Abstract
We discuss a solution method based on evolutionary technology for the optimal component allocation problem in a series-parallel redundant system. A series-parallel system consists of subsystems that are connected in series and each subsystem consists of interchangeable components in parallel. There are some heuristic methods to approximately solve the optimal component allocation problem for series-parallel systems. We have 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 (Pareto solutions) of the problems in an efficient way. Because this problem is one of the NP-complete problems, it is difficult to obtain the optimal solution for the large scale problems and methods that obtain the exact solutions are not known. The algorithm utilizes 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 execution time for not so large scale problems. In order to solve larger scale problems, we propose a Multi-objective Genetic Algorithm (MOGA). We evaluate the ability of the MOGA by comparison with the exact solution method by using various scale problems. Through those experiments, we discuss the characteristics of this problem and analyze the effectiveness of our method.
