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Efficient Genetic Algorithm for Optimal Arrangement in a Linear Consecutivekoutofn: F System
Koji SHINGYOCHI Hisashi YAMAMOTO
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E92A
No.7
pp.15781584 Publication Date: 2009/07/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E92.A.1578
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Recent Advances in Technologies for Assessing System Reliability) Category: Keyword: linear consecutivekoutofn: F system, optimal arrangement problem, genetic algorithm, ordinal representation,
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Summary:
A linear consecutivekoutofn: 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 highperformance computer. Hanafusa and Yamamoto proposed applying Genetic Algorithm (GA) to obtain quasi optimal arrangement in a linear consecutivekoutofn: 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.

