Generation of Tree Decompositions by Iterated Local Search

Many instances of NP-hard problems can be solved efficiently if the treewidth of their corresponding graph is small. Finding the optimal tree decompositions is an NP-hard problem and different algorithms have been proposed in the literature for generation of tree decompositions of small width. In this paper we propose a novel iterated local search algorithm to find good upper bounds for treewidth of an undirected graph. We propose two heuristics, and their combination for generation of the solutions in the construction phase. The iterated local search algorithm further includes the mechanism for perturbation of solution, and the mechanism for accepting solutions for the next iteration. The proposed algorithm iteratively applies the heuristic for finding good elimination ordering, the acceptance criteria, and the perturbation of solution. We proposed and evaluated different perturbation mechanisms and acceptance criteria. The proposed algorithms are tested on DIMACS instances for vertex coloring, and they are compared with the existing approaches in literature. Our algorithms have a good time performance and for 17 instances improve the best existing upper bounds for the treewidth.