In this paper, we consider an effective search method for large scale combinatorial optimization problems, only by means of neighborhood operations, not by means of such operation as crossover in genetic algorithm. 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, a new method for searching for solutions is constructed, on the basis of the self-convolution and the inverse self-convolution. We have applied the local search method, the previously proposed method, and the newly proposed method to traveling salesman problems and maximum satisfiability problems. The effectiveness of the newly proposed method is shown by the computational experiments.
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