(t) τmin is required

+is can effectively avoid that the amount of pheromoneon one path is much larger than the rest so that all ants areconcentrated on the same path resulting in a local optimalsituation

54 Algorithm Flowchart In summary the multiobjectiveant colony algorithm flowchart is as shown in Figure 3

6 Case Study

Take Chinarsquos multimodal transport network with 10 cities asan example it involves 10 cities the origination is Chengduand the destination is Shanghai as shown in Table 2 Sincethere are many inland cities in this multimodal transportnetwork and the water transport is poor we considered three

transport modes road railway and air in this case+e nodecities in the multimodal transport network are numberedsequentially and the schematic diagram of the multimodaltransport network of this case is made accordingly as shownin Figure 4

+is case involves three transportation modes We needto consider how to clearly express the antrsquos choice behaviorfor transportation mode when using the ant colony algo-rithm +erefore we have simply dealt with the multimodaltransport network Each transport node is expanded intomultiple virtual subnodes according to the number oftransport modes For example transfer node 3 is extended torailway node highway node and airport node In theprocessed network diagram there is a transport problemamong multiple subnodes of the same node But it is not theant to select the next arrival node that is to say there is nosequence between the subnodes which is the same levelparallel relationship +e network deformation diagram isshown in Figure 5

+e transportation mileage time delay coefficient andaccident damage coefficient of different transportationmodes among node cities are shown in Table 3 +e timedelay coefficient is given according to the road condition ofeach node city and the different characteristics of trans-portation mode +e accident damage coefficient is given bythe traffic management status of each node city and thetechnical performance of each transportation mode

+e requirements for freight volume transportationtime limit and unit value of goods by freight forwarders andthe requirements for carbon emission limit by governmentofficials are shown in Table 4

+e unit transit cost and unit transit time betweendifferent modes of transport are shown in Table 5

+e transportation cost average speed and carbonemission factors of each transportation mode are shown inTable 6

61 Resultsrsquo Analysis +e multiobjective ant colony algo-rithm is used to write the algorithm code on theMATLAB R2014a platform +e algorithm parameters areset as follows λ 3 α 1 β 3 q 2 ρ 09 the numberof ants is 100 and the number of iterations is 200y1 10000 y2 20000 Taking the weight of the objectivefunction as 13 as an example the optimal path of multi-modal transport is Chengdu to Chongqing to Wuhan toHefei to Nanjing and the total cost is 331750 To explore theresults of multimodal transport route optimization con-sidering different cost factors the weight of each objectivefunction is assigned in turn and the following conclusionsare drawn in this paper

62ObjectiveWeight SensitivityAnalysis In order to explorethe multimodal path optimization results when consideringdifferent cost factors this paper analyzes the sensitivity ofthe objective function weights as shown in Table 7 and drawsthe following conclusions

In Figure 6 Experiment (1 5) and (2 4) are compared itis found that when the weight of damage compensation cost

Journal of Advanced Transportation 7

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

multiobjective optimization problem in discrete spacehowever the basic ant colony algorithm has the problems ofslow running efficiency premature convergence and easy tofall into a local optimal solution +is paper combines thesolution requirements of the multimodal transport pathselection model In order to improve the effectiveness of thealgorithm the basic algorithm is improved accordingly

51 Node Transition Probability Although the objectivefunction of the model in this paper is the total cost value in

the transportation process the time penalty cost is deter-mined by the length of the transportation time +e modeltarget expectation cost and time are as small as possible so inthe improved ant colony algorithm a cost heuristic functionand a time heuristic function need to be set at the same timeIt will mainly rely on the influence of path pheromoneconcentration cost heuristic experience and time heuristicexperience when choosing to reach the node

Pkij(t)

ταij(t)ηβij(t)θλij(t)

1113936sisinallowedkταis(t)ηβis(t)θλis(t)

j isin allowedk

0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

ηij 1

1113936sisinSQcsij d

sijVS1113872 1113873x

sij + 1113936sisinSθQESd

sijx

sij + 1113936sisinSψ

sijx

sijQπ + 1113936sisinS1113936sprimeisinSQc

ssprimei y

ssprimei

(15)

θij 1

1113936sisinS dsijVS1113872 1113873x

sij + 1113936

sisinS1113936

sprimeisinST

ssprimei y

ssprimei (16)

Formula (14) is the node transition probability formulain the multiobjective ant colony algorithm where α is theinformation heuristic factor β is the cost expectationheuristic factor λ is the time expectation heuristic factorand τij is the pheromone concentration on path (i j)Formula (15) is a cost heuristic function whose value isinversely proportional to the sum of transportation costcarbon emission cost and damage compensation cost onpath 1 and transit cost of inode Formula (16) is a timeheuristic function whose value is inversely proportional tothe sum of transportation time on path (i j) and transittime of inode

52 Pheromone Update Rule +e principle of the positivefeedback mechanism of ant colony algorithm is based on thecontinuous update of pheromone so the pheromone updaterule is the key to solving the problem of speed and accuracyof ant colony algorithm +is paper considers the basic ideaof ant colony algorithm with elite strategy at the end of eachcycle additional pheromone enhancement is given to theoptimal solution found in this cycle in order to make theoptimal solution found so far more attractive to the ants inthe next cycle +e pheromone is updated according to thefollowing formula

τij(t + n) (1 minus ρ)τij(t) + Δτij(t t + n) + Δτlowastij(t t + n) (17)

Δτlowastij(t t + n) σ middot

q

Clowast If path (i j) is part of the optimal path in this cycle

0 otherwise

⎧⎪⎪⎨

⎪⎪⎩(18)

Formula (17) is the pheromone concentration on path(i j) at time t + n and ρ is the pheromone global vola-tilization coefficient Δτij(t t + n) is the amount ofpheromone increase on path (i j) from time t totime t + n Formula (18) is the amount of pheromoneincrease on path (i j) caused by elite ants from time t totime t + n q is the pheromone intensity σ is the numberof elite ants and Clowast is the optimal solution value found inthis cycle

Using the elite strategy can make the ant system find abetter solution through fewer cycles and the solution speedis faster However after using the elite strategy the at-tractiveness of the current optimal solution increases so thatthe search process is concentrated near the optimal solutionfound so far thereby preventing further searches for a bettersolution +e problem of premature convergence is morelikely to occur In order to maintain the selection pressurethis paper extends the concept of ranking in genetic

6 Journal of Advanced Transportation

algorithms to the elite mechanism and calculatesΔτij(t t + n)

by a weighted method After completing a cycle the ants aresorted according to the size of the target value found in thecycle and the antrsquos contribution to the pheromone update isconsidered to be inversely proportional to the target value ofthe path the ant passes +e contribution of the ant to thepheromone update is weighted according to the ranking ofthe ant (ξ) In order to ensure the speed of the solution whileexpanding the solution space it is considered that only thetop (m4) ants can contribute to the pheromone update andthe amount of pheromone obtained by the path it passes isproportional to the antrsquos ranking Δτij(t t + n) is calculatedas follows

Δτij(t t + n) 1113944

(m4)

μ1Δτξij(t t + n) (19)

Δτξij(t t + n)

Cav minus Cξ

Cav minus Clowast middot

q

Cξ if ant ξ passes the path (i j)

0 otherwise

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(20)

Formula (20) represents the contribution of the ant ξ tothe increase in the amount of pheromone on the path (i j) ξis the ranking of the ants Cav represents the average value ofthe target of this cycle and Cξ represents the target valuefound by the ant ξ

53 Pheromone Limit Interval Although the aforemen-tioned improved pheromone update rule can solve theproblems of solution speed and precocious convergence it iseasy to fall into the dilemma of local optimization and thealgorithm stops searching +erefore in this paper the ideaof MMAS is introduced in the process of pheromoneupdating +e upper and lower limits are imposed on thepheromone and the limiting interval of the pheromone is setto[τmin τmax] When performing pheromone updateaccording to the aforementioned pheromone update rulesthe following is obtained

(1) If τij(t)gt τmax occurs τij(t) τmax is required(2) If τij(t)lt τmin occurs τij(t) τmin is required

+is can effectively avoid that the amount of pheromoneon one path is much larger than the rest so that all ants areconcentrated on the same path resulting in a local optimalsituation

54 Algorithm Flowchart In summary the multiobjectiveant colony algorithm flowchart is as shown in Figure 3

6 Case Study

Take Chinarsquos multimodal transport network with 10 cities asan example it involves 10 cities the origination is Chengduand the destination is Shanghai as shown in Table 2 Sincethere are many inland cities in this multimodal transportnetwork and the water transport is poor we considered three

transport modes road railway and air in this case+e nodecities in the multimodal transport network are numberedsequentially and the schematic diagram of the multimodaltransport network of this case is made accordingly as shownin Figure 4

+is case involves three transportation modes We needto consider how to clearly express the antrsquos choice behaviorfor transportation mode when using the ant colony algo-rithm +erefore we have simply dealt with the multimodaltransport network Each transport node is expanded intomultiple virtual subnodes according to the number oftransport modes For example transfer node 3 is extended torailway node highway node and airport node In theprocessed network diagram there is a transport problemamong multiple subnodes of the same node But it is not theant to select the next arrival node that is to say there is nosequence between the subnodes which is the same levelparallel relationship +e network deformation diagram isshown in Figure 5

+e transportation mileage time delay coefficient andaccident damage coefficient of different transportationmodes among node cities are shown in Table 3 +e timedelay coefficient is given according to the road condition ofeach node city and the different characteristics of trans-portation mode +e accident damage coefficient is given bythe traffic management status of each node city and thetechnical performance of each transportation mode

+e requirements for freight volume transportationtime limit and unit value of goods by freight forwarders andthe requirements for carbon emission limit by governmentofficials are shown in Table 4

+e unit transit cost and unit transit time betweendifferent modes of transport are shown in Table 5

+e transportation cost average speed and carbonemission factors of each transportation mode are shown inTable 6

61 Resultsrsquo Analysis +e multiobjective ant colony algo-rithm is used to write the algorithm code on theMATLAB R2014a platform +e algorithm parameters areset as follows λ 3 α 1 β 3 q 2 ρ 09 the numberof ants is 100 and the number of iterations is 200y1 10000 y2 20000 Taking the weight of the objectivefunction as 13 as an example the optimal path of multi-modal transport is Chengdu to Chongqing to Wuhan toHefei to Nanjing and the total cost is 331750 To explore theresults of multimodal transport route optimization con-sidering different cost factors the weight of each objectivefunction is assigned in turn and the following conclusionsare drawn in this paper

62ObjectiveWeight SensitivityAnalysis In order to explorethe multimodal path optimization results when consideringdifferent cost factors this paper analyzes the sensitivity ofthe objective function weights as shown in Table 7 and drawsthe following conclusions

In Figure 6 Experiment (1 5) and (2 4) are compared itis found that when the weight of damage compensation cost

Journal of Advanced Transportation 7

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

algorithms to the elite mechanism and calculatesΔτij(t t + n)

by a weighted method After completing a cycle the ants aresorted according to the size of the target value found in thecycle and the antrsquos contribution to the pheromone update isconsidered to be inversely proportional to the target value ofthe path the ant passes +e contribution of the ant to thepheromone update is weighted according to the ranking ofthe ant (ξ) In order to ensure the speed of the solution whileexpanding the solution space it is considered that only thetop (m4) ants can contribute to the pheromone update andthe amount of pheromone obtained by the path it passes isproportional to the antrsquos ranking Δτij(t t + n) is calculatedas follows

Δτij(t t + n) 1113944

(m4)

μ1Δτξij(t t + n) (19)

Δτξij(t t + n)

Cav minus Cξ

Cav minus Clowast middot

q

Cξ if ant ξ passes the path (i j)

0 otherwise

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(20)

Formula (20) represents the contribution of the ant ξ tothe increase in the amount of pheromone on the path (i j) ξis the ranking of the ants Cav represents the average value ofthe target of this cycle and Cξ represents the target valuefound by the ant ξ

53 Pheromone Limit Interval Although the aforemen-tioned improved pheromone update rule can solve theproblems of solution speed and precocious convergence it iseasy to fall into the dilemma of local optimization and thealgorithm stops searching +erefore in this paper the ideaof MMAS is introduced in the process of pheromoneupdating +e upper and lower limits are imposed on thepheromone and the limiting interval of the pheromone is setto[τmin τmax] When performing pheromone updateaccording to the aforementioned pheromone update rulesthe following is obtained

(1) If τij(t)gt τmax occurs τij(t) τmax is required(2) If τij(t)lt τmin occurs τij(t) τmin is required

+is can effectively avoid that the amount of pheromoneon one path is much larger than the rest so that all ants areconcentrated on the same path resulting in a local optimalsituation

54 Algorithm Flowchart In summary the multiobjectiveant colony algorithm flowchart is as shown in Figure 3

6 Case Study

Take Chinarsquos multimodal transport network with 10 cities asan example it involves 10 cities the origination is Chengduand the destination is Shanghai as shown in Table 2 Sincethere are many inland cities in this multimodal transportnetwork and the water transport is poor we considered three

transport modes road railway and air in this case+e nodecities in the multimodal transport network are numberedsequentially and the schematic diagram of the multimodaltransport network of this case is made accordingly as shownin Figure 4

+is case involves three transportation modes We needto consider how to clearly express the antrsquos choice behaviorfor transportation mode when using the ant colony algo-rithm +erefore we have simply dealt with the multimodaltransport network Each transport node is expanded intomultiple virtual subnodes according to the number oftransport modes For example transfer node 3 is extended torailway node highway node and airport node In theprocessed network diagram there is a transport problemamong multiple subnodes of the same node But it is not theant to select the next arrival node that is to say there is nosequence between the subnodes which is the same levelparallel relationship +e network deformation diagram isshown in Figure 5

+e transportation mileage time delay coefficient andaccident damage coefficient of different transportationmodes among node cities are shown in Table 3 +e timedelay coefficient is given according to the road condition ofeach node city and the different characteristics of trans-portation mode +e accident damage coefficient is given bythe traffic management status of each node city and thetechnical performance of each transportation mode

+e requirements for freight volume transportationtime limit and unit value of goods by freight forwarders andthe requirements for carbon emission limit by governmentofficials are shown in Table 4

+e unit transit cost and unit transit time betweendifferent modes of transport are shown in Table 5

+e transportation cost average speed and carbonemission factors of each transportation mode are shown inTable 6

61 Resultsrsquo Analysis +e multiobjective ant colony algo-rithm is used to write the algorithm code on theMATLAB R2014a platform +e algorithm parameters areset as follows λ 3 α 1 β 3 q 2 ρ 09 the numberof ants is 100 and the number of iterations is 200y1 10000 y2 20000 Taking the weight of the objectivefunction as 13 as an example the optimal path of multi-modal transport is Chengdu to Chongqing to Wuhan toHefei to Nanjing and the total cost is 331750 To explore theresults of multimodal transport route optimization con-sidering different cost factors the weight of each objectivefunction is assigned in turn and the following conclusionsare drawn in this paper

62ObjectiveWeight SensitivityAnalysis In order to explorethe multimodal path optimization results when consideringdifferent cost factors this paper analyzes the sensitivity ofthe objective function weights as shown in Table 7 and drawsthe following conclusions

In Figure 6 Experiment (1 5) and (2 4) are compared itis found that when the weight of damage compensation cost

Journal of Advanced Transportation 7

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

is the same and the weight of the sum of transportation costtransshipment cost and carbon emission cost is high theoptimal path is the railway-road combined transportation+e railway-road combined transport pays more attention tothe cost of transport It pays more attention to the size of thecost incurred in the transportation processWhen the weight

All ants complete asearch process

Start

Initialization parameters

Put M ants into thestarting point

Select the next arriving node based onthe node transition probability

(roulette method)

Global pheromone update

End of iteration

End

N

N

Y

Y

Limit the amount ofpheromone to the pheromone

limit interval

Construct cost heuristic functionand time heuristic function

Iteration number + 1

Figure 3 Multiobjective ant colony algorithm flowchart

Table 2 Node city number

Number 1 2 3 4 5Name of node city Chengdu Xirsquoan Chongqing Guiyang ZhengzhouNumber 6 7 8 9 10Name of node city Wuhan Changsha Hefei Nanchang Nanjing

1 3

4

2 5

7

69

810

Railway transportRoad transportAir transport

Figure 4 Multimodal network diagram

1 2 3

Road transportRailway transport Water transport

Conversion modeof transport

1 2 3

3Prime

3prime

2Prime

2prime

1Prime

1prime

Figure 5 Transit node deformation

8 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

of time penalty cost is high the optimal route is mainly air-railway combined transportation and more attention is paidto the length of transportation time As the carbon emissionfactor of road transportation is relatively high and thetransport time of railway transportation is relatively longthe carbon emission cost of Experiment 1 and 2 is relativelyhigh and the time penalty cost is relatively high Due to thepoor safety of air transport compared with other modes of

transport the cost of compensation for damages in Ex-periment 4 and 5 is relatively high

Generally speaking in the comprehensive considerationof cost time energy saving and transportation safetywhether it is air-railway combined transport or road-railwaycombined transport railway occupies a large proportionwhich also proves that multimodal transport based on railwaytransportation can indeed maximize the transport benefits

Table 4 Parameter selection

Parameter Freight (t) Transportation time limit (h) Carbon emission limit (kg) Value of goods (yuant)Value 100 45 10000 1000

Table 5 Transit cost and transit time of transit node

TransitRail transport Road transport Air transport

Cost (yuant) Time (ht) Cost (yuant) Time (ht) Cost (yuant) Time (ht)Rail transport mdash mdash 12 001 12 002Road transport 10 001 mdash mdash 15 003Air transport 12 002 15 003 mdash mdashNote +e unit of transit cost is yuant and the unit of transit time is ht

Table 6 Transport mode parameters

Mode of transport Transportation cost (yuantmiddotkm) Average speed (kmh) Unit carbon emissions(kgtmiddotkm)Highway 15 100 012Railway 1 75 0025Waterway 5 600 105

Table 7 Weight assignment experiment number

Number 1 2 3 4 5

Weight assignment ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω307 01 02 05 02 03 13 13 13 02 05 03 01 07 02

Table 3 Transport distance and time delay coefficient between node pairs

Adjacent node (1 2) (1 3) (1 4) (2 5) (3 6) (4 7) (5 8)Railway mileage (km) 842 504 967 511 1233 956 645Time delay coefficient 019 008 012 021 007 016 010Accident damage coefficient 004 001 006 008 002 007 003Highway mileage (km) 719 326 721 479 898 872 673Time delay coefficient 014 011 009 017 007 013 019Accident damage coefficient 009 002 008 005 002 008 013Waterway mileage (km) 612 270 521 434 752 645 465Time delay coefficient 016 012 012 019 009 014 015Accident damage coefficient 015 002 012 007 008 005 006Adjacent node (5 10) (6 8) (6 9) (7 9) (7 10) (8 10) (9 10)Railway mileage (km) 695 1181 365 418 1200 312 838Time delay coefficient 018 011 015 013 014 010 017Accident damage coefficient 005 003 006 004 005 005 007Highway mileage (km) 698 495 370 399 921 178 603Time delay coefficient 015 017 010 016 020 012 018Accident damage coefficient 006 005 018 005 014 002 009Waterway mileage (km) 564 316 264 290 705 145 468Time delay coefficient 019 013 016 018 017 011 015Accident damage coefficient 004 005 004 005 005 001 017

Journal of Advanced Transportation 9

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

63 Analysis of Transportation Reliability and TransportationSafety In order to explore the practicability of the model allcost weights are set to 13 and the ant colony algorithm isused to solve the problem without considering the trans-portation reliability and transportation safety

From Table 8 it can be concluded that the highway has ahigher proportion in the optimal path solved withoutconsidering the transportation reliability and transportationsafety However the transportation reliability and trans-portation safety of road transportation are poor so the totalcost of this optimal path in the model constructed in thispaper exceeds the total cost of multimodal transportationoptimal path based on railway transportation +is result isalso in line with Chinarsquos policy of transitioning from roadtransport to railway transport because railway transport ismore stable and safer and it can transport goods safely andin a timely manner With the continuous development ofother modes of transportation in the future China or othercountries may have a multimodal transport mode based onroad transport or other modes of transport Howevertransportation reliability and transportation safety are thefactors that must be considered in the multimodal path

optimization problem therefore the model established inthis paper is still applicable to the route selection and op-timization of other transportation modes

7 Conclusions

+e paper analyzes and demonstrates the important positionof railway transportation in multimodal transport and es-tablishes a multimodal transport route selection modelbased on railway transportation In view of some problemsthat often occur during transportation this paper focuses ontransportation reliability and transportation safety introducestime penalty cost and damage compensation cost and definestime delay coefficient and accident damage coefficient re-spectively Taking a multimodal transport network in Chinaas a case and the network is transformed according to thecharacteristics of the ant colony algorithm Sensitivity analysisof cost weights proves that the multimodal transport based onrailway transportation can maximize transportation effi-ciency +e analysis of transportation reliability and trans-portation safety shows that the model constructed in thispaper has strong practicability and wide application range

Table 8 Comparison of total cost of optimal path

Optimal path Transportation mode Total cost (transport stability and transport safetyare not considered)

Total cost (transportation stability andsafety are considered)

1-3-7-9-10 Railway-highway-highway-highway $312689 $349854

2 3 41 5Number

Carbon emission costDamage compensation cost

706560555045403530252015100501

003002001

Cos

t100

00yu

an

Time penalty cost

Total costTransportation cost

Figure 6 Sensitivity analysis of cost weights

10 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was supported by the National Key RampDProgram of China (2017YFB1200702) National NaturalScience Foundation of China (Project nos 52072314 and71971182) Sichuan Science and Technology Program(Project nos 2020YJ0268 2020YJ0256 2021YFQ0001 and2021YFH0175) Chengdu Science and Technology PlanResearch Program (Project nos 2019-YF05-01493-SN 2020-RK00-00036-ZF and 2020-RK00-00035-ZF) Science andTechnology Plan of China Railway Corporation (Project nosP2018T001 and 2019KY10) the Natural Science Foundationof Zhejiang Province China (LQ18G030012) and the Hu-manities and Social Sciences Fund of Ministry of EducationChina (18YJC630190)

References

[1] Y M Bontekoning C Macharis and J J Trip ldquoIs a newapplied transportation research field emerging A review ofintermodal rail-truck freight transport literaturerdquo Trans-portation Research Part A Policy and Practice vol 38 no 1pp 1ndash34 2003

[2] T Christine and L Sabine ldquoScenario-based analysis for in-termodal transport in the context of service network designmodelsrdquo Transportation research interdisciplinary perspec-tives vol 2 2019

[3] E Demir W Burgholzer M Hrusovsky E ArıkanW Jammernegg and T V Woensel ldquoA green intermodalservice network design problem with travel time uncertaintyrdquoTransportation Research Part B Methodological vol 93 no 7pp 789ndash807 2016

[4] M L Chen X J Zhao X G Deng et al ldquoMultimodaltransport path optimization under uncertain conditionsrdquoJournal of Highway and Transportation Research and Devel-opment vol 38 no 1 pp 143ndash150 2021

[5] M Ghazanfari L Sara R Daphne and Q Liron ldquoCommuterbehavior under travel time uncertaintyrdquo Performance Eval-uation vol 148 2021

[6] M Hrusovsky E Demir W Jammernegg and W VanldquoHybrid simulation and optimization approach for greenintermodal transportation problem with travel time uncer-taintyrdquo International Journal of Flexible Manufacturing Sys-tems vol 30 no 3 pp 486ndash516 2018

[7] X Wang and Q Meng ldquoDiscrete intermodal freight trans-portation network design with route choice behavior of in-termodal operatorsrdquo Transportation Research Part BMethodological vol 95 no 1 pp 76ndash104 2017

[8] X Q Cheng and C Jin ldquoRoute selection problem in mul-timodal transportation with traffic congestion consideredunder low-carbon policiesrdquo Operations Research and Man-agement Science vol 28 no 4 pp 67ndash77 2019

[9] S Fazayeli A Eydi and I N Kamalabadi ldquoLocation-routingproblem in multimodal transportation network with time

windows and fuzzy demands presenting a two-part geneticalgorithmrdquo Computers amp Industrial Engineering vol 119no 5 pp 233ndash246 2018

[10] H Li and L Su ldquoMultimodal transport path optimizationmodel and algorithm considering carbon emission multitaskrdquoJe Journal of Supercomputing vol 76 no 12 pp 9355ndash93732020

[11] J Wan and S Wei ldquoMulti-objective multimodal trans-portation path selection based on hybrid algorithmrdquo Journalof Tianjin University vol 52 no 3 pp 285ndash292 2019

[12] A Idri M Oukarfi A Boulmakoul K Zeitouni and AMasrildquoA distributed approach for shortest path algorithm in dy-namic multimodal transportation networksrdquo TransportationResearch Procedia vol 27 no 12 pp 294ndash300 2017

[13] C-H Chen ldquoAn arrival time prediction method for bussystemrdquo IEEE Internet of Jings Journal vol 5 no 5pp 4231-4232 2018

[14] N Koohathongsumrit and W Meethom ldquoRoute selection inmultimodal transportation networks a hybrid multiple cri-teria decision-making approachrdquo Journal Of Industrial AndProduction Engineering vol 38 no 3 pp 171ndash185 2021

[15] S Liu C Yin D Chen H Lv and Q Zhang ldquoCascadingfailure in multiple critical infrastructure interdependentnetworks of syncretic railway systemrdquo IEEE Transactions onIntelligent Transportation Systems vol 2021 pp 1ndash14 2021

[16] Z Tian G Sun D Chen Z Qiu and Y Ma ldquoMethod fordetermining the valid travel route of railways based ongeneralised cost under the syncretic railway networkrdquo Journalof Advanced Transportation vol 2020 no 2 12 pages 2020

[17] F Russo and U Sansone ldquo+e terminal cycle time in road-railcombined transportrdquo Wit Transactions on Ecology amp theEnvironment vol 186 pp 875ndash886 2014

[18] A Abderrahman A Ahmede and B Jaouad ldquoRobust opti-mization of the intermodal freight transport problemmodeling and solving with an efficient hybrid approachrdquoJournal of Computational Science vol 30 no 1 pp 127ndash1422019

[19] Y Jiang and X C Zhang ldquoTransport plan design for rail-truckintermodal transportationrdquo Journal of Transporation SystemsEngineering amp Information Technology vol 18 no 6pp 222ndash228 2018

[20] X Liu Y Bai and J Chen ldquoAn intermodal transportationgeospatial network modeling for containerized soybeanshippingrdquo Journal of Ocean Engineering and Science vol 2no 2 pp 143ndash153 2017

[21] D Chen S Ni C A Xu and X Jiang ldquoOptimizing the draftpassenger train timetable based on node importance in arailway networkrdquo Transportation Letters vol 11 no 1pp 20ndash32 2019

[22] M Verma V Verter and N Zufferey ldquoA bi-objective modelfor planning and managing rail-truck intermodal trans-portation of hazardous materialsrdquo Transportation ResearchPart E Logistics and Transportation Review vol 48 no 1pp 132ndash149 2011

[23] I Toumazis and C Kwon ldquoRouting hazardous materials ontime-dependent networks using conditional value-at-riskrdquoTransportation Research Part C Emerging Technologiesvol 37 no 3 pp 73ndash92 2013

[24] Z Xu Q Zhang D Chen and Y He ldquoCharacterizing theconnectivity of railway networksrdquo IEEE Transactions on In-telligent Transportation Systems vol 21 no 4 pp 1491ndash15022020

[25] Y Sun and M Lang ldquoBi-objective optimization for multi-modal transportation routing planning problem based on

Journal of Advanced Transportation 11

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation

Pareto optimalityrdquo Journal of Industrial Engineering andManagement vol 8 no 3 pp 1195ndash1217 2015

[26] C-H Chen F-J Hwang and H-Y Kung ldquoTravel timeprediction system based on data clustering for waste collec-tion vehiclesrdquo IEICE Transactions on Information and Sys-tems vol 102 no 7 pp 1374ndash1383 2019

[27] Z Elisabeth and R V Gloria ldquoOptimized allocation ofstraddle carriers to reduce overall delays at multimodalcontainer terminalsrdquo Flexible Services and ManufacturingJournal vol 27 no 2-3 pp 300ndash330 2015

[28] S Bret and B Kendon ldquoEnvironmental public health andsafety assessment of fuel pipelines and other freight trans-portation modesrdquo Applied Energy vol 171 pp 266ndash276 2016

[29] T Yang X Peng D Chen F Yang and M Muneeb AbidldquoResearch on trans-region integrated traffic emergency dis-patching technology based on multi-agentrdquo Journal of In-telligent amp Fuzzy Systems vol 385 no 5 pp 5763ndash5774 2020

[30] H Y Luo J Yang and X Nan ldquoPath and transport modeselection in multimodal transportation with time windowrdquo inProceedings of the 3rd IEEE Advanced Information TechnologyElectronic and Automation Control Conference (IAEAC)pp 162ndash166 Chongqing China 2018

12 Journal of Advanced Transportation