webinar: a bi-objective multiperiod fuzzy scheduling for a multimodal urban transport system

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


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

Avila-Lopez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 2 / 26

BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Introduction

Contexto

Figure : Transport planning process [3].


BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Introduction

Descripcion del problema

Figure : Network transportation system.


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Modelling approach

Interval and headway policies

Figure : First departure.

Figure : Consecutive departure.

Figure : Last departure.


BRT COE 2015


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]


BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Preprocessing

Constraints

Algorithm for selecting frequency method (Ceder)[3]


BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Preprocessing

presynch

Preprocessing synchronizations


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

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.


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Experimental design


BRT COE 2015


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.


BRT COE 2015


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.


BRT COE 2015


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


BRT COE 2015


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


BRT COE 2015


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


Introduction

Fuzzyprogramming

Modellingapproach

Preprocessing

Methodology

Experimentaldesign

Conclusions

Bibliography

Questions

Questions


IntroductionFuzzy programmingModelling approachPreprocessingMethodologyExperimental designConclusionsQuestions

webinar: a bi-objective multiperiod fuzzy scheduling for a multimodal urban transport system

Science

uma brt coe

xproposal x x x x xtable

caballero pisisuanl

fernando lopez irarragorri

x xtilahun ong

transport process

transport planning process

scheduling horizon