確率的制約充足アルゴリズムにおける局所最適構造

抄録

Many stochastic search algorithms have recently been developed to make more remarkable progress than systematic search algorithms because stochastic algorithms sometimes solve large-scale constraint satisfaction problems in a practical time. However, such stochastic algorithms have the drawback of getting stuck in local optima which are not acceptable as final solutions. We analyze an iterative improvement algorithm from the viewpoint of constraint structures causing local optima. Using the graph-coloring problem with three colors, an archetype problem to evaluate constraint satisfaction algorithms, we study the local graph structures around which so many conflicts thrash. We propose a key constraint structure, an LM pair, which may induce a local optimum, and clarify the mechanism of how conflicting colors for an LM pair obstruct the stepwise refinement of hill-climbing. Experimental results show that LM pairs are strongly correlated with the search efficiency of the stochastic search algorithm.