Quantum binary particle swarm optimization-based algorithm for solving a class of bi-level competitive facility location problems

This paper deals with a special class of competitive facility location problems, in which two non-cooperative firms compete to capture the most of a given market, in order to maximize their profit. This paper intends to present a simple and effective nested strategy based on the quantum binary particle swarm optimization (QBPSO) method for solving the bi-level mathematical model of the problem. In solution approach, an improvement procedure is embedded into QBPSO to increase the convergence speed and generate more accurate solutions. Taguchi's method is employed to systematically determine the optimal values of QBPSO parameters. Finally, computational results on large-scale instances with up to 300 locations and 350 clients (more than 100,000 variables and 300,000 constraints at each level) confirmed the method efficiency in terms of solution quality and time.

[1]  Yury Kochetov,et al.  Heuristic and Exact Methods for the Discrete (r |p)-Centroid Problem , 2010, EvoCOP.

[2]  Gilbert Laporte,et al.  Competitive Location Models: A Framework and Bibliography , 1993, Transp. Sci..

[3]  Ellips Masehian,et al.  Efficient and Robust Parameter Tuning for Heuristic Algorithms , 2013 .

[4]  Shuyuan Yang,et al.  A quantum particle swarm optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[5]  Franz Pichler,et al.  Computer Aided Systems Theory – EUROCAST 2011 , 2011, Lecture Notes in Computer Science.

[6]  Gilbert Laporte,et al.  Competitive spatial models , 1989 .

[7]  I. K. Altinel,et al.  Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution , 2011, Eur. J. Oper. Res..

[8]  Qiuwang Wang,et al.  Optimization of heat exchangers with vortex-generator fin by Taguchi method , 2010 .

[9]  Gilbert Laporte,et al.  Sequential location problems , 1997 .

[10]  Artur Alves Pessoa,et al.  A branch-and-cut algorithm for the discrete (r∣p)-centroid problem , 2013, Eur. J. Oper. Res..

[11]  YURY KOCHETOV Sobolev,et al.  BILEVEL FACILITY LOCATION : DISCRETE MODELS AND COMPUTATIONAL METHODS , 2010 .

[12]  Tong Zhen,et al.  A Particle Swarm Optimization Algorithm for the Open Vehicle Routing Problem , 2009, 2009 International Conference on Environmental Science and Information Application Technology.

[13]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[14]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[15]  V. Beresnev,et al.  A mathematical model of market competition , 2010 .

[16]  V. Beresnev,et al.  Approximate algorithms for the competitive facility location problem , 2011 .

[17]  S. Hakimi.  On locating new facilities in a competitive environment , 1983 .

[18]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[19]  Zahid A. Khan,et al.  Application of the Taguchi method for optimization of parameters to maximize text message entering performance of mobile phone users , 2009 .

[20]  Ahmad Makui,et al.  A robust model for a leader–follower competitive facility location problem in a discrete space , 2013 .

[21]  V. Beresnev.  Upper bounds for objective functions of discrete competitive facility location problems , 2009 .

[22]  I. K. Altinel,et al.  A leader-follower game in competitive facility location , 2012, Comput. Oper. Res..

[23]  Dominik Kress,et al.  Sequential competitive location on networks , 2013, Eur. J. Oper. Res..

[24]  Jie-min Zhou,et al.  Optimization of parameters for an aluminum melting furnace using the Taguchi approach , 2012 .

[25]  S. A. MirHassani,et al.  Lagrangean relaxation-based algorithm for bi-level problems , 2015, Optim. Methods Softw..

[26]  Vladimir L. Beresnev,et al.  Branch-and-bound algorithm for a competitive facility location problem , 2013, Comput. Oper. Res..

[27]  Roberto Moreno-Díaz,et al.  Computer Aided Systems Theory EUROCAST 2005: 10th International Conference on Computer Aided Systems Theory, Las Palmas de Gran Canaria, Spain, February ... Papers (Lecture Notes in Computer Science) , 2005 .

[28]  Robert G. Jeroslow,et al.  The polynomial hierarchy and a simple model for competitive analysis , 1985, Math. Program..

[29]  Lynda L. McGhie,et al.  World Wide Web , 2011, Encyclopedia of Information Assurance.

[30]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..