Adaptive Combinatorial Optimization Method Based on Hierarchical Structure in Solution Space and Long-term Search

Abstract

Multipoint combinatorial optimization methods based on the hierarchical structure of the solution space are known to fail to achieve an appropriate balance between diversification and intensification due to the degeneracy of the search point set, resulting in degraded long-term search performance. This paper proposes an adaptive combinatorial optimization method that has a mechanism to achieve an appropriate balance between diversification and intensification from the viewpoint of long-term search dynamics while reducing the degeneracy of the search point set. The usefulness of the proposed adaptive combinatorial optimization method is confirmed by numerical experiments using well-known benchmark problems of traveling salesman problems, 0-1 knapsack problems, flow-shop scheduling problems, and quadratic assignment problems.