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Developing equilibrium optimization methods for hub location problems

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Abstract

This paper develops three new equilibrium optimization models for \(p\)-hub center problem, in which the travel times are characterized by fuzzy random variables. The proposed equilibrium optimization methods are to find the locations of hub facilities and demand nodes so as to maximize equilibrium service levels of uncertain travel times. Under mild assumptions, we first handle equilibrium service levels and reduce them to their equivalent probability constraints. According to structural characteristics of equivalent stochastic programming models, we design a new parametric decomposition-based hybrid tabu search (PD-HTS) algorithm that incorporates parametric decomposition (PD), sample average approximation and tabu search algorithm. To demonstrate the effectiveness of designed solution method, we conduct some numerical experiments by using Australian Post data set and randomly generated data set. The comparison study shows that the PD-HTS algorithm exhibits better performance than the parametric decomposition-based hybrid genetic algorithm.

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Acknowledgments

The authors wish to thank Editors and anonymous reviewers, whose valuable comments led to an improved version of the paper. This work was supported by the National Natural Science Foundation of China (No. 61374184), and the Training Foundation of Hebei Province Talent Engineering.

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Authors and Affiliations

  1. Risk Management and Financial Engineering Lab, College of Mathematics and Computer Science, Hebei University, Baoding, 071002, Hebei, China

    Kai Yang & Yankui Liu

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  1. Kai Yang
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  2. Yankui Liu
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Correspondence to Yankui Liu.

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Communicated by V. Loia.

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Yang, K., Liu, Y. Developing equilibrium optimization methods for hub location problems. Soft Comput 19, 2337–2353 (2015). https://doi.org/10.1007/s00500-014-1427-1

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