BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
A bi-objetive multiperiod fuzzy schedulingfor a multimodal urban transport system
M.C. Paulina Alejandra Avila Torres
Advisors: Fernando Lopez Irarragorri, Rafael Caballero Fernandez
Programa de Ingeniera de SistemasFacultad de Ingeniera Mecanica y Electrica
Universidad Autonoma de Nuevo Leon
February 2015Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 1 / 26
BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Contenido
Agenda
1 Introduction
2 Fuzzy programming
3 Modelling approach
4 Preprocessing
5 Methodology
6 Experimental design
7 Conclusions
8 Questions
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Introduction
Contexto
Figure : Transport planning process [3].
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Introduction
Descripcion del problema
Figure : Network transportation system.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Introduction
Descripcion del problema
Main characteristics of the problem
1 Minimal frequency determination depends of headwaysdefinition.
2 Split the scheduling horizon into smaller time periods.
3 There are more than one transportation mode with their ownregulations.
4 Demand is unknown but follows certain patterns.
5 There are transfer nodes.
6 There are bunching nodes.
7 Variable and fixed cost.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Introduction
Literature review
Author Multiobjective Multiperiod Multimodal Multiactivity UncertaintyChakroborty et al.[2003],79 xYan et al.[2006],91 x xCeder [2007],216 xZhao & Zeng [2008],78 xZhi-Chun et al.[2010],12 xZhang et al.[2011],13 x x xTilahun & Ong [2012],7 x xHadas & Shnaider [2012],6 xBaskaran & Krishnaiah [2012],3 xXiao Fu et al.[2014],3 x xDemeyer et al.[2014],0 xSzeto & Wu [2014],43 xPerez et al. [2014],0 x xProposal x x x x x
Table : Previous work.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Introduction
Justificacion
Motivation
1 Frequency and timetabling, problems faced everyday.
2 DMs plan and modify the scheduling based on their experience.
3 Every change affects the next activities of the transport process.
4 Most companies in Mexico do not have a computerized systemfor timetable construction.
Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 7 / 26
BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Fuzzy programming
Fuzzy programming:
MILP: Partial fuzzy or complete fuzzy.
Fuzzy numbers: Triangular, trapezoidal, etc..
Methods to compare fuzzy numbers.
Fuzzy programming vs. Stochastic programming.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Modelling approach
Constraints
Modelling departures
(a) Typical
(b) Proposal
Figure : Differences of how to represent departures
Departures as decision variables.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Modelling approach
Interval and headway policies
Figure : First departure.
Figure : Consecutive departure.
Figure : Last departure.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Modelling approach
Synchronizations
Synchronizations are modelled as decision variables.
A huge amount of decision variables representingsynchonizations.
It is very important to reduce the total amount ofsynchronization variables.
Figure : Types of synchronization nodes [2]
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Preprocessing
Constraints
Algorithm for selecting frequency method (Ceder)[3]
Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 12 / 26
BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Preprocessing
presynch
Preprocessing synchronizations
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Preprocessing
pre-proc-fuzzy
Fuzzy to crisp model:FreMinvi (FreMinvi ,FreMinvi ,FreMinvi )
k-prefence method
One fuzzy constraint 2 crisp constraints.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Methodology
Decision support methodology
Phase ActionI.- Inteligence Model
II.- Design OptimizationIII.- Selection Interactive method
Table : Decision making phases.
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Introduction
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Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Methodology
Phase II: S-Augmecon
S-Augmecon is a new derivation of the method -constraintaugmented.
S-Augmecon allows to generate all efficient solutions of themultiobjective problem.
Aceleration algorithms.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Experimental design
We generated 32 instances, randomly.
Characteristics Minimum MaximumRoutes 8 20Periods 2 12Nodes 10 150
Density 2 12Headways 5-10 5-20
Table : Characteristics of the instances.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Experimental design
Experimental design: The objective is to investigate the impact ofthese factor in the instance complecity.
Factorial design 23
Factors:
Confidence levelDemand level.Fuzziness of demand.
Each factor has a low and high level.
Every instance is executed for all factors combinations.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Experimental design
Used OPL, Unix server, Cplex 12.2.
Maximum execution time 3600 sec (for compiling a solution).
Domain reduction, priority of variables, pre-processing.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Experimental design
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Experimental design
Cost and synchronization practically independent.
Correlation between time and cost.
Variation on execution time:
Periods, routes and nodes.Confidence.Density, headways and demand.Fuzziness.
Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 21 / 26
BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Conclusions
Conclusions:
We propose a mathematical model for the frequency andtimetable integrated problem.
We consider demand uncertainty.
We employed fuzzy programming.
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Bibliography
Bibliografa
[Ceder et al.] Ceder, A.; Golany, B. & Tal, O.
Creating bus timetables with maximal synchronization
Transportation Research Part A: Policy and Practice, 35(10), 913-928.
[Desaulniers et al.] Desaulniers, Guy & Hickman, Mark D.
Public Transit
Transportation, 14, 69-127, 2007.
[Ceder] Ceder, Avishai
Public transit planning and operation: theory, modelling and practice
Ed. 1, Elsevier, 2007.
[Weihua Zhang & Marc Reimann],
A simple augmented e-constraint method for multi-objective mathematicalinteger programming problems
European Journal of Operations Research, 234, 15-24, 2014
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BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Bibliography
Bibliografa
[Eranki Anitha] Eranki, Anitha
A model to create bus timetables to attain maximum synchronizationconsidering waiting times at transfer stops.
University of South Florida, 2004.
[Ibarra-Rojas & Ros-Sols] Ibarra-Rojas, Omar J. & Rios-Solis, Yasmin A.
Synchronization of bus timetable, 2011
[Ceder, Avishai] Ceder, Avishai
Designing public transport network and routes, Captulo 3, 2003
[Nezan Mahdavi-Amiri et al.] Nezan Mahdavi-Amiri, Seyed Hadi Nasseri,Alahbakhsh Yazdani
Fuzzy Primal Simplex Algorithm for solving fuzzy linear programmingproblems
Irian Journal of Operations Research
Vol. 1, No. 2, 2009, pag. 68-84
[L. Campos y J.L. Verdegay] L. Campos y J.L. Verdegay
Linear programming problems and ranking of fuzzy numbers
Fuzzy set and systems 32 (1989) 1-11
Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 24 / 26
BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Bibliography
Bibliografa
[Nguyen Van Hop] Nguyen Van Hop
Solving fuzzy linear programming problems using superiority and inferioritymethods
Information Sciences 177 (2007) 1977-1991
[Paulina Avila et al.]Paulina Avila, Fernando Lopez, Rafael Caballero]
An integrated model for the frequency and timetabling problem
Junio 2012, UANL, Graduate Program in Systems Engineering
[Nezan Mahdavi-Amiri et al.] Nezan Mahdavi-Amiri, Seyed Hadi Nasseri,Alahbakhsh Yazdani
Fuzzy Primal Simplex Algorithm for solving fuzzy linear programmingproblems
Irian Journal of Operations Research
Vol. 1, No. 2, 2009, pag. 68-84
[Luis Miguel Prado LLanes],
Clasificacion multicriterio aplicada a la caracterizacion de la maduracionosea en ninos y adolescentes con oclusion normal y edades entre 9 y 16 anos
Universidad Autonoma de Nuevo Leon, 2009
[Molina et al.] Molina, Julian; Laguna, Manuel; Mart, Rafael & Caballero,Rafael.
SSPMO: A Scatter Tabu Search Procedure for Non-Linear MultiobjectiveOptimization
INFORMS Journal on Computing, 19(1), 91-100, 2007.Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 25 / 26
BRT COE 2015
Avila-Lopez-Caballero
Introduction
Fuzzyprogramming
Modellingapproach
Preprocessing
Methodology
Experimentaldesign
Conclusions
Bibliography
Questions
Questions
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IntroductionFuzzy programmingModelling approachPreprocessingMethodologyExperimental designConclusionsQuestions