Phased Local Search for the Maximum Clique Problem

Abstract

This paper introduces Phased Local Search (PLS), a new stochastic reactive dynamic local search algorithm for the maximum clique problem. (PLS) interleaves sub-algorithms which alternate between sequences of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, where vertices of the current clique are swapped with vertices not contained in the current clique. The sub-algorithms differ in their vertex selection techniques in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree or randomly selecting within vertex penalties that are dynamically adjusted during the search. In addition, the perturbation mechanism used to overcome search stagnation differs between the sub-algorithms. (PLS) has no problem instance dependent parameters and achieves state-of-the-art performance for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances.