Combinatorial Optimization Method Based on Hierarchical Structure in Solution Space

In this paper, we introduce a new concept of hierarchical structure into solution space of a combinatorial optimization problem, and develop a novel combinatorial optimization method based on the concept. The introduction of the above new hierarchical structure concept basin of attraction, which is a set binding solution by utilizing properties of local optimal solutions, enables us to construe solution space as not only set of solutions but also set of basins of attraction hierarchically. It is well known that the appropriate balance of two policies, intensification and diversification, is essential in the search of metaheuristics. The proposed method clarifies the search policy by relating the hierarchical structure in solution space with intensification and diversification. With regard to diversification, we incorporate a movement strategy that has longer term or more macroscopic viewpoint than before in the algorithm by utilizing the concept basin of attraction. The performance of the proposed combinatorial optimization method is inspected by numerical experiments using some typical benchmark problems of a traveling salesman problem, a knapsack problem, a flow-shop scheduling problem, and a quadratic assignment problem. (C) 2016 Wiley Periodicals, Inc.