Multi-point Combinatorial Optimization Method with Estimation Mechanism for Landscape of Combinatorial Optimization Problems

Based on the Proximate Optimality Principle (POP) and a big valley structure in combinatorial optimization problems, an estimation mechanism for quantitatively estimating structural characteristics (landscape) of combinatorial optimization problems is developed in this paper. Using the results of a numerical evaluation of landscape for several types of combinatorial optimization problems including a traveling salesman problem, a 0-1 knapsack problem, a flow-shop scheduling problem and a quadratic assignment problem, a new multi-point combinatorial optimization method having the landscape estimation mechanism is also proposed. The proposed combinatorial optimization method uses the estimated landscape information of a given combinatorial optimization problem to control diversification and intensification during a search. The search capabilities of the proposed combinatorial optimization method are examined based on the results of numerical experiments using typical benchmark problems.