Decomposition Based Search - A theoretical and experimental evaluation

In this paper we present and evaluate a search strategy called Decomposition Based Search (DBS) which is based on two steps: subproblem generation and subproblem solution. The generation of subproblems is done through value ranking and domain splitting. Subdomains are explored so as to generate, according to the heuristic chosen, promising subproblems first. We show that two well known search strategies, Limited Discrepancy Search (LDS) and Iterative Broadening (IB), can be seen as special cases of DBS. First we present a tuning of DBS that visits the same search nodes as IB, but avoids restarts. Then we compare both theoretically and computationally DBS and LDS using the same heuristic. We prove that DBS has a higher probability of being successful than LDS on a comparable number of nodes, under realistic assumptions. Experiments on a constraint satisfaction problem and an optimization problem show that DBS is indeed very effective if compared to LDS.