Solving the maximum clique problem by k-opt local search

Abstract

This paper presents a local search algorithm based on variable depth search, called the k-opt local search, for the maximum clique problem. The k-opt local search performs add and drop moves, each of which can be interpreted as 1-opt move, to search a k-opt neighborhood solution at each iteration until no better k-opt neighborhood solution can be found. To evaluate our k-opt local search algorithm, we repeatedly apply the local search for each of DIMACS benchmark graphs and compare with the state-of-the-art metaheuristics such as the genetic local search and the iterated local search reported previously. The computational results show that in spite of the absence of major metaheuristic components, the k-opt local search is capable of finding better (at least the same) solutions on average than those obtained by these metaheuristics for all the graphs.