Analysis of an Iterated Local Search Algorithm for Vertex Coloring

Hybridizations of evolutionary algorithms and local search are among the best-performing algorithms for vertex coloring. However, the theoretical knowledge about these algorithms is very limited and it is agreed that a solid theoretical foundation is needed. We consider an iterated local search algorithm that iteratively tries to improve a coloring by applying mutation followed by local search. We investigate the capabilities and the limitations of this approach using bounds on the expected number of iterations until an optimal or near-optimal coloring is found. This is done for two different mutation operators and for different graph classes: bipartite graphs, sparse random graphs, and planar graphs.

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