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On Evolutionary Algorithms for Large Cliques in Random Graphs

Mohammad M. Javidi, Saeed Mehrabi


The maximum clique problem (MCP) is an old NP-complete problem which has been frequently used for delivering the NP-completeness of many other problems with respect to computational complexity literature. In this paper, we give a heuristic based genetic algorithm for solving this problem. By incorporating a heuristic into the crossover operator, we speed up the convergence rate of our algorithm - GACP (genetic algorithm for clique problem). GACP has been tested on a variety of challenging benchmarks including DIMACS instances and compared with two recently efficient algorithms. Experimental results show that GACP not only competes consistently with these algorithms but also performed well at solving the maximum clique problem.


Algorithmic Graph Theory, Combinatorial Optimization, Maximum Clique Problem.

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