An effective local search for the maximum clique problem

In this paper, we propose an effective local search algorithm based on variable depth search (VDS) for the MCP. The VDS has been first successfully applied by Lin and Kernighan to the traveling salesman problem [5] and the graph partitioning problem [4]. Their algorithms are often called k-opt local search. The basic concept of the k-opt local search based on VDS is to search a portion of large (k-opt) neighborhood while keeping a reasonable amount of computation time. Recently, some local search algorithms based on VDS have been proposed for the hard problems, e.g., the generalized assignment problem [8] and the binary quadratic programming problem [7]. These are known to be one of the most effective local search algorithms for each of the problems.