ADesign-Task-OrientedModelAssignmentMethodin Model ...downloads.hindawi.com/journals/mpe/2020/8595790.pdf · ResearchArticle ADesign-Task-OrientedModelAssignmentMethodin Model-BasedSystemEngineering

Research ArticleA Design-Task-Oriented Model Assignment Method inModel-Based System Engineering

Xiaofei Wang 12 Wenhe Liao1 Yu Guo1 Daoyuan Liu1 and Weiwei Qian1

1College of Mechanical and Electrical Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China2Nanjing Research Institute of Electronics Technology Nanjing 210039 China

Correspondence should be addressed to Xiaofei Wang wangxiaofeinjnuaaeducn

Received 4 May 2020 Revised 19 July 2020 Accepted 6 August 2020 Published 24 August 2020

Guest Editor Juan Carlos Leyva-Lopez

Copyright copy 2020 Xiaofei Wang 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

In model-based system engineering (MBSE) reuse of existing models in the development of a new system can be advantageousAutomatic assignment of existing models to each design task within a design task set has been proven to be feasible Howeverwhile several studies have discussed the significance of models in MBSE and methodologies for models reuse solving the modelreusability problem through a model assignment method has not been discussed Additionally a significant challenge in modelassignment is to address the conflict between the maximization of the model value summations which are yielded by assigning themodels to a design task set and the minimization of the execution cycle of the task set is study (a) proposes a design-task-oriented model assignment method that establishes a multiobjective model based on a model assignment integration frameworkand (b) designs a differential-evolution-combined adaptive nondominated sorting genetic algorithm-II to provide an optimaltradeoff between maximizing the total model values and minimizing the execution cycle of the task set By comparing theperformance of the algorithm in resolving the assignment of models to a design task set with those of two conventional algorithmsin a phased-array radar development project the algorithmrsquos performance and promotion of system development are verified tobe superiore newmethod can be applied for developingmodel scheduling software forMBSE-compliant product developmentprojects to improve using effects of the models and development cycle

1 Introduction

Considering the increasingly sophisticated customer de-mands and the growing requirements for increased productdevelopment capabilitiesmdashgiven that products are moreintegrated and intelligent in various industries includingaviation and spacemdashthe traditional product developmentmode is no longer satisfactory [1] Model-based systemengineering (MBSE) accomplishes the development ofcomplex products with a new mode and is capable offorecasting product behaviors thereby improving the pro-ductivity of the product development process Arguably thedevelopments of aviation and space systems which areregarded as the most complex cyber-physical systems (CPSs)in the industry [2] have adopted the MBSE approach tofacilitate the implementation of all the phases of the productlifecycle [3ndash8] e widespread use of MBSE has tended to

shift emphasis from data management to model manage-ment throughout the entire productrsquos lifecycle [9]

MBSE is the formalized application of modeling used tosupport system requirements design analysis and verifi-cation and validation activities beginning with the con-ceptual design phase and continuing throughout thedevelopment and later lifecycle phases [10] e output ofthe MBSE activities is a coherent model of the system (iesystem model) whereby the emphasis is placed on theevolution and the refinement of the model using model-based methods and tools [11]erefore the model plays themost important role in each stage of the productrsquos lifecycle

In the concept and design phases a shared systemmodelis needed to support the exchange of information acrossvarious aspects Accordingly this systemmodel serves as thecore model of the system to provide information andmaintain consistency with domain-specific models For

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 8595790 15 pageshttpsdoiorg10115520208595790

example the Space SystemsWorking Group of InternationalCouncil on Systems Engineering developed the CubeSatreference model for mission-specific CubeSat teams [6] eGerman Aerospace Center presented the conceptual datamodel as an abstraction of domain-specific models [5] Inthe development of mechatronic systems Barbieri et al usedthe conceptual model as the information source for domain-specific models of every functional module [12] Researchersfrom nine leading Chinese academic and industrial insti-tutions have gathered to discuss the definition and appli-cation of MBSE-compliant product meta-models [9]

MBSE has also found application in the early tenderphases of complex CPS development wherein the complexCPS customer can use the MBSE approach to generate amodel-based request for tenders and pass it on to thesupplier who can use the model to perform system devel-opment Australiarsquos Defense Science and Technology Or-ganization pioneered the adoption of a whole-of-systemanalytical framework for information transfer across thecontractual interface [8]e integrated designmethodologyproposed in [12] also demonstrated that the MBSE approachcan be used to fulfill stakeholder requirements by adoptingthem in the system requirements In addition to the abovestages MBSE can also be used as an effective method forproduct manufacturing system planning in themanufacturing phase [13 14]

At a higher level a model-based system analysisframework is needed to provide the capability to accessintegrate and transform disparate data into actionable in-formation for the design and analysis of complex systemse United States (US) Air Force (AF) established thedigital thread initiative [3 15] that generates an engineeringanalytical framework based on an authoritative digitalsurrogate representation throughout the entire productrsquoslifecycle

emost commonly usedmodeling language inMBSE isthe system modeling language (SysML) a general-purposegraphical modeling language that supports analysis speci-fication design verification and validation of complexsystems [11 16] and has been adopted by many MBSEprojects [1 9 12 13 17] Despite the fact that it is acceptedby the Object Management Organization as a standardmodeling language SysML is not easy to adapt for systemengineers who have not been exposed to object-orientedconcepts because like the unified modeling language(UML) it emphasizes familiarity with these concepts Forease of use organizations have developed some modelinglanguages including the modeling and analysis of real-timeembedded (MARTE) systems [18] architecture analysis anddesign language (AADL) [2] domain-specific modelinglanguage (DSML) [19] and others Based on these languagessome powerful MBSE platforms and tools have been de-veloped For example alesrsquo ARCADIAtrade and Capellatradeworkbench [20 21] support requirement analyses andsystem design in the areas of transportation aviation spaceand radars while Tucson Embedded Systemsrsquo AWESUMtradetool suite supports the US Armyrsquos joint common archi-tecture project [2] In addition the US Department of

Defensersquos high-performance computing modernizationprogram has developed a computational research engi-neering acquisition tools environment for air vehicles [3]and realized the digital thread of the US AF

With the increasing application of the MBSE approachin the industry numerous models built using variousmodeling languages have been stored by various orga-nizations adopting MBSE However the models are oftennot reused effectively When faced with a new develop-ment project the development teams often create newmodels rather than reusing the existing models availablewithin each discipline is repetition of work amounts toan unnecessary expenditure of cost and time for theproject To reuse existing models appropriate modelsshould be identified and assigned to each of the designtasks in the development project While literature onmodel reuse has described approaches for applying de-velopment environments [22] ontologies [23] and modelrepositories [24 25] no previous studies have discussedmodel assignments erefore this study focuses on theestablishment of a design-task-oriented model assign-ment method to support model reuse in MBSE e studyincludes the following main components

(i) An integration framework capable of assigning themodels in the repository to the design task set isestablished In existing MBSE approaches simplyintegrating the tools into the product lifecycle de-velopment environment [2 3] does not enablemodel reuse because it does not consider how thestored models are assigned to the design tasks of theproject e framework proposes an optimizationscheme for matching the models and the designtasks to support the needs of the MBSE platformand tools for models reuse

(ii) e value of each model for a design task isquantifiedis captures the suitability of the modelfor the task e literature regarding model man-agement in MBSE and software engineering hasfocused on model management platform [26]model repository building methods [27] and so onbut has not provided a method for the evaluation ofmodel value for the task is study applies anadvantage-number-based analytical technique toevaluate the models to be assigned from the per-spective of value and accordingly preferentiallyfilters the models to establish a design-task-orientedpreferred model set

(iii) A mathematics model for design-task-orientedmodel assignment and an optimization algorithmare proposed is study suggests a multiobjectivemodel of design-task-oriented model assignmentsto minimize the task set execution cycle andmaximize the actual value summation of themodels Additionally to solve the proposed mul-tiobjective model the study has designed a differ-ential-evolution-combined adaptive nondominatedsorting genetic algorithm-II (DA-NSGA-II)

2 Mathematical Problems in Engineering

Finally based on a case study the new algorithm isproven to have better performance and promotionof system development than the traditional non-dominated sorting genetic algorithm-II (NSGA-II)and particle swarm optimization (PSO)

e rest of this paper is organized as follows e secondsection describes a design-task-oriented model assignmentintegration framework In the third section a multiobjectivemodel of model assignment is established according to thequantification of model value e fourth section proposesan improved NSGA-II to solve the multiobjective model Acase study based on a phased-array radar developmentproject is discussed in the fifth section Finally the sixthsection focuses on the studyrsquos conclusion and the potentialavenues for future work

2 Design-Task-Oriented Model AssignmentIntegration Framework

In the field of MBSE model reuse is able to improve theefficiency and reduce the cost of system development It is afeasible method to assign the existing models to the taskswithin a design task set under the condition of disciplinematching between the models and the tasks Using themethod a suitable model is selected for each task accordingto the model value for a design task and the execution cycleof the task set following the assignment of the models to thetask

Owing to the different properties of the model fordifferent tasks such as integrality and reliability the samemodel would yield different values when applied to var-ious tasks A model is considered to yield a high value if itcan improve the execution effect of a task that it isassigned to By contrast the same model is considered toyield low value if it would worsen the execution effect ofanother task that it is assigned to In general model as-signment attempts to achieve the highest possible sum-mation of the modelsrsquo actual values once the models areassigned to the tasks

In addition the execution cycle of a single task isdifferent when different models are applied For a giventask set restricted by the temporal relation of the tasks theapplied model assignment strategy determines the exe-cution cycle of the task set us to complete the task setas soon as possible another objective of the model as-signment is the minimization of the task set executioncycle

For a simple system the existing models can be manuallyassigned to each task in the design task set with ease Howeverwhen the developed system is relatively complex the modelvalues for a task cannot be directlymeasured due to the complexmodel properties and wide task ranges us it is difficult todirectly compare the values of a set of models for a particulartask Moreover in the development of a complex system asingle model assignment scheme cannot simultaneously satisfythe requirements of maximizing the total model value andminimizing the task set execution cycle e model assignmentsolutionsmust be optimized to determine the optimum scheme

However the optimization cannot be performed by a humandue to the large number of models and tasks in a complexsystem

Consequently a framework for model assignmentintegration must be established in the field of MBSE inorder to quantitatively evaluate the model values andperform an optimal tradeoff between the maximizationof the total model values and the minimization of theexecution cycle By doing so an optimum solution isobtained allowing the assignment of models to the designtask set e current study establishes a design-task-oriented model assignment integration framework aspresented in Figure 1 e key features of the frameworkare as follows

(i) A model repository needs to be defined and theexisting models of previous projects should be savedin the repository

(ii) e design task set is derived from task planning(iii) e values of the models from the model repository

with respect to the design tasks are evaluatedquantitatively Next a preferred model set is gen-erated after an optimal selection of models based onthe quantitative values of the models

(iv) According to the preferred model set value andcycle matrices concerning the design task set amultiobjective model that relates the maximizationof the modelsrsquo actual value summation and theminimization of the task set execution cycle isestablished

(v) e model assignment scheme is obtained by amultiobjective optimization algorithm

3 Modeling of Design-Task-OrientedMultiobjective Model Assignment

31 Calculation of Modelrsquos Actual Value for Task Based onthe model assignment integration framework models areselected from the model repositoryis process involves thecalculation of the actual values of different models for eachof the specified tasks

e given development project applies the mode ofMBSE assuming that the task set T T1 T2 middot middot middot Tn1113864 1113865 has nmodels Additionally the model repository related to thetask set has l models with M M1 M2 middot middot middot Ml1113864 1113865 as themodel set and S s1 s2 middot middot middot sk1113864 1113865 as set of the modelsrsquoattributes

Definition 1 e value of the model Mi for task Tj is vij

vij 1113944k

g1wgc

ij sg1113872 1113873 (1)

where g 1 2 middot middot middot k i 1 2 middot middot middot l j 1 2 middot middot middot n wg is theweight of the modelrsquos attribute and ci

j(sg) which isexpressed by the five-demarcation method as 1 3 5 7 9 isthe value of the attribute sg of modelMi after it is assigned totask Tj

Mathematical Problems in Engineering 3

Here the modelrsquos attribute weight wg is determinedusing a method based on the significance of the Pawlakattribute in the decision table according to rough set theory[28] To list the model values of the decision table select theoriginal assessment data of lprime models from the model

repository as the universe of discourseU condition attributeset S as the set of model attributes s1 s2 middot middot middot sk1113864 1113865 formulatethe decision attribute setD as the set of model values v andassign the field value according to high middle low edecision table is thus obtained

Cycle matrix

Value matrix

Task set

Save the models in the repository

Value optimal selection

Object 1the minimization ofthe execution cycle

Object 2the maximization of

the total value

Multiobjective optimization algorithm

Model assignment scheme

Multiobjective model

Define a model repositoryCreate the models

hellip

Preferred model set

Model reuse

v11 v12 v1nv21 v22 v2n vm1 vm2 vmn

d11 d12 d1nd21 d22 d2n dm1 dm2 dmn

Figure 1 Design-task-oriented model assignment integration framework


e significance of model attribute sg in Table 1 varieswith decision attribute v In order to determine the sig-nificance we investigate how the decision table classificationvaries with the removal of the model attribute from thedecision table Generally if model attribute sg is deletedfrom condition attribute set S then the impact of deleting sg

on the classification ability of S relative to decision attribute v

increases with the value of cIND(S)(v) minus cIND(Sminussg)(v)namely sg becomes more significant for S relative to de-cision attribute v

Definition 2 e significance of the model attribute sg forthe condition attribute set S relative to the decision attributev is formulated as

sig sg S v1113872 1113873 cIND(S)(v) minus cIND Sminussg( 1113857(v)

pos(S)(v)1113868111386811138681113868

1113868111386811138681113868 minus posSminussg( 1113857

(v)

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

|U| g 1 2 middot middot middot k

(2)

where cIND(S)(v) is the approximation quality of v by ScIND(Sminussg)(v) is the approximation quality of v by Sminus sgpos(S)(v) is the S- positive region of v and pos(Sminussg)(v) is the(Sminus sg)- positive region of v

erefore the weight of the model attribute sg is ob-tained as follows

wg sig sg S v1113872 1113873

1113944k

g1sig sg S v1113872 1113873 (3)

32 Model Selection Based on Advantage Number AnalysisTo improve the development efficiency an optimal selectionmust be conducted before the model assignment to filter outparts of the preferredmodels for specific tasks given that notall the models would be applied in all the tasks In this casethe model selection uses an approach based on advantagenumber analysis

According to Definition 1 the values of the l modelsM1 M2 middot middot middot Ml for task Tj provide the value vectorVj (v1j v2j middot middot middot vlj)

T Set the highest value component ofVj as the ordinal number one the second-highest valuecomponent as the ordinal number two and so on FurtherVj can be converted in the ordinal number vector Rj

(r1j r2j middot middot middot rlj)T of the values of l models for task Tj

whereby rij (i 1 2 middot middot middot l) denotes the order of modelMi inthe model value list for task Tj

Correspondingly in the task set n tasks produce nordinal number vectors and all the ordinal number vectorswould constitute a model value ordinal number matrix withltimes n dimensions

R

r11 r12 middot middot middot r1n


middot middot middot middot middot middot middot middot middot middot middot middot

rl1 rl2 middot middot middot rln

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Based on the advantage number analysis method therespective advantage number of each element in matrix Rwould be

aij l + 1 minus rij (5)

e ordinal number rij can be converted to an advantagenumber aij Apparently a lower ordinal number generates ahigher model value on the specific task and a bigger ad-vantage numbererefore the model value ordinal numbermatrix can be converted to a model value advantage numbermatrix

A

a11 a12 middot middot middot a1n



al1 al2 middot middot middot aln

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)

By summing up all the advantage numbers on each lineinA the advantage number summation of the specificmodelcorresponding to the line is obtained

Ai 1113944n

j1aij i 1 2 l (7)

Upon selection of a proper threshold λ all the Ai ge λmodels are the assignable models selected from themodel repository Assuming that the number of theselected models is m the value matrix of m selectedmodels for n tasks of the task set can form an m times ndimensional matrix

V

v11 v12 middot middot middot v1n



vm1 vm2 middot middot middot vmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)

33 Establishment of a Multiobjective Model of ModelAssignment Without considering possible constraints onresources the problem associated with the design-task-oriented model assignment in MBSE involves n taskswithin a development project that applies an MBSE

Table 1 Decision table of model values

Universe of discourse UModel attributes Value

s1 s2 middot middot middot sk v

1 Middle Low middot middot middot High Low2 Middle High middot middot middot Middle Middlemiddot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot

lprime Low High middot middot middot High High


mode Precedence relations exist between some of thetasks that prohibit the onset of the task Tj (j 2 3 middot middot middot n)before all of its precedence tasks Th (h isinPj) are com-pleted Secondly the model repository involves m se-lected models for all the specified tasks Task Tj (j 1 2middot middot middot n) has to choose one of the selected models to beperformed and the model cannot be ceased or changedto another model form during the task once the model isassigned selectively e actual value of model Mi isdifferent after it has been assigned to different tasksMeanwhile for task Tj the cycle varies depending on theapplication of different models us the cycle matrix of

m selected models for n tasks in the task set can beexpressed as

D

d11 d12 middot middot middot d1n



dm1 dm2 middot middot middot dmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

e model assignment must meet the two objectivesnamely the minimization of the task set execution cycle andthe maximization of the modelsrsquo actual value summation

A decision variable can be introduced as

xijt 1 modelMi is assigned to taskTj and taskTj is accomplished at phase t

0 others1113896 (10)

us the design-task-oriented model assignment inMBSE is presented as a multiobjective model according to

minFn 1113944m

i11113944

LFn

tEFn

t middot xijt (11)

maxV 1113944m

i11113944

n

j1xijtvij (12)

such that

1113944

m

i11113944

LFj

tEFj

xijt 1 j 1 2 middot middot middot n (13)

1113944

m

i11113944

LFh

tEFh

t middot xiht le 1113944m

i11113944

LFj

tEFj

t minus dij1113872 1113873xijt

j 2 3 middot middot middot n h isin Pj

(14)

xijt isin 0 1 i 1 2 middot middot middot m j 1 2 middot middot middot n

t EFj middot middot middot LFj

(15)

Equations (11) and (12) are objective functions thatrespectively denote the minimization of the task set ex-ecution cycle and the maximization of the modelsrsquo actualvalue summation (after the models are assigned to thetasks) Equation (13) indicates that each task requires onlya single model and can be executed only once Equation(14) indicates that task Tj can only be started if all theprecedence tasks Th are accomplished Equation (15)defines the range of values of the variable Correspond-ingly a solution of the multiobjective model is achievedafter the determination of each modelrsquos assignmentmanner and each taskrsquos completion time Fj

4 Algorithm for the Solution of theMultiobjective Model Assignment

e design-task-oriented model assignment problem is amultiobjective optimization problem Many optimizationalgorithms have been developed to solve the optimizationproblem [29 30] such as NSGA-II presented by Deb et al[31 32] and PSO developed by Kennedy and Eberhart [33]e algorithm was proved to be superior to other evolu-tionary algorithms regarding the overall fitness [34] InMBSE projects the algorithm was applied to aviation [15]space [7 35] software [36] andmanufacturing [37] In theseapplications the researchers of NSGA-II achievedimprovements

is study introduces the DA-NSGA-II algorithm tosolve the proposed design-task-oriented model assignmente algorithm framework is shown in Figure 2 and theoperating procedures are described below

Procedure 1 establishment of the initial populatione codes of the chromosomes are generated based onthe different task assignment manners of each selectedmodel e code length equals the task quantity n andthe code bits denote the corresponding tasks e valuerange of each code bit ranges from 1 to m while theactual value is decided by the model code that is beingassigned to the specific task represented by code bitsAccording to the coding rule the initial population isobtained to utilize the individuals that are randomlygenerated according to the population size to meet theconstraintsProcedure 2 the first fast nondominated sorting Uponthe calculation of each individualrsquos execution cycle of thetask set and the actual value summation of themodels thefitness values of the individuals are obtained Each in-dividualrsquos ordinal number and crowding distance are thenobtained by fast sorting the individuals in a non-domination manner based on the fitness value


Procedure 3 crossover andmutation Consider some ofthe individuals selected via tournament selection asparents First the children with an equal number of theparents are achieved with precedence operationcrossover (POX) and neighborhood mutation To in-crease the diversity of the children a differential evo-lution (DE) algorithm is used on the parents to generate

the second batch of children with an equal number ofthe parentsProcedure 4 the second fast nondominated sortinge two batches of children obtained based on cross-over mutation and DE are introduced in the pop-ulation and each individualrsquos ordinal number andcrowding distance can then be obtained by executingthe second fast nondominated sorting on the newpopulationProcedure 5 we introduce an adaptive algorithm in theelite-reserve solution and reserve the elitist individualsfrom the lowest ordinal number to the highest one asthe next generation until the number of individualsreaches the defined population size In the cases ofindividuals with the same ordinal numbers those withlarger crowding distances are preferred to be reservede reservation rate is

ρ 1

1 + eminust (16)

where t indicates the number of iterationsProcedure 6 we output the results once the stop cri-terion is satisfied which in our case is the maximumnumber of generations Alternatively the executionjumps to Procedure 3

5 Case Study

51 Assignment Solution of Models to the Design Task Set in aPhased-Array Radar Development Project e MBSEmethod was applied in a phased-array radar developmentproject e projectrsquos task set involved 14 tasks T1 forlogical architecture decomposition T2 for the simula-tions of the main lobe and the side-lobe characteristics ofthe radar antenna T3 for interference suppression sim-ulations T4 for clutter suppression simulations T5 for theassignment of component functions T6 for componentinterface definitions T7 for amplitudendashphase consistencydesign T8 for radio frequency (RF) modeling T9 for RFsimulations T10 for scan matching simulations T11 forsmall-scale modeling T12 for small-scale simulations T13for radar cross section simulations and T14 for virtualsystem integration analysis e temporal relationsamong tasks are precedence restrictions (ie startndashendrelations) (see Figure 3 for the temporal relations)

ere are 15 models whose disciplines match the task setEach model involves five attributes that is model integrity (s1)simulation operating efficiency (s2) simulation confidence (s3)model compatibility (s4) and model interoperability (s5) SeeTable 2 for the execution cycles of each task when separatemodels are applied

e objective of the case is to find the optimal solution thatassigns themodels to the design tasks in the task set based on theproposed method We first perform an optimal selection of themodels To calculate the model values the weights of the modelattributes have to be determined as a prerequisite Selecting 12

Create initial population byrandomly generating the individuals

that meet the constraints

Initialize parameters populationscale max generations gmax

crossover probability Pc mutationprobability Pm differential zoom

factor F differential evolution (DE)crossover probability CR

Precedenceoperation crossover

Fastly sort the individuals innondomination to obtain their ordinal

numbers and crowding distance

Neighborhoodmutation

Reserve the elitist solutions as thenext generation through adaptive

elite-reserve strategy

Is the stop criterionsatisfied

DE mutation

DE crossover

Calculate the fitness values of theindividuals

Choose the individuals as parents viatournament selection

Output the results

Fast nondominated sorting on thenew population

Mix the parents and children to forma new population

Start

End

Y

N

Figure 2 DA-NSGA-II framework


original data of model value assessment as the universe ofdiscourse U the conditional attribute set indicates the modelattributes s1 s2 s3 s4 s51113864 1113865 and the decision attribute setindicates the model value v thus establishing the decisiontable with the model values as shown in Table 3

According to (2) and (3) the weights of the model at-tributes s1 s2 s3 s4 and s5 would be

w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)

According to Definition 1 model values can be obtainedfor various tasks For instance the 15 model values for taskT1 are listed in Table 4

erefore the value vector of the 15 models for task T1is V1 (5099 5205 4889 5311 3835 4787 5731 3731

4679 4997 3945 4571 5627 3521 4995)T and it wouldbe transformed to the ordinal number vector R1

(5 4 8 3 13 9 1 14 10 6 12 11 2 15 7)T According to(4) the ordinal number matrix R composed of the ordinalnumber vectors of all the tasks from the task set can beformulated According to (5) the advantage number matrixA can be realized based on the conversion from the ordinalnumber matrix Finally based on (7) the advantage numbersummations of each model can be achieved as listed inTable 5

According to the experience choosing the thresholdλ 106 the assignable selected model set in the model re-pository shall be M1 M2 M4 M5 M6 M8 M1113864

9 M11 M12 M13 e value matrix of the 10 models in theselected model set for the 14 tasks in the task set can beexpressed as Table 6

We attempted to solve the assignment of each selectedmodel to the task set by utilizing DA-NSGA-II according tothe objective functions of (11) and (12) based on the as-sumption of the following parameters 200 for the initial

T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14

Figure 3 Temporal relations between model-based design tasks of a phased-array radar

Table 2 Execution cycles of each task when separate models are applied (unit day)

Model T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14M1 3 5 18 9 4 6 8 3 2 4 8 10 11 7M2 3 4 11 11 5 9 8 4 4 4 9 9 9 8M3 2 6 14 10 3 7 7 3 3 7 6 11 10 6M4 3 5 16 13 4 8 10 5 5 5 8 8 12 8M5 5 7 12 10 6 5 9 6 2 5 11 12 11 7M6 4 9 9 8 4 7 8 2 2 3 7 14 9 12M7 3 5 11 12 4 6 8 4 3 4 10 9 13 10M8 6 8 17 15 6 4 11 3 1 6 8 10 10 5M9 5 6 13 9 5 10 9 6 3 4 12 7 15 11M10 4 8 12 7 7 9 6 3 4 5 7 15 17 9M11 5 7 15 14 4 6 10 2 1 3 11 9 14 7M12 6 4 13 11 5 7 9 4 5 6 10 13 10 9M13 2 3 14 12 6 8 11 5 2 7 8 8 8 6M14 4 6 10 8 5 5 7 3 4 5 9 11 12 7M15 3 5 12 9 3 6 12 5 3 4 9 9 16 10


Table 3 Decision table with a phased-array radarrsquos model values

Universe of discourse UConditional attributes S Decision attribute D

s1 s2 s3 s4 s5 v

1 Middle Low Middle Middle Middle Low2 Middle High Middle Middle Middle Middle3 Middle High Middle Middle High High4 Middle Low Low Middle Low Low5 Middle Low Middle Middle Low Middle6 Middle High Middle High Middle High7 Low High High Middle Low Middle8 Low Low Middle Middle Low Low9 High High Middle Middle Middle High10 Middle Low Middle High Low Middle11 Middle Low Middle Low Low Low12 Middle High High Middle Low High

Table 4 Model values for task T1

Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210

M1 3 7 5 7 5 5099M2 7 5 7 1 7 5205M3 3 3 7 7 5 4889M4 5 5 3 7 5 5311M5 1 9 7 3 5 3835M6 7 1 5 5 3 4787M7 5 3 1 7 9 5731M8 3 1 9 1 7 3731M9 5 7 9 3 3 4679M10 9 5 3 1 5 4997M11 7 3 1 1 5 3945M12 1 3 7 5 9 4571M13 5 1 1 9 7 5627M14 3 3 9 1 5 3521M15 5 9 1 5 5 4995

Table 5 Advantage number summations of each studied model

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15

108 140 99 129 110 131 98 109 119 101 107 132 118 85 105

Table 6 Value matrix of the selected models for all tasks

Model T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14M1 5099 3309 5209 3523 6155 4573 4047 4575 5523 2155 5099 6153 1839 6469M2 5205 5311 5417 5835 4785 6151 4467 4891 4681 4787 4781 5835 7203 6151M4 5311 5941 8151 4993 3733 3103 5839 8151 6361 6995 3311 4047 3521 3101M5 3835 4891 3627 7205 6575 4259 2575 3733 5627 5413 4259 3627 4679 5519M6 4787 4997 4891 3521 4785 7729 1841 6783 4997 2259 7835 6993 5523 6571M8 3731 2889 5627 3733 4467 5419 3311 1209 5519 7731 6151 6677 5627 2679M9 4679 5519 4783 4465 6363 4783 5731 4891 5207 5417 4471 6257 1419 4261M11 3945 5205 6365 6255 3735 6361 3101 6889 4785 1735 2577 2995 5625 4365M12 4571 3521 6153 5419 5101 4045 6571 3209 4049 4573 7309 7099 5099 7415M13 5627 5523 3101 4573 5521 6889 3313 4155 4993 4787 4365 6677 4363 2261


Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993


population size 200 for maximum generations probabilityof crossover Pc 09 probability of mutation Pm 01differential zoom factor F 05 and probability of DEcrossover CR 07 A set of Pareto optimal solutions wereobtained and the objective values are presented in Table 7

In the phased-array radar development project we canselect one of the solutions from the Pareto optimal solutionset by considering the practical constraint of the executioncycle and the expectation of the of the model value sum-mation to determine the eventual model assignment schemeFor example the assignment scheme demonstrated by so-lution 10 is listed in Table 8

52 Algorithms Comparison

521 Performances Comparison e traditional NSGA-IIand PSO have also been used to solve the model assignmentmodel to verify the performance of the proposed algorithme same parameters are preset in both NSGA-II and DA-NSGA-II e initial population size and maximum gen-erations of PSO are equal to those of DA-NSGA-II with theremaining PSO parameters set as follows accelerationconstants c1 08 and c2 08 inertia weight ωmax 12 andωmin 01 e comparison diagram of the Pareto frontsgenerated by the three algorithms is shown in Figure 4

From Figure 4 we can always find superior solutions inthe Pareto front of DA-NSGA-II by comparing to the Paretofront of the traditional NSGA-II and PSO is proves thatthe convergence of DA-NSGA-II is superior to that ofNSGA-II and PSO

To conduct a quantitative evaluation on the performanceof DA-NSGA-II the study applied the S- andM-measures asthe evaluating indicators Based on the solutions of themodel assignment with DA-NSGA-II NSGA-II and PSOTable 9 presents a comparison of S- and M-measures of thethree Pareto optimal solutions achieved by executing sep-arately the three algorithms 10 different times

Table 9 demonstrates that the mean value of theS-measure in the DA-NSGA-II case is lower than thoseassociated with NSGA-II and PSO and themean value of theM-measure in the DA-NSGA-II case is higher than thoseobtained from the execution of NSGA-II and PSO It alsoshows that the standard deviations of the S- andM-measuresin the DA-NSGA-II case are lower than those in the NSGA-II and PSO cases ese results indicate that the distributionuniformity and the range of the solution outcomes generatedby the DA-NSGA-II algorithm are superior to those of theNSGA-II and PSO algorithms-based solutions and theoutputs of DA-NSGA-II are more stable than those ofNSGA-II and PSO

Figure 5 compares the execution cycles and model valuesummations outputted by DA-NSGA-II NSGA-II and PSO

from generations 1 to 200 e value of each execution cycleis the minimum execution cycle in the Pareto solution setoutputted by the algorithms at each generation (Figure 5(a))Each model value summation is the maximum summationof the model values in the Pareto solution set outputted bythe algorithms at each generation (Figure 5(b)) e exe-cution cycle and model value summations achieved by DA-NSGA-II begin to converge before generation 20 whilethose of DA-NSGA-II begin to converge at generations 21and 37 respectively PSO is not able to attain the optimalvalues until generations 101 and 135 respectively eseresults indicate the faster convergence rate of DA-NSGA-IIcompared to those of NSGA-II and PSO

522 Optimizing Effects Comparison In this section wecompare the optimizing effects via DA-NSGA-II NSGA-IIand PSO First the execution cycles of the task set corre-sponding to themodel assignment schemes optimized by thethree algorithms are compared e comparison is per-formed between solutions with equal model value sum-mations However from DA-NSGA-II Pareto optimalsolution set we cannot determine a solution with modelvalue summation exactly equal to that of the Pareto optimalsolution from NSGA-II or PSO erefore solution sets Aand B in the Pareto front generated by DA-NSGA-II arecalculated via interpolation e model value summationscorresponding to the solutions in solution set A (B) are equal

Table 8 Models for various tasks demonstrated by solution 10 in Table 7

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14M13 M13 M6 M5 M1 M6 M12 M4 M4 M8 M6 M2 M2 M12

Neg

ativ

e sum

mat

ion

of m

odel

val

ues

DAndashNSGAndashIINSGAndashIIPSO

ndash100

ndash95

ndash90

ndash85

ndash80

ndash75

40 42 44 46 48 50 52 54 5638Execution cycle (day)

Figure 4 Comparison of the Pareto fronts generated by DA-NSGA-II NSGA-II and PSO


DA-NSGA-IINSGA-IIPSO

37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)

Figure 5 Comparison of the objective values outputted by DA-NSGA-II NSGA-II and PSO across multiple generations (a) Executioncycles of the three algorithms from generations 1 to 200 (b) Model value summations of the three algorithms from generations 1 to 200

EC1EC2(EC1 ndash EC2)EC1

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)

Figure 6 Comparison of the task set execution cycles optimized by the three algorithms assuming equal model value summations (a)Comparison of EC2 obtained by DA-NSGA-II and EC1 obtained by NSGA-II Numbers 1ndash10 indicate the model value summations in thePareto optimal solution set from NSGA-II of 773 811 848 874 896 912 934 941 949 and 956 respectively (b) Comparison of EC4determined by DA-NSGA-II and EC3 determined by PSO Numbers 1ndash12 indicate the model value summations in the Pareto optimalsolution set from PSO of 797 812 858 861 886 893 908 914 930 940 941 and 944 respectively

Table 9 Comparison of the performances of the three algorithms

Evaluation indexDA-NSGA-II NSGA-II PSO

Mean value Standard deviation Mean value Standard deviation Mean value Standard deviationS-measure 08201 01602 08784 04468 12693 08716M-measure 237390 25971 210179 36404 232693 33199


to those of the Pareto optimal solutions based on NSGA-II(PSO) We denote the execution cycle of the task set relatedto the Pareto optimal solution from NSGA-II set A PSOand set B as EC1 EC2 EC3 and EC4 respectively Figure 6presents the comparison between EC1 and EC2 and betweenEC3 and EC4 under the condition that the correspondingsummations of the model values are equal

e bar chart in Figure 6(a) compares EC1 and EC2 withequal model value summations from the Pareto optimalsolution sets generated by DA-NSGA-II and NSGA-II re-spectively while the line graph presents the percentagedecrease of EC2 compared to EC1 EC2 is 28ndash92 lowerthan EC1 Similarly the bar chart in Figure 6(b) comparesEC3 and EC4 with equal model value summations from thePareto optimal solution sets generated by DA-NSGA-II andPSO respectively while the line graph presents the per-centage decrease of EC4 compared to EC3 EC4 is 61ndash187lower than EC3 us the design efficiency of the modelassignment solution optimized by DA-NSGA-II is higherthan those optimized by NSGA-II and by PSOe efficiencyimproved on average by 42 and 110 respectively

Second the model value summations corresponding tothe model assignment solutions optimized by the three al-gorithms are compared We define the model value sum-mation of the Pareto optimal solution generated by NSGA-II PSO and DA-NSGA-II as SV1 SV2 and SV3 respectivelyFigure 7 compares SV1 SV2 and SV3 under the condition ofequal task set execution cycles

e bar chart in Figure 7 compares SV1 SV2 and SV3 forequal task set execution cycles from the Pareto optimal so-lution sets obtained by the three algorithms while the linegraph presents the percentage increase of SV3 compared toSV1 and that of SV3 compared to SV2 SV3 is 11ndash57 greaterthan SV1 with an average increase of 32 while SV3 is44ndash111 greater than SV2 with an average increase of 68erefore the model assignment solution optimized by DA-

NSGA-II promotes the design task set to a greater extentcompared with those optimized by NSGA-II and PSO

6 Conclusions

e proposed design-task-oriented model assignmentframework that involves model value selection multi-objective model establishment and the multiobjective op-timization algorithm provides a solution for the problem ofmodel assignment in the model repository to the designtasks in MBSE

In MBSE design-task-oriented model assignment basedon model value quantification involves the use of multi-objective optimization is study applies an advantage-number-based analytical technique to quantify the modelsrsquovalues and consequently obtains the value matrix of themodels e goals of the multiobjective model of modelassignment which is established based on the modelsrsquo cycleand value matrices on the specified tasks are the minimi-zation of the task set execution cycle and the maximizationof the modelsrsquo actual value summation

e proposed DA-NSGA-II algorithm increases thediversity of the population and reserves more elite solutionsbased on the introduction of the DE algorithm and theadaptive elite-reserve solution e convergence distribu-tion uniformity and ranges of the solution outcomes of thealgorithm are superior to those of the traditional NSGA-IIand PSO Moreover the algorithm is more conducive toimproving the design efficiency and effect than NSGA-II andPSO e algorithm is therefore favorable for the solution ofproblems that involve design-task-oriented modelassignments

Further research should focus on the following twoadditional perspectives (1) In the current study the es-tablishment of a multiobjective model assumed a precon-dition of unlimited resources However resources that

SV1SV2SV3

(SV3 ndash SV1)SV1(SV3 ndash SV2)SV2

75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No

Figure 7 Comparison of the model value summations optimized by the three algorithms under equal task set execution cycles Numbers1ndash15 indicate the task set execution cycles of 39 40 41 42 43 44 45 46 47 48 50 51 52 53 and 55 (unit day) respectively


include human resources cash cost and other factors areconstrained in a realistic product development projectFuture research should execute the model establishmentover resource-constrained conditions to further enhanceand broaden the applicability of the algorithm (2) For anMBSE-compliant product development project modelscheduling software is capable of improving the usage effectsof the models and the development cycles According to thefindings of this study one can develop a model schedulingsoftware based on the proposed multiobjective model andDA-NSGA-II algorithm

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by National Natural ScienceFoundation of China (grant no 51575274)

References

[1] K Bhasin P Barnes J Reinert and B Golden ldquoApplyingmodel based systems engineering to NASArsquos space commu-nications networksrdquo in Proceedings of the 7th Annual IEEEInternational Systems Conference pp 325ndash330 Orlando FLUSA April 2013

[2] S M Simi S P Mulholland and W G Tanner ldquoTES-SAViAWESUM model-based systems engineering (MBSE) forFACE applicationsrdquo in Proceedings of the 2014 IEEE Aero-space Conference p 17 Big Sky MT USA March 2014

[3] E M Kraft ldquoHPCMP CREATEtrade-AV and the air force digitalthreadrdquo in Proceedings of the 53rd AIAA Aerospace SciencesMeeting p 13 Kissimmee FL USA January 2015

[4] J J Zhang Z Liu F Li et al ldquoEmploying model-basedsystems engineering (MBSE) on a civil aircraft researchproject a case studyrdquo in Proceedings of the 2018 Asia-PacificInternational Symposium on Aerospace Technologypp 2178ndash2186 Chengdu China October 2018

[5] P M Fischer D Ludtke C Lange F-C RoshaniF Dannemann and A Gerndt ldquoImplementing model-basedsystem engineering for the whole lifecycle of a spacecraftrdquoCEAS Space Journal vol 9 no 3 pp 351ndash365 2017

[6] D Kaslow and A M Madni ldquoValidation and verification ofMBSE-compliant CubeSat reference modelrdquo DisciplinaryConvergence in Systems Engineering Research A M MadniB Boehm R G Ghanem et al Eds pp 381ndash393 SpringerCham Switzerland 2018

[7] J Stern S Wachtel J Colombi D Meyer and R CobbldquoMultiobjective optimization of geosynchronous earth orbitspace situational awareness systems via parallel executablearchitecturesrdquo in Proceedings of the Conference on SystemsEngineering Research (CSER 2017) pp 599ndash615 RedondoBeach CA USA March 2017

[8] Q Do S Cook and M Lay ldquoAn investigation of MBSEpractices across the contractual boundaryrdquo Procedia Com-puter Science vol 28 pp 692ndash701 2014

[9] C Wang ldquoMBSE-compliant product lifecycle model man-agementrdquo in Proceedings of the 14th Annual ConferenceSystem of Systems Engineering pp 248ndash253 Anchorage AKUSA 2019

[10] International Council on Systems Engineering (INCOSE)Systems Engineering Vision 2020 Version 203 INCOSE SanDiego CA USA 2007

[11] S Friedenthal A Moore and R Steiner A Practical Guide toSysML Ae Systems Modeling Language Morgan KaufmannPublishers Waltham MA USA 2012

[12] G Barbieri C Fantuzzi and R Borsari ldquoA model-baseddesign methodology for the development of mechatronicsystemsrdquo Mechatronics vol 24 no 7 pp 833ndash843 2014

[13] C Steimera J Fischerb and J C Aurich ldquoModel-baseddesign process for the early phases of manufacturing systemplanning using SysMLrdquo in Proceedings of the 27th CIRPDesign Conference pp 163ndash168 Cranfield UK May 2017

[14] K Kubler S Scheifele C Scheifele and O Riedel ldquoModel-based systems engineering for machine tools and productionsystems (model-based production engineering)rdquo ProcediaManufacturing vol 24 pp 216ndash221 2018

[15] D J L Siedlak O J Pinon P R Schlais T M Schmidt andD N Mavris ldquoA digital thread approach to supportmanufacturing-influenced conceptual aircraft designrdquo Re-search in Engineering Design vol 29 no 2 pp 285ndash308 2018

[16] K Hampson ldquoTechnical evaluation of the systems modelinglanguage (SysML)rdquo Procedia Computer Science vol 44pp 403ndash412 2015

[17] S Gao W Cao L Fan and J Liu ldquoMBSE for satellitecommunication system Architectingrdquo IEEE Access vol 7pp 164051ndash164067 2019

[18] H Xia J Jiao and J Dong ldquoExtend UML based timelinessmodeling approach for complex systemrdquo in Proceedings of the2018 International Conference on Mathematics ModelingSimulation and Statistics Application p 6 Shanghai ChinaDecember 2018

[19] M Challenger G Kardas and B Tekinerdogan ldquoA systematicapproach to evaluating domain-specific modeling languageenvironments for multi-agent systemsrdquo Software QualityJournal vol 24 no 3 pp 775ndash795 2016

[20] P Roques ldquoMBSE with the ARCADIA method and the ca-pella toolrdquo in Proceedings of the 8th European Congress onEmbedded Real Time Software and Systems p 10 ToulouseFrance January 2016

[21] A Soltan S Addouche M Zolghadri M Barkallah andM Haddar ldquoSystem Engineering for dependency analysis - aBayesian approach application to obsolescence studyrdquo Pro-cedia CIRP vol 84 pp 774ndash782 2018

[22] Y Ye and G Fischer ldquoReuse-conducive development envi-ronmentsrdquo Automated Software Engineering vol 12 no 2pp 199ndash235 2005

[23] U Shani ldquoCan ontologies prevent MBSE models from be-coming obsoleterdquo in Proceedings of the 2017 Annual IEEEInternational Systems Conference p 8 Montreal CanadaApril 2017

[24] H Zhao J Liang X Yin et al ldquoDomain-specific ModelWareto make the machine learning model reusable and repro-duciblerdquo in Proceedings of the 12th ACMIEEE InternationalSymposium on Empirical Software Engineering and Mea-surement p 2 Oulu Finland October 2018


[25] B Hamid ldquoAssessment of the SEMCO model-based reposi-tory approach for software system engineeringrdquo in Pro-ceedings of the 7th International Conference on Model andData Engineering pp 111ndash125 Barcelona Spain October2017

[26] C Ponsard R Darimont andM Touzani ldquoRobust design of acollaborative platform for model-based system engineeringexperience from an industrial deploymentrdquo in Proceedings ofthe 9th International Conference on Model and Data Engi-neering pp 333ndash347 Toulouse France October 2019

[27] B Hamid ldquoA model repository description langua-gendashMRDLrdquo in Proceedings of the 15th International Confer-ence on Software Reuse pp 350ndash367 Limassol Cyprus June2016

[28] Z Pawlak ldquoRough sets and decision tablesrdquo in Proceedings ofthe 5th Symposium on Computation Aeory pp 187ndash196Zaborόw Poland December 1984

[29] F P Mahdi P Vasant V Kallimani J Watada P Y S Faiand M Abdullah-Al-Wadud ldquoA holistic review on optimi-zation strategies for combined economic emission dispatchproblemrdquo Renewable and Sustainable Energy Reviews vol 81no 2 pp 3006ndash3020 2018

[30] J M Granado-Criado S Santander-Jimenez M A Vega-Rodrıguez and A Rubio-Largo ldquoA multi-objective optimi-zation procedure for solving the high-order epistasis detectionproblemrdquo Expert Systems with Applications vol 142 ArticleID 113000 2020

[31] K Deb S Agrawal A Pratap and T Meyarivan ldquoA fast elitistnon-dominated sorting genetic algorithm for multi-objectiveoptimization NSGA-IIrdquo in Proceedings of the 6th Interna-tional Conference on Parallel Problem Solving from Naturepp 849ndash858 Paris France September 2000

[32] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2pp 182ndash197 2002

[33] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceedings of the IEEE International Conference on NeuralNetwork pp 1942ndash1948 Perth Australia November 1995

[34] Y Li T Yue S Ali and L Zhang ldquoZen-ReqOptimizer asearch-based approach for requirements assignment opti-mizationrdquo Empirical Software Engineering vol 22 no 1pp 175ndash234 2017

[35] C J Lowe and M Macdonald ldquoRapid model-based inter-disciplinary design of a CubeSat missionrdquo Acta Astronauticavol 105 no 1 pp 321ndash332 2014

[36] S Rahmoun A Mehiaoui-Hamitou E Borde L Pautet andE Soubiran ldquoMulti-objective exploration of architecturaldesigns by composition of model transformationsrdquo Softwareamp Systems Modeling vol 18 no 1 pp 107ndash127 2019

[37] RWang and C H Dagli ldquoComputational system architecturedevelopment using a holistic modeling approachrdquo ProcediaComputer Science vol 12 pp 13ndash20 2012


example the Space SystemsWorking Group of InternationalCouncil on Systems Engineering developed the CubeSatreference model for mission-specific CubeSat teams [6] eGerman Aerospace Center presented the conceptual datamodel as an abstraction of domain-specific models [5] Inthe development of mechatronic systems Barbieri et al usedthe conceptual model as the information source for domain-specific models of every functional module [12] Researchersfrom nine leading Chinese academic and industrial insti-tutions have gathered to discuss the definition and appli-cation of MBSE-compliant product meta-models [9]

MBSE has also found application in the early tenderphases of complex CPS development wherein the complexCPS customer can use the MBSE approach to generate amodel-based request for tenders and pass it on to thesupplier who can use the model to perform system devel-opment Australiarsquos Defense Science and Technology Or-ganization pioneered the adoption of a whole-of-systemanalytical framework for information transfer across thecontractual interface [8]e integrated designmethodologyproposed in [12] also demonstrated that the MBSE approachcan be used to fulfill stakeholder requirements by adoptingthem in the system requirements In addition to the abovestages MBSE can also be used as an effective method forproduct manufacturing system planning in themanufacturing phase [13 14]

At a higher level a model-based system analysisframework is needed to provide the capability to accessintegrate and transform disparate data into actionable in-formation for the design and analysis of complex systemse United States (US) Air Force (AF) established thedigital thread initiative [3 15] that generates an engineeringanalytical framework based on an authoritative digitalsurrogate representation throughout the entire productrsquoslifecycle

emost commonly usedmodeling language inMBSE isthe system modeling language (SysML) a general-purposegraphical modeling language that supports analysis speci-fication design verification and validation of complexsystems [11 16] and has been adopted by many MBSEprojects [1 9 12 13 17] Despite the fact that it is acceptedby the Object Management Organization as a standardmodeling language SysML is not easy to adapt for systemengineers who have not been exposed to object-orientedconcepts because like the unified modeling language(UML) it emphasizes familiarity with these concepts Forease of use organizations have developed some modelinglanguages including the modeling and analysis of real-timeembedded (MARTE) systems [18] architecture analysis anddesign language (AADL) [2] domain-specific modelinglanguage (DSML) [19] and others Based on these languagessome powerful MBSE platforms and tools have been de-veloped For example alesrsquo ARCADIAtrade and Capellatradeworkbench [20 21] support requirement analyses andsystem design in the areas of transportation aviation spaceand radars while Tucson Embedded Systemsrsquo AWESUMtradetool suite supports the US Armyrsquos joint common archi-tecture project [2] In addition the US Department of

Defensersquos high-performance computing modernizationprogram has developed a computational research engi-neering acquisition tools environment for air vehicles [3]and realized the digital thread of the US AF

With the increasing application of the MBSE approachin the industry numerous models built using variousmodeling languages have been stored by various orga-nizations adopting MBSE However the models are oftennot reused effectively When faced with a new develop-ment project the development teams often create newmodels rather than reusing the existing models availablewithin each discipline is repetition of work amounts toan unnecessary expenditure of cost and time for theproject To reuse existing models appropriate modelsshould be identified and assigned to each of the designtasks in the development project While literature onmodel reuse has described approaches for applying de-velopment environments [22] ontologies [23] and modelrepositories [24 25] no previous studies have discussedmodel assignments erefore this study focuses on theestablishment of a design-task-oriented model assign-ment method to support model reuse in MBSE e studyincludes the following main components

(i) An integration framework capable of assigning themodels in the repository to the design task set isestablished In existing MBSE approaches simplyintegrating the tools into the product lifecycle de-velopment environment [2 3] does not enablemodel reuse because it does not consider how thestored models are assigned to the design tasks of theproject e framework proposes an optimizationscheme for matching the models and the designtasks to support the needs of the MBSE platformand tools for models reuse

(ii) e value of each model for a design task isquantifiedis captures the suitability of the modelfor the task e literature regarding model man-agement in MBSE and software engineering hasfocused on model management platform [26]model repository building methods [27] and so onbut has not provided a method for the evaluation ofmodel value for the task is study applies anadvantage-number-based analytical technique toevaluate the models to be assigned from the per-spective of value and accordingly preferentiallyfilters the models to establish a design-task-orientedpreferred model set

(iii) A mathematics model for design-task-orientedmodel assignment and an optimization algorithmare proposed is study suggests a multiobjectivemodel of design-task-oriented model assignmentsto minimize the task set execution cycle andmaximize the actual value summation of themodels Additionally to solve the proposed mul-tiobjective model the study has designed a differ-ential-evolution-combined adaptive nondominatedsorting genetic algorithm-II (DA-NSGA-II)




















vij 1113944k

g1wgc

ij sg1113872 1113873 (1)






Cycle matrix

Value matrix

Task set





the total value





hellip

Preferred model set

Model reuse










pos(S)(v)1113868111386811138681113868


(v)

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868


(2)



wg sig sg S v1113872 1113873

1113944k

g1sig sg S v1113872 1113873 (3)







R





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)




A





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Ai 1113944n

j1aij i 1 2 l (7)


V





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)










D





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




0 others1113896 (10)


minFn 1113944m

i11113944

LFn

tEFn

t middot xijt (11)

maxV 1113944m

i11113944

n

j1xijtvij (12)

such that

1113944

m

i11113944

LFj

tEFj


1113944

m

i11113944

LFh

tEFh


i11113944

LFj

tEFj



(14)



(15)









ρ 1

1 + eminust (16)


5 Case Study
















DE mutation

DE crossover



Output the results



Start

End

Y

N





w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References


























































vij 1113944k

g1wgc

ij sg1113872 1113873 (1)






Cycle matrix

Value matrix

Task set





the total value





hellip

Preferred model set

Model reuse










pos(S)(v)1113868111386811138681113868


(v)

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868


(2)



wg sig sg S v1113872 1113873

1113944k

g1sig sg S v1113872 1113873 (3)







R





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)




A





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Ai 1113944n

j1aij i 1 2 l (7)


V





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)










D





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




0 others1113896 (10)


minFn 1113944m

i11113944

LFn

tEFn

t middot xijt (11)

maxV 1113944m

i11113944

n

j1xijtvij (12)

such that

1113944

m

i11113944

LFj

tEFj


1113944

m

i11113944

LFh

tEFh


i11113944

LFj

tEFj



(14)



(15)









ρ 1

1 + eminust (16)


5 Case Study
















DE mutation

DE crossover



Output the results



Start

End

Y

N





w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References










































Cycle matrix

Value matrix

Task set





the total value





hellip

Preferred model set

Model reuse










pos(S)(v)1113868111386811138681113868


(v)

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868


(2)



wg sig sg S v1113872 1113873

1113944k

g1sig sg S v1113872 1113873 (3)







R





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)




A





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Ai 1113944n

j1aij i 1 2 l (7)


V





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)










D





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




0 others1113896 (10)


minFn 1113944m

i11113944

LFn

tEFn

t middot xijt (11)

maxV 1113944m

i11113944

n

j1xijtvij (12)

such that

1113944

m

i11113944

LFj

tEFj


1113944

m

i11113944

LFh

tEFh


i11113944

LFj

tEFj



(14)



(15)









ρ 1

1 + eminust (16)


5 Case Study
















DE mutation

DE crossover



Output the results



Start

End

Y

N





w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References













































pos(S)(v)1113868111386811138681113868


(v)

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868


(2)



wg sig sg S v1113872 1113873

1113944k

g1sig sg S v1113872 1113873 (3)







R





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)




A





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Ai 1113944n

j1aij i 1 2 l (7)


V





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)










D





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




0 others1113896 (10)


minFn 1113944m

i11113944

LFn

tEFn

t middot xijt (11)

maxV 1113944m

i11113944

n

j1xijtvij (12)

such that

1113944

m

i11113944

LFj

tEFj


1113944

m

i11113944

LFh

tEFh


i11113944

LFj

tEFj



(14)



(15)









ρ 1

1 + eminust (16)


5 Case Study
















DE mutation

DE crossover



Output the results



Start

End

Y

N





w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References










































D





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)




0 others1113896 (10)


minFn 1113944m

i11113944

LFn

tEFn

t middot xijt (11)

maxV 1113944m

i11113944

n

j1xijtvij (12)

such that

1113944

m

i11113944

LFj

tEFj


1113944

m

i11113944

LFh

tEFh


i11113944

LFj

tEFj



(14)



(15)









ρ 1

1 + eminust (16)


5 Case Study
















DE mutation

DE crossover



Output the results



Start

End

Y

N





w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References










































ρ 1

1 + eminust (16)


5 Case Study
















DE mutation

DE crossover



Output the results



Start

End

Y

N





w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References










































w1 sig s1 S v( 1113857

11139445g1sig sg S v1113872 1113873

051584

0316

w2 sig s2 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w3 sig s3 S v( 1113857

11139445g1sig sg S v1113872 1113873

01671584

0105

w4 sig s4 S v( 1113857

11139445g1sig sg S v1113872 1113873

04171584

0263

w5 sig s5 S v( 1113857

11139445g1sig sg S v1113872 1113873

03331584

0210

(17)








T2

T1 T3

T4

T6

T10 T11

T13

T12

T5 T7 T8 T9 T14







s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References










































s1 s2 s3 s4 s5 v



Model s1 s2 s3 s4 s5 vi10316 0105 0105 0263 0210




108 140 99 129 110 131 98 109 119 101 107 132 118 85 105




Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References








































Tabl

e7

Objectiv

evalues

correspo

ndingto

thePa

reto

optim

alsolutio

nsetw

ithDA-N

SGA-II

Object

Solutio

n1

Solutio

n2

Solutio

n3

Solutio

n4

Solutio

n5

Solutio

n6

Solutio

n7

Solutio

n8

Solutio

n9

Solutio

n10

Solutio

n11

Solutio

n12

Solutio

n13

Solutio

n14

Solutio

n15

Solutio

n16

Solutio

n17

Solutio

n18

Execution

cycle

3839

4041

4243

4445

4647

4849

5051

5253

5455

Value

summation

776

817

854

886

901

923

939

947

952

956

961

963

972

979

981

989

991

993














Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References




















































Neg

ativ

e sum

mat

ion

of m

odel

val

ues


ndash100

ndash95

ndash90

ndash85

ndash80

ndash75





37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References









































37

38

39

40

41

42

43

44

45

46

47

Exec

utio

n cy

cle (

day)

20 40 60 80 100 120 140 160 180 2000Generation

(a)


75

80

85

90

95

100

Mod

el v

alue

sum

mat

ion

20 40 60 80 100 120 140 160 180 2000Generation

(b)



35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)

2 3 4 5 6 7 8 9 101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(a)

35

40

45

50

55

60

65

Exec

utio

n cy

cle (

day)


2 3 4 5 6 7 8 9 1211101No

ndash100

ndash50

00

50

100

150

200

Perc

enta

ge o

f dec

reas

e (

)

(b)











6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References













































6 Conclusions





SV1SV2SV3


75

80

85

90

95

100

105

110

115

120

125

Mod

el v

alue

sum

mat

ion

ndash80

ndash60

ndash40

ndash20

00

20

40

60

80

100

120

Perc

enta

ge o

f inc

reas

e (

)

2 3 4 5 6 7 8 9 10 11 12 13 14 151No




Data Availability




Acknowledgments


References









































Data Availability




Acknowledgments


References






















































Documents

ADesign-Task-OrientedModelAssignmentMethodin Model ...downloads.hindawi.com/journals/mpe/2020/8595790.pdf · ResearchArticle ADesign-Task-OrientedModelAssignmentMethodin Model-BasedSystemEngineering