Two grouping-based metaheuristics for clique partitioning problem

Abstract

Given a connected, undirected graph G = (V,E), where V is the set of vertices and E is the set of edges, the clique partitioning problem (CPP) seeks on this graph a partition of set V into minimum number of subsets such that each subset is a clique. The CPP is an $\mathcal {NP}$-Hard problem and finds numerous practical applications in diverse domains like digital design synthesis, clustering etc. Despite its computational complexity and its numerous applications, only problem-specific heuristics have been developed so far for this problem in the literature. In this paper, two metaheuristic techniques – a steady-state grouping genetic algorithm and an artificial bee colony algorithm – are proposed for the CPP. Both the proposed approaches are designed in such a way that the grouping structure of the CPP is exploited effectively while generating new solutions. Since artificial bee colony algorithm is comparatively a new metaheuristic technique, special attention has been given to the design of this algorithm for the CPP and we came out with a new neighboring solution generation method utilizing solution components from multiple solutions. The proposed approaches have been tested on publicly available 37 DIMACS graph instances. Computational results show the effectiveness of the proposed approaches.