A maximum entropy optimization model for origin-destination trip matrix estimation with fuzzy entropic parameters

Héctor López-Ospina; Cristián E. Cortés; Juan Eduardo Pérez; Romario Peña; Juan Carlos Figueroa-García; Jorge Urrutia-Mosquera

doi:10.1080/23249935.2021.1913257

A maximum entropy optimization model for origin-destination trip matrix estimation with fuzzy entropic parameters

Héctor López-Ospina, Cristián E. Cortés, Juan Eduardo Pérez^*, Romario Peña, Juan Carlos Figueroa-García, Jorge Urrutia-Mosquera

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We formulate a bi-objective distribution model for urban trips constrained by origins and destinations while maximizing entropy. We develop a flexible and consistent approach in which the estimations of generated/attracted parameters are fuzzy with entropic membership functions. Based on a fuzzy-entropy approach, we measure the uncertainty associated with fuzzy variables. We solve the problem by means of compromise programming considering a weighted sum objective function. We compute and extend concepts such as accessibility, attractiveness, and generalized cost, typically obtained in transport economic analyzes. Considering that our formulation is convex, we solve the problem in one step only, maintaining the uniqueness of the the optimization problem solution. We present two numerical examples to illustrate the proposed methodology, analyzing the impact of the results based on strong mathematical and statistical arguments. Finally, we show that our approach has better prediction capabilities than traditional fuzzy models regarding aggregated indicators and structural distribution patterns.

Original language	English
Pages (from-to)	963-1000
Number of pages	38
Journal	Transportmetrica A: Transport Science
Volume	18
Issue number	3
DOIs	https://doi.org/10.1080/23249935.2021.1913257
State	Published - 2021

Bibliographical note

Funding Information:
The authors are grateful for the financial support provided under Projects Fondo Nacional de Desarrollo Científico y Tecnológico ANID/FONDECYT/Regular 1191200, ANID/FONDECYT 11160320, Complex Engineering Systems Institute ANID PIA/APOYO AFB180003 and project 4.148 of Fundación para la Promoción de la Investigación y la Tecnología. Banco de la República. Colombia. The authors are grateful for the financial support provided under Projects ANID/FONDECYT/Regular 1191200, CONICYT/FONDECYT 11160320, Instituto Sistemas Complejos de Ingeniería (ANID PIA/APOYO AFB180003) and project 4.148 of Fundación para la Promoción de la Investigación y la Tecnología. Banco de la República. Colombia.

Funding Information:
The authors are grateful for the financial support provided under Projects ANID/FONDECYT/Regular 1191200, CONICYT/FONDECYT 11160320, Instituto Sistemas Complejos de Ingeniería (ANID PIA/APOYO AFB180003) and project 4.148 of Fundación para la Promoción de la Investigación y la Tecnología. Banco de la República. Colombia.

Publisher Copyright:
© 2021 Hong Kong Society for Transportation Studies Limited.

Keywords

Entropy optimization
Fuzzy entropy
Fuzzy sets
Origin-destination trip matrix
Transport distribution

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10.1080/23249935.2021.1913257

Cite this

@article{0f93a75354654f55bd71d297be101668,

title = "A maximum entropy optimization model for origin-destination trip matrix estimation with fuzzy entropic parameters",

abstract = "We formulate a bi-objective distribution model for urban trips constrained by origins and destinations while maximizing entropy. We develop a flexible and consistent approach in which the estimations of generated/attracted parameters are fuzzy with entropic membership functions. Based on a fuzzy-entropy approach, we measure the uncertainty associated with fuzzy variables. We solve the problem by means of compromise programming considering a weighted sum objective function. We compute and extend concepts such as accessibility, attractiveness, and generalized cost, typically obtained in transport economic analyzes. Considering that our formulation is convex, we solve the problem in one step only, maintaining the uniqueness of the the optimization problem solution. We present two numerical examples to illustrate the proposed methodology, analyzing the impact of the results based on strong mathematical and statistical arguments. Finally, we show that our approach has better prediction capabilities than traditional fuzzy models regarding aggregated indicators and structural distribution patterns.",

keywords = "Entropy optimization, Fuzzy entropy, Fuzzy sets, Origin-destination trip matrix, Transport distribution",

author = "H{\'e}ctor L{\'o}pez-Ospina and Cort{\'e}s, {Cristi{\'a}n E.} and P{\'e}rez, {Juan Eduardo} and Romario Pe{\~n}a and Figueroa-Garc{\'i}a, {Juan Carlos} and Jorge Urrutia-Mosquera",

note = "Funding Information: The authors are grateful for the financial support provided under Projects Fondo Nacional de Desarrollo Cient{\'i}fico y Tecnol{\'o}gico ANID/FONDECYT/Regular 1191200, ANID/FONDECYT 11160320, Complex Engineering Systems Institute ANID PIA/APOYO AFB180003 and project 4.148 of Fundaci{\'o}n para la Promoci{\'o}n de la Investigaci{\'o}n y la Tecnolog{\'i}a. Banco de la Rep{\'u}blica. Colombia. The authors are grateful for the financial support provided under Projects ANID/FONDECYT/Regular 1191200, CONICYT/FONDECYT 11160320, Instituto Sistemas Complejos de Ingenier{\'i}a (ANID PIA/APOYO AFB180003) and project 4.148 of Fundaci{\'o}n para la Promoci{\'o}n de la Investigaci{\'o}n y la Tecnolog{\'i}a. Banco de la Rep{\'u}blica. Colombia. Funding Information: The authors are grateful for the financial support provided under Projects ANID/FONDECYT/Regular 1191200, CONICYT/FONDECYT 11160320, Instituto Sistemas Complejos de Ingenier{\'i}a (ANID PIA/APOYO AFB180003) and project 4.148 of Fundaci{\'o}n para la Promoci{\'o}n de la Investigaci{\'o}n y la Tecnolog{\'i}a. Banco de la Rep{\'u}blica. Colombia. Publisher Copyright: {\textcopyright} 2021 Hong Kong Society for Transportation Studies Limited.",

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doi = "10.1080/23249935.2021.1913257",

language = "English",

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AU - López-Ospina, Héctor

AU - Cortés, Cristián E.

AU - Pérez, Juan Eduardo

AU - Peña, Romario

AU - Figueroa-García, Juan Carlos

AU - Urrutia-Mosquera, Jorge

N1 - Funding Information: The authors are grateful for the financial support provided under Projects Fondo Nacional de Desarrollo Científico y Tecnológico ANID/FONDECYT/Regular 1191200, ANID/FONDECYT 11160320, Complex Engineering Systems Institute ANID PIA/APOYO AFB180003 and project 4.148 of Fundación para la Promoción de la Investigación y la Tecnología. Banco de la República. Colombia. The authors are grateful for the financial support provided under Projects ANID/FONDECYT/Regular 1191200, CONICYT/FONDECYT 11160320, Instituto Sistemas Complejos de Ingeniería (ANID PIA/APOYO AFB180003) and project 4.148 of Fundación para la Promoción de la Investigación y la Tecnología. Banco de la República. Colombia. Funding Information: The authors are grateful for the financial support provided under Projects ANID/FONDECYT/Regular 1191200, CONICYT/FONDECYT 11160320, Instituto Sistemas Complejos de Ingeniería (ANID PIA/APOYO AFB180003) and project 4.148 of Fundación para la Promoción de la Investigación y la Tecnología. Banco de la República. Colombia. Publisher Copyright: © 2021 Hong Kong Society for Transportation Studies Limited.

PY - 2021

Y1 - 2021

N2 - We formulate a bi-objective distribution model for urban trips constrained by origins and destinations while maximizing entropy. We develop a flexible and consistent approach in which the estimations of generated/attracted parameters are fuzzy with entropic membership functions. Based on a fuzzy-entropy approach, we measure the uncertainty associated with fuzzy variables. We solve the problem by means of compromise programming considering a weighted sum objective function. We compute and extend concepts such as accessibility, attractiveness, and generalized cost, typically obtained in transport economic analyzes. Considering that our formulation is convex, we solve the problem in one step only, maintaining the uniqueness of the the optimization problem solution. We present two numerical examples to illustrate the proposed methodology, analyzing the impact of the results based on strong mathematical and statistical arguments. Finally, we show that our approach has better prediction capabilities than traditional fuzzy models regarding aggregated indicators and structural distribution patterns.

AB - We formulate a bi-objective distribution model for urban trips constrained by origins and destinations while maximizing entropy. We develop a flexible and consistent approach in which the estimations of generated/attracted parameters are fuzzy with entropic membership functions. Based on a fuzzy-entropy approach, we measure the uncertainty associated with fuzzy variables. We solve the problem by means of compromise programming considering a weighted sum objective function. We compute and extend concepts such as accessibility, attractiveness, and generalized cost, typically obtained in transport economic analyzes. Considering that our formulation is convex, we solve the problem in one step only, maintaining the uniqueness of the the optimization problem solution. We present two numerical examples to illustrate the proposed methodology, analyzing the impact of the results based on strong mathematical and statistical arguments. Finally, we show that our approach has better prediction capabilities than traditional fuzzy models regarding aggregated indicators and structural distribution patterns.

KW - Entropy optimization

KW - Fuzzy entropy

KW - Fuzzy sets

KW - Origin-destination trip matrix

KW - Transport distribution

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U2 - 10.1080/23249935.2021.1913257

DO - 10.1080/23249935.2021.1913257

M3 - Article

AN - SCOPUS:85105189568

SN - 2324-9935

VL - 18

SP - 963

EP - 1000

JO - Transportmetrica A: Transport Science

JF - Transportmetrica A: Transport Science

IS - 3

ER -

A maximum entropy optimization model for origin-destination trip matrix estimation with fuzzy entropic parameters

Abstract

Bibliographical note

Keywords

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