Decomposition Based Search - A theoretical and experimental evaluation

TL;DR

This paper introduces Decomposition Based Search (DBS), a new search strategy that combines subproblem generation and solution, showing theoretical advantages over LDS and effective results in experiments.

Contribution

The paper presents DBS, a novel search strategy unifying LDS and IB, with theoretical analysis and experimental validation demonstrating its effectiveness.

Findings

DBS can emulate IB's search pattern without restarts.

DBS has higher success probability than LDS under certain conditions.

Experimental results show DBS outperforms LDS in constraint satisfaction and optimization problems.

Abstract

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.