A Scatter Search algorithm for the Maximum Clique Problem

The objective of tile Maximum Clique Problem (MCP) is to find the largest complete subgraph in a given graph. The problem is known as NP-hard and we have developed a heuristic algorithm based on a Scatter Search (SS) framework to find a lower bound for this maximization problem. The proposed algorithm was developed with two search features: a guidance search and a local search feature. For the first feature a Scatter Search algorithm was chosen with the purpose of extensively exploring regions with strategically combined solutions. The new solutions obtained in the combination phase axe thereafter improved by a neighborhood search procedure based on tabu search for implementing the second feature. The computational results obtained with DIMACS clique benchmark instances show that the proposed algorithm finds solutions comparable to the ones provided by some of the most competitive algorithms for the MCP.