The Island Confinement Method for Reducing Search Space in Local Search Methods.pdfVIP

The Island Confinement Method for Reducing Search Space in Local Search Methods∗ H. Fang † Y. Kilani ‡ J.H.M. Lee § P.J. Stuckey ¶ July 14, 2006 Abstract Typically local search methods for solving constraint satisfaction problems such as GSAT, WalkSAT, DLM, and ESG treat the problem as an optimization problem. Each constraint contributes part of a penalty function in assessing trial valuations. Local search examines the neighbours of the current valuation, using the penalty function to determine a “better” neighbour valuation to move to, until finally a solution which sat- isfies all constraints is found. In this paper we investigate using some of the constraints as “hard” constraints, that are always satisfied by every trial valuation visited, rather than as part of a penalty function. In this way these constraints reduce the possible neighbours in each move and also the overall search space. The treating of some con- straints as hard requires that the space of valuations that are satisfied is “connected” in order to guarantee that a solution can be found from any starting position within the region; thus the concept of islands and the name “island confinement method” arise. Treating some constraints as hard provides new difficulties for the search mechanism since the search space becomes more jagged, and there are more deep local minima. A new escape strategy is needed. To demonstrate the feasibility and generality of our approach, we show how the island confinement method can be incorporated in and significantly improve the search performance of two successful local search procedures, DLM and ESG, o