A method of seeking feasible solutions based on distributed problem solving

A problem of seeking feasible solutions under a large number of constraints is decomposed into a set of interconnected subproblems. If two subproblems share same variables, equality constraints arise between the subproblems. These equality constraints represent the interconnections of subproblems. This paper first shows that such a problem can further be transformed into a two-level optimization problem composed of small-scale optimization subproblems and one coordination problem. Auxiliary coordination variables are introduced to coordinate the common decision variables included in two or more subproblems. It second proposes a method of seeking feasible solutions based on cooperative in distributed problem solving. Feasible solutions are sought through the minimization with respect to the decision variables in each subproblem of the first level and through the minimization with respect to the coordination variables in the second level. If many feasible solutions exist, the coordination in the second level causes a multimodal problem. The paper also discusses a problem of separating peaks from multimodal function. The feasible solution seeking method proposed here seems to easily manage knowledge necessary to problem solving, to decrease effects of curse of dimensionality, and to have potential possibilities of parallel processing. [In Japanese.]