Genetic algorithmic approach to find the maximum weight independent set of a graph

In this paper, Genetic Algorithm (GA) is used to find the Maximum Weight Independent Set (MWIS) of a graph. First, MWIS problem is formulated as a 0-1 integer programming optimization problem with linear objective function and a single quadratic constraint. Then GA is implemented with the help of this formulation. Since GA is a heuristic search method, exact solution is not reached in every run. Though the suboptimal solution obtained is very near to the exact one. Computational result comprising an average performance is also presented here.

[1]  Egon Balas,et al.  On the Maximum Weight Clique Problem , 1987, Math. Oper. Res..

[2]  Egon Balas,et al.  Finding a Maximum Clique in an Arbitrary Graph , 1986, SIAM J. Comput..

[3]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[4]  Shuji Tsukiyama,et al.  A New Algorithm for Generating All the Maximal Independent Sets , 1977, SIAM J. Comput..

[5]  Robert E. Tarjan,et al.  Finding a Maximum Independent Set , 1976, SIAM J. Comput..

[6]  Madhumangal Pal,et al.  Genetic algorithm to solve the p-centre and p-radius problem on a network , 2005, Int. J. Comput. Math..

[7]  D. E. Goldberg,et al.  Genetic Algorithm in Search , 1989 .

[8]  P. Pardalos,et al.  A global optimization approach for solving the maximum clique problem , 1990 .

[9]  Madhumangal Pal,et al.  An efficient pram algorithm for maximum-weight independent set on permutation graphs , 2005 .

[10]  Michel Gendreau,et al.  An Efficient Implicit Enumeration Algorithm for the Maximum Clique Problem , 1988 .

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[13]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[14]  Panos M. Pardalos,et al.  An algorithm for finding a maximum weighted independent set in an arbitrary graph , 1991, Int. J. Comput. Math..