An Evolutionary Approach to the Maximum Edge Weight Clique Problem

Abstract

Background: This work addresses the maximum edge weight clique problem (MEWC), an important generalization of the well-known maximum clique problem. Methods: The MEWC problem can be used to model applications in many fields including broadband network design, computer vision, pattern recognition, and robotics. We propose a random key genetic algorithm to find good quality solutions for this problem. Computational experiments are reported for a set of benchmark problem instances derived from the DIMACS maximum clique instances. Results: The results obtained show that our algorithm is both effective and efficient, as for most of the problem instances tested, we were able to match the best-known solutions with very small computational time requirements. Keywords: Genetic algorithms, network optimization, maximum clique, weight clique, genetic representation, genes.