Developing equilibrium optimization methods for hub location problems

This paper develops three new equilibrium optimization models for $$p$$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.

[1]  Dervis Karaboga,et al.  Training recurrent neural networks by using parallel tabu search algorithm based on crossover operation , 2004, Eng. Appl. Artif. Intell..

[2]  James F. Campbell,et al.  Integer programming formulations of discrete hub location problems , 1994 .

[3]  Kai Yang,et al.  Solving fuzzy p-hub center problem by genetic algorithm incorporating local search , 2013, Appl. Soft Comput..

[4]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[5]  Timothy J. Lowe,et al.  The p-hub center allocation problem , 2007, Eur. J. Oper. Res..

[6]  Vladimir Marianov,et al.  Location models for airline hubs behaving as M/D/c queues , 2003, Comput. Oper. Res..

[7]  Bahar Yetis Kara,et al.  On the single-assignment p-hub center problem , 2000, Eur. J. Oper. Res..

[8]  Yian-Kui Liu,et al.  Fuzzy Random Variables: A Scalar Expected Value Operator , 2003, Fuzzy Optim. Decis. Mak..

[9]  Barrett W. Thomas,et al.  The stochastic p-hub center problem with service-level constraints , 2009, Comput. Oper. Res..

[10]  Mitsuo Gen,et al.  Genetic Algorithms , 1999, Wiley Encyclopedia of Computer Science and Engineering.

[11]  Shengyong Chen,et al.  Efficient multi-objective tabu search for emergency equipment maintenance scheduling in disaster rescue , 2013, Optim. Lett..

[12]  Huifu Xu,et al.  A note on uniform exponential convergence of sample average approximation of random functions , 2012 .

[13]  Jinwu Gao,et al.  The Independence of Fuzzy Variables with Applications to Fuzzy Random Optimization , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[15]  Xin Zhang,et al.  Stochastic p-Hub Center Problem with Discrete Time Distributions , 2011, ISNN.

[16]  Morton E. O'Kelly,et al.  The Location of Interacting Hub Facilities , 1986, Transp. Sci..

[17]  Yian-Kui Liu,et al.  The Approximation Method for Two-Stage Fuzzy Random Programming With Recourse , 2007, IEEE Transactions on Fuzzy Systems.

[18]  Sibel A. Alumur,et al.  Network hub location problems: The state of the art , 2008, Eur. J. Oper. Res..

[19]  Gerhard J. Woeginger,et al.  Uncapacitated single and multiple allocation p-hub center problems , 2009, Comput. Oper. Res..

[20]  Asoke Kumar Bhunia,et al.  Genetic algorithm based multi-objective reliability optimization in interval environment , 2012, Comput. Ind. Eng..

[21]  Yian-Kui Liu,et al.  Fuzzy random programming with equilibrium chance constraints , 2005, Inf. Sci..

[22]  Kai Yang,et al.  An improved hybrid particle swarm optimization algorithm for fuzzy p-hub center problem , 2013, Comput. Ind. Eng..

[23]  Claude-Nicolas Fiechter,et al.  A Parallel Tabu Search Algorithm for Large Traveling Salesman Problems , 1994, Discret. Appl. Math..

[24]  Ahmad Makui,et al.  A fuzzy programming approach for dynamic virtual hub location problem , 2012 .

[25]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[26]  Jean-Charles Billaut,et al.  A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem , 2008, Eur. J. Oper. Res..

[27]  Gilbert Laporte,et al.  Stochastic uncapacitated hub location , 2011, Eur. J. Oper. Res..

[28]  Yian-Kui Liu,et al.  Measurability criteria for fuzzy random vectors , 2006, Fuzzy Optim. Decis. Mak..

[29]  Chien-Chang Chou,et al.  An integrated quantitative and qualitative FMCDM model for location choices , 2010, Soft Comput..

[30]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

[31]  Yuhan Liu,et al.  Uncertain random variables: a mixture of uncertainty and randomness , 2013, Soft Comput..

[32]  Yujun Zheng,et al.  Emergency transportation planning in disaster relief supply chain management: a cooperative fuzzy optimization approach , 2013, Soft Comput..

[33]  Andreas T. Ernst,et al.  Efficient algorithms for the uncapac-itated single allocation p-hub median problem , 1996 .

[34]  Ebru Angün,et al.  A risk-averse approach to simulation optimization with multiple responses , 2011, Simul. Model. Pract. Theory.

[35]  M. O'Kelly,et al.  A quadratic integer program for the location of interacting hub facilities , 1987 .

[36]  Ta-Hui Yang,et al.  Stochastic air freight hub location and flight routes planning , 2009 .

[37]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[38]  M. Laguna,et al.  SOLVING THE MULTIPLE-MACHINE WEIGHTED FLOW TIME PROBLEM USING TABU SEARCH , 1993 .

[39]  Marcus Randall,et al.  Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution , 2013 .

[40]  Sibel A. Alumur,et al.  Hub location under uncertainty , 2012 .

[41]  Martin Branda,et al.  Sample approximation technique for mixed-integer stochastic programming problems with several chance constraints , 2012, Oper. Res. Lett..

[42]  Masao Fukushima,et al.  Tabu search for attribute reduction in rough set theory , 2008, Soft Comput..