Comparative study with several GAs for optimal component arrangement in a circular consecutiev-k-out-of-n: F system

A circular consecutive-k-out-of-n: F system consists of n components arranged along a circular path. This system fails if no less than k consecutive components fail. One of the most important problems about 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 increases, however, the amount of calculation would be too large to obtain the solution within a reasonable computing time. In this paper, we propose four kinds of genetic algorithms to obtain quasi optimal solutions. They employ the ordinal representation scheme we have developed on the basis of ideas that eliminates arrangements with the same system reliabilities produced by rotation and/or reversal of certain arrangements, and allocates components with low failure probabilities at equal intervals. We have compared their performances and investigated how many components with low failure probabilities should be allocated at equal intervals to obtain good solution through the numerical experiments.