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We discuss the optimal system component allocation problem for series-parallel systems with interchangeable elements. A series-parallel system consists of subsystems that are connected in series and each subsystem consists of components in parallel. There are some heuristic methods to obtain quasi optimal solutions for the component allocation problem of series-parallel systems. Because this problem is one of the NP-complete problems, it is difficult to obtain the exact solutions for large scale problems. We had formulated this problem as a multi-objective optimization problem minimizing the system cost and maximizing the system reliability, and proposed an algorithm that obtains the exact solutions of the problems in an efficient way. The algorithm utilized the depth-first search method to eliminate useless searches and employs the branch-and-bound method to obtain the Pareto solutions. According to the results of our numerical experiments, the algorithm searches the Pareto solutions in practical time for not so large problems. In order to solve larger problems, in this paper, we propose a Multi-Objective Genetic Algorithm (MOGA). In comparison with the exact solution method we had proposed and the MOGA method, we assure the MOGA method produces the best compromised solutions and the later can solve large scale problems. We have conducted experiments for reasonably large scale problems and have demonstrated reasonably good performance of our method.