A heuristic approach for the max-min diversity problem based on max-clique

In this paper we discuss a heuristic approach for the solution to the max-min diversity problem. The approach relies on the equivalence between this problem and the classical max-clique: it solves different decision problems about the existence of cliques with a given size. The idea is rather simple but, according to the experiments and the comparison with the existing literature, appears as particularly promising and outperforms, both in quality and CPU time, the existing state of the art algorithms.

[1]  Patric R. J. Östergård,et al.  A fast algorithm for the maximum clique problem , 2002, Discret. Appl. Math..

[2]  E. Erkut The discrete p-dispersion problem , 1990 .

[3]  F. Glover,et al.  Analyzing and Modeling the Maximum Diversity Problem by Zero‐One Programming* , 1993 .

[4]  G DowneyRod,et al.  Fixed-Parameter Tractability and Completeness I , 1995 .

[5]  Micael Gallego,et al.  GRASP and path relinking for the max-min diversity problem , 2010, Comput. Oper. Res..

[6]  Abraham Duarte,et al.  Tabu search and GRASP for the maximum diversity problem , 2007, Eur. J. Oper. Res..

[7]  R. Chandrasekaran,et al.  Location on Tree Networks: P-Centre and n-Dispersion Problems , 1981, Math. Oper. Res..

[8]  Roberto Cordone,et al.  Tabu Search versus GRASP for the maximum diversity problem , 2008, 4OR.

[9]  Wayne J. Pullan,et al.  Simple ingredients leading to very efficient heuristics for the maximum clique problem , 2008, J. Heuristics.

[10]  Luiz Satoru Ochi,et al.  Experimental Comparison of Greedy Randomized Adaptive Search Procedures for the Maximum Diversity Problem , 2004, WEA.

[11]  Jay B. Ghosh,et al.  Computational aspects of the maximum diversity problem , 1996, Oper. Res. Lett..

[12]  Michael R. Fellows,et al.  FIXED-PARAMETER TRACTABILITY AND COMPLETENESS , 2022 .

[13]  Fabrizio Grandoni,et al.  Measure and conquer: a simple O(20.288n) independent set algorithm , 2006, SODA '06.

[14]  Gerhard J. Woeginger,et al.  Exact Algorithms for NP-Hard Problems: A Survey , 2001, Combinatorial Optimization.

[15]  Michael R. Fellows,et al.  Fixed Parameter Tractability and Completeness , 1992, Complexity Theory: Current Research.

[16]  Burak Eksioglu,et al.  Lagrangian solution of maximum dispersion problems , 2000 .

[17]  S. S. Ravi,et al.  Facility Dispersion Problems: Heuristics and Special Cases (Extended Abstract) , 1991, WADS.

[18]  F. Glover,et al.  Heuristic algorithms for the maximum diversity problem , 1998 .

[19]  Rex K. Kincaid Good solutions to discrete noxious location problems via metaheuristics , 1992, Ann. Oper. Res..