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
• Origin-destination trip matrix
• Transport distribution
• Fuzzy sets
• Fuzzy entropy

Acknowledgments

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.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

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.