A Combinatorial Optimization Method for Large Scale Problems Based on a Probabilistic Model of Solution Space

Abstract

In this paper we consider, from the point of view of probability theory, an effective search method for large scale combinatorial optimization problems. The fundamental ideas on which our method is based are the following: 1) Many different neighborhood operations, which consist of the iterations of unit neighborhood operations, are applied to solutions. 2) The probability distribution of the objective function values of the neighborhood solutions is estimated, from the data obtained in the search process. 3) The neighborhood operation, which maximizes the expected value of the amount of the improvement of the current solution, is selected to be applied. From these ideas and the fundamentals of probability theory, a new method for searching for solutions is derived. We have applied the local search method, the genetic algorithm, and the proposed method to traveling salseman problems and maximum satisfiability problems. The effectiveness of the proposed method is shown by the computational experiments.