Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
BRT COE 2015
´Avila-L´opez-
Caballero
Introduction
Fuzzy
programming
Modelling
approach
Preprocessing
Methodology
Experime...
Upcoming SlideShare
Loading in …5
×

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

650 views

Published on

2015-02-05 by Paula Ávila

Get the video and more info here:
http://www.brt.cl/webinar-a-bi-objetive-multiperiod-fuzzy-scheduling-for-a-multimodal-urban-transport-system

Published in: Science
  • Be the first to comment

  • Be the first to like this

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

  1. 1. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions A bi-objetive multiperiod fuzzy scheduling for a multimodal urban transport system M.C. Paulina Alejandra ´Avila Torres Advisors: Fernando L´opez Irarragorri, Rafael Caballero Fern´andez Programa de Ingenier´ıa de Sistemas Facultad de Ingenier´ıa Mec´anica y El´ectrica Universidad Aut´onoma de Nuevo Le´on February 2015 ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 1 / 26
  2. 2. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Agenda 1 Introduction 2 Fuzzy programming 3 Modelling approach 4 Preprocessing 5 Methodology 6 Experimental design 7 Conclusions 8 Questions ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 2 / 26
  3. 3. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Introduction Figure : Transport planning process [3]. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 3 / 26
  4. 4. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Introduction Figure : Network transportation system. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 4 / 26
  5. 5. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Introduction Main characteristics of the problem 1 Minimal frequency determination depends of headways definition. 2 Split the scheduling horizon into smaller time periods. 3 There are more than one transportation mode with their own regulations. 4 Demand is unknown but follows certain patterns. 5 There are transfer nodes. 6 There are bunching nodes. 7 Variable and fixed cost. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 5 / 26
  6. 6. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Introduction Literature review Author Multiobjective Multiperiod Multimodal Multiactivity Uncertainty Chakroborty et al.[2003],79 x Yan et al.[2006],91 x x Ceder [2007],216 x Zhao & Zeng [2008],78 x Zhi-Chun et al.[2010],12 x Zhang et al.[2011],13 x x x Tilahun & Ong [2012],7 x x Hadas & Shnaider [2012],6 x Baskaran & Krishnaiah [2012],3 x Xiao Fu et al.[2014],3 x x Demeyer et al.[2014],0 x Szeto & Wu [2014],43 x P´erez et al. [2014],0 x x Proposal x x x x x Table : Previous work. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 6 / 26
  7. 7. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Introduction 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 system for timetable construction. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 7 / 26
  8. 8. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design 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. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 8 / 26
  9. 9. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Modelling approach Modelling departures (a) Typical (b) Proposal Figure : Differences of how to represent departures Departures as decision variables. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 9 / 26
  10. 10. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Modelling approach Interval and headway policies Figure : First departure. Figure : Consecutive departure. Figure : Last departure. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 10 / 26
  11. 11. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Modelling approach Synchronizations Synchronizations are modelled as decision variables. A huge amount of decision variables representing synchonizations. It is very important to reduce the total amount of synchronization variables. Figure : Types of synchronization nodes [2] ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 11 / 26
  12. 12. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Preprocessing Algorithm for selecting frequency method (Ceder)[3] ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 12 / 26
  13. 13. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Preprocessing Preprocessing synchronizations ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 13 / 26
  14. 14. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Preprocessing Fuzzy to crisp model: FreMinv i → (FreMinv i , FreMinv i , FreMinv i ) k-prefence method One fuzzy constraint → 2 crisp constraints. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 14 / 26
  15. 15. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Methodology Decision support methodology Phase Action I.- Inteligence Model II.- Design Optimization III.- Selection Interactive method Table : Decision making phases. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 15 / 26
  16. 16. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Methodology Phase II: S-Augmecon S-Augmecon is a new derivation of the method -constraint augmented. S-Augmecon allows to generate all efficient solutions of the multiobjective problem. Aceleration algorithms. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 16 / 26
  17. 17. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Experimental design We generated 32 instances, randomly. Characteristics Minimum Maximum Routes 8 20 Periods 2 12 Nodes 10 150 Density 2 12 Headways 5-10 5-20 Table : Characteristics of the instances. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 17 / 26
  18. 18. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Experimental design Experimental design: The objective is to investigate the impact of these factor in the instance complecity. Factorial design 23 Factors: Confidence level Demand level. Fuzziness of demand. Each factor has a low and high level. Every instance is executed for all factors combinations. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 18 / 26
  19. 19. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design 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. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 19 / 26
  20. 20. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Experimental design ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 20 / 26
  21. 21. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design 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-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 21 / 26
  22. 22. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Conclusions Conclusions: We propose a mathematical model for the frequency and timetable integrated problem. We consider demand uncertainty. We employed fuzzy programming. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 22 / 26
  23. 23. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Bibliography [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 mathematical integer programming problems European Journal of Operations Research, 234, 15-24, 2014 ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 23 / 26
  24. 24. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Bibliography [Eranki Anitha] Eranki, Anitha A model to create bus timetables to attain maximum synchronization considering waiting times at transfer stops. University of South Florida, 2004. [Ibarra-Rojas & R´ıos-Sol´ıs] Ibarra-Rojas, Omar J. & Rios-Solis, Yasmin A. Synchronization of bus timetable, 2011 [Ceder, Avishai] Ceder, Avishai Designing public transport network and routes, Cap´ıtulo 3, 2003 [Nezan Mahdavi-Amiri et al.] Nezan Mahdavi-Amiri, Seyed Hadi Nasseri, Alahbakhsh Yazdani Fuzzy Primal Simplex Algorithm for solving fuzzy linear programming problems 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-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 24 / 26
  25. 25. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Bibliography [Nguyen Van Hop] Nguyen Van Hop Solving fuzzy linear programming problems using superiority and inferiority methods Information Sciences 177 (2007) 1977-1991 [Paulina Avila et al.]Paulina Avila, Fernando L´opez, 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 programming problems Irian Journal of Operations Research Vol. 1, No. 2, 2009, pag. 68-84 [Luis Miguel Prado LLanes], Clasificaci´on multicriterio aplicada a la caracterizaci´on de la maduraci´on ´osea en ni˜nos y adolescentes con oclusi´on normal y edades entre 9 y 16 a˜nos Universidad Aut´onoma de Nuevo Le´on, 2009 [Molina et al.] Molina, Julian; Laguna, Manuel; Mart´ı, Rafael & Caballero, Rafael. SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization INFORMS Journal on Computing, 19(1), 91-100, 2007. ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 25 / 26
  26. 26. BRT COE 2015 ´Avila-L´opez- Caballero Introduction Fuzzy programming Modelling approach Preprocessing Methodology Experimental design Conclusions Bibliography Questions Questions ´Avila-L´opez-Caballero (PISIS-UANL-UMA) BRT COE 2015 February 2015 26 / 26

×