Combinatorial Optimization Method Based on Hierarchical Structure in Solution Space

In this paper, we introduce a new concept into solution space of combinatorial optimization problems, and propose an optimization method algorithm based on hierarchical structure in solution space. The introduced new concept: "basin of attraction" is a set binding solutions by utilizing properties of local optimal solution. We become able to construe solution space as not only set of solutions but also set of basins of attraction hierarchically. The proposed method clarifies the search policy by relating hierarchical structure in solution space with intensification and diversification. We inspect performance of the proposed method by numerical experiment using typical benchmark problems.