Annealed replication: a new heuristic for the maximum clique problem

In this paper, a new heuristic for approximating the maximum clique problem is proposed, based on a detailed analysis of a class of continuous optimization models which yield a complete solution to this NP-hard combinatorial problem. The idea is to alter a regularization parameter iteratively in such a way that an iterative procedure with the updated parameter value would avoid unwanted, ine cient local solutions, i.e., maximal cliques which contain less than the maximum possible number of vertices. The local search procedure is performed with the help of the replicator dynamics, and the regularization parameter is chosen deliberately as to render dynamical instability of the (formerly) stable solutions which we want to discard in order to get an improvement. In this respect, the proposed procedure di ers from usual simulated annealing approaches which mostly use a \black-box" cooling schedule. To demonstrate the validity of this approach, we report on the performance applied to selected DIMACS benchmark graphs.