Applying two efficient hybrid heuristics for hub location problem with fully interconnected backbone and access networks

Abstract This paper considers the design of two-layered networks with fully interconnected backbone and access networks. The problem, a specific application of hub location to network design, is known as fully interconnected network design problem (FINDP). A novel mathematical programming formulation advantageous over an earlier formulation is presented to model the problem. Two hybrid heuristics are proposed to solve the problem, namely SAVNS and TSVNS which incorporate a variable neighborhood search (VNS) algorithm into the framework of simulated annealing (SA) and tabu search (TS). The proposed algorithms are able to easily obtain the optimal solutions for 24 small instances existing in the literature in addition to efficiently solve new generated medium and large instances. Results indicate that the proposed algorithms generate high quality solutions in a quite short CPU time.

[1]  T. Aykin.  On “a quadratic integer program for the location of interacting hub facilities” , 1990 .

[2]  D. M. Deighton,et al.  Computers in Operations Research , 1977, Aust. Comput. J..

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

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

[5]  Thomas R. Stidsen,et al.  The generalized fixed-charge network design problem , 2007, Comput. Oper. Res..

[6]  Nenad Mladenovic,et al.  A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem , 2009, Eur. J. Oper. Res..

[7]  Sue Abdinnour-Helm,et al.  Using simulated annealing to solve the p‐Hub Median Problem , 2001 .

[8]  Sancho Salcedo-Sanz,et al.  A Parallel evolutionary algorithm for the hub location problem with fully interconnected backbone and access networks , 2009, 2009 IEEE Congress on Evolutionary Computation.

[9]  Sue Abdinnour-Helm,et al.  A hybrid heuristic for the uncapacitated hub location problem , 1998, Eur. J. Oper. Res..

[10]  D. Skorin-Kapov,et al.  Tight linear programming relaxations of uncapacitated p-hub median problems , 1996 .

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

[12]  Jesper Larsen,et al.  A hub location problem with fully interconnected backbone and access networks , 2007, Comput. Oper. Res..

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

[14]  Haluk Topcuoglu,et al.  Solving the uncapacitated hub location problem using genetic algorithms , 2005, Comput. Oper. Res..

[15]  J. G. Klincewicz,et al.  Heuristics for the p-hub location problem , 1991 .

[16]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[17]  Teodor Gabriel Crainic,et al.  Bundle-based relaxation methods for multicommodity capacitated fixed charge network design , 2001, Discret. Appl. Math..

[18]  Alysson M. Costa.  A survey on benders decomposition applied to fixed-charge network design problems , 2005, Comput. Oper. Res..

[19]  Gilbert Laporte,et al.  Generalized network design problems , 2003, Eur. J. Oper. Res..

[20]  J. G. Klincewicz,et al.  HUB LOCATION IN BACKBONE/TRIBUTARY NETWORK DESIGN: A REVIEW , 1998 .

[21]  Munirpallam A. Venkataramanan,et al.  Solution approaches to hub location problems , 1998, Ann. Oper. Res..

[22]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

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

[24]  Claudio B. Cunha,et al.  New simple and efficient heuristics for the uncapacitated single allocation hub location problem , 2009, Comput. Oper. Res..

[25]  J. G. Klincewicz,et al.  Avoiding local optima in thep-hub location problem using tabu search and GRASP , 1993, Ann. Oper. Res..