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The Multi-stage Genetic Algorithm, MGA, is introduced to solve a class of compositional design problems. The problem with complicated constraints is formulated as a set of local subproblems with simple constraints and a supervising problem. Every subproblem is solved by GA to generate a set of suboptimal solutions. And in the supervising problem, the elements of each set are optimally combined by GA to yield the optimal solution for the original problem. The method is a learning method where the empirical knowledge obtained by solving the problem is effectively utilized to solve similar problems efficiently. Extended knapsack problems are solved to demonstrate the proposed method, and the efficiency of the method is shown. In addition, the method is successfully applied to optimal realization of cooperative robot soccer behaviors.