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Linearly-Constrained Entropy Maximization Problem with Quadratic Cost and Its Applications to Transportation Planning Problems

Author

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  • S. C. Fang

    (North Carolina State University, Operations Research Program and Industrial Engineering Department, Raleigh, North Carolina 27695)

  • H.-S. J. Tsao

    (University of California, Institute of Transportation Studies, Berkeley, California 94720)

Abstract

Many transportation problems can be formulated as a linearly-constrained convex programming problem whose objective function consists of entropy functions and other cost-related terms. In this paper, we propose an unconstrained convex programming dual approach to solving these problems. In particular, we focus on a class of linearly-constrained entropy maximization problem with quadratic cost, study its Lagrangian dual, and provide a globally convergent algorithm with a quadratic rate of convergence. The theory and algorithm can be readily applied to the trip distribution problem with quadratic cost and many other entropy-based formulations, including the conventional trip distribution problem with linear cost, the entropy-based modal split model, and the decomposed problems of the combined problem of trip distribution and assignment. The efficiency and the robustness of this approach are confirmed by our computational experience.

Suggested Citation

  • S. C. Fang & H.-S. J. Tsao, 1995. "Linearly-Constrained Entropy Maximization Problem with Quadratic Cost and Its Applications to Transportation Planning Problems," Transportation Science, INFORMS, vol. 29(4), pages 353-365, November.
    • Handle: RePEc:inm:ortrsc:v:29:y:1995:i:4:p:353-365
    DOI: 10.1287/trsc.29.4.353
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    Cited by:

    1. da Silva, Marcelino Aurélio Vieira & de Almeida D’Agosto, Marcio, 2013. "A model to estimate the origin–destination matrix for soybean exportation in Brazil," Journal of Transport Geography, Elsevier, vol. 26(C), pages 97-107.
    2. Tsao, H. S. Jacob & Zhang, Lan & Lin, Lin & Batni, Deepa, 2004. "Evaluation of Bus and Truck Automation Operations Concepts," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2f41h8fv, Institute of Transportation Studies, UC Berkeley.
    3. de Grange, Louis & Troncoso, Rodrigo & Ibeas, Angel & González, Felipe, 2009. "Gravity model estimation with proxy variables and the impact of endogeneity on transportation planning," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(2), pages 105-116, February.
    4. Louis Grange & Angel Ibeas & Felipe González, 2011. "A Hierarchical Gravity Model with Spatial Correlation: Mathematical Formulation and Parameter Estimation," Networks and Spatial Economics, Springer, vol. 11(3), pages 439-463, September.
    5. He, Mingyi & Bogomolov, Yuri & Khulbe, Devashish & Sobolevsky, Stanislav, 2023. "Distance deterrence comparison in urban commute among different socioeconomic groups: A normalized linear piece-wise gravity model," Journal of Transport Geography, Elsevier, vol. 113(C).
    6. Louis Grange & Felipe González & Juan Muñoz & Sebastián Raveau, 2014. "An Improved Stirling Approximation for Trip Distribution Models," Networks and Spatial Economics, Springer, vol. 14(3), pages 531-548, December.

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