Efficient Genetic Algorithm for Optimal Arrangement in a Linear Consecutive-k-out-of-n: F System

Koji SHINGYOCHI  Hisashi YAMAMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.7   pp.1578-1584
Publication Date: 2009/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1578
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Recent Advances in Technologies for Assessing System Reliability)
Category: 
Keyword: 
linear consecutive-k-out-of-n: F system,  optimal arrangement problem,  genetic algorithm,  ordinal representation,  

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Summary: 
A linear consecutive-k-out-of-n: F system is an ordered sequence of n components. This system fails if, and only if, k or more consecutive components fail. Optimal arrangement is one of the main problems for such kind of system. In this problem, we want to obtain an optimal arrangement of components to maximize system reliability, when all components of the system need not have equal component failure probability and all components are mutually statistically independent. As n becomes large, however, the amount of calculation would be too much to solve within a reasonable computing time even by using a high-performance computer. Hanafusa and Yamamoto proposed applying Genetic Algorithm (GA) to obtain quasi optimal arrangement in a linear consecutive-k-out-of-n: F system. GA is known as a powerful tool for solving many optimization problems. They also proposed ordinal representation, which produces only arrangements satisfying the necessary conditions for optimal arrangements and eliminates redundant arrangements with same system reliabilities produced by reversal of certain arrangements. In this paper, we propose an efficient GA. We have modified the previous work mentioned above to allocate components with low failure probabilities, that is to say reliable components, at equal intervals, because such arrangements seem to have relatively high system reliabilities. Through the numerical experiments, we observed that our proposed GA with interval k provides better solutions than the previous work for the most cases.