GENETIC ALGORITHM FOR SOLVING OPTIMAL COMPONENT ARRANGEMENT PROBLEM OF CIRCULAR CONSECUTIVE-K-OUT-OF-N: F SYSTEM

摘要

A circular consecutive-k-out-of-n: F system consists of n components arranged along acircular path. This system fails if no less than k consecutive components fail. One of the most important problems for this system is to obtain the optimal component arrangement that maximizes the system reliability. In order to obtain the exact solution for this problem, one needs to calculate n! system reliabilities. As n becomes large, however, the amount of calculation would be intolerably large. In this paper, we propose two kinds of genetic algorithm to obtain the quasi optimal solution for this problem within a reasonable computing time. One employs Grefenstette's direct ordinal representation scheme. The other employs special ordinal representation scheme we have developed. The latter scheme eliminates arrangements with same system reliability produced by rotation and/or reversal of certain arrangements. In addition to that, we have improved the scheme to produce only arrangements that allocate components with low failure probabilities at every k-th position, because system reliabilities of such arrangements should be high. We compared their performance and demonstrated the advantage of the scheme we have developed through numerical experiments.