The linear consecutive-k-out-of-n: failure (good) (Lin/Con/k/n:F(G)) system consists of n interchangeable
components that have different reliabilities. These components are arranged in a line path and different
component assignments change the system reliability. The optimization of Lin/Con/k/n:F(G) system is to find
an optimal component assignment to maximize the system reliability. As the number of components increases, the
computation time for this problem increases considerably. In this paper, we propose a Birnbaum importance-based
ant colony optimization (BIACO) algorithm to obtain quasi optimal assignments for such problems. We compare
its performance using the Birnbaum importance based two-stage approach (BITA) and Birnbaum importancebased
genetic local search (BIGLS) algorithm from previous researches. The experimental results show that the
BIACO algorithm has a good performance in the optimization of Lin/Con/k/n:F(G) system.
WANG Wei (王伟), CAI Zhiqiang (蔡志强), ZHAO Jiangbin (赵江滨), SI Shubin (司书宾)
. Optimization of Linear Consecutive-k-Out-of-n Systems with Birnbaum Importance Based Ant Colony Optimization Algorithm[J]. Journal of Shanghai Jiaotong University(Science), 2020
, 25(2)
: 253
-260
.
DOI: 10.1007/s12204-019-2125-z
[1] DERMAN C, LIEBERMAN G J, ROSS S M. On optimal assembly of systems [J]. Naval Research Logistics,2010, 19(4): 569-574.
[2] LIN Y K, YEH C T. Multistate components assignment problem with optimal network reliability subject to assignment budget [J]. Applied Mathematics and Computation, 2011, 217(24): 10074-10086.
[3] COIT D W, SMITH A E. Reliability optimization of series-parallel systems using a genetic algorithm [J].IEEE Transactions on Reliability, 1996, 45(2): 254-260.
[4] PENTICO D W. Assignment problems: A golden anniversary survey [J]. European Journal of Operational Research, 2007, 176(2): 774-793.
[5] GRIFFITH WS. Optimal reliability modeling: Principles and applications [J]. Technometrics, 2002, 46(1):541-547.
[6] CHIANG D T, NIU S C. Reliability of consecutive-kout-of-n:F system [J]. IEEE Transactions on Reliability,1981, 30(1): 87-89.
[7] CHAO M T, FU J C, KOUTRAS M V. Survey of reliability studies of consecutive-k-out-of-n:F & related systems [J]. IEEE Transactions on Reliability, 1995,44(1): 120-127.
[8] GEBRE B A, RAMIREZ-MARQUEZ J E. Element substitution algorithm for general two-terminal network reliability analyses [J]. IIE Transactions, 2007,39(3): 265-275.
[9] KONTOLEON J M. Optimum link allocation of fixed topology networks [J]. IEEE Transactions on Reliability,1979, 28(2): 145-147.
[10] SHINGYOCHI K, YAMAMOTO H. Efficient genetic algorithm for optimal arrangement in a linear consecutive-k-out-of-n:F system [J]. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2009, 92(7): 1578-1584.
[11] LIN Y K, YEH C T. A two-stage approach for a multi-objective component assignment problem for a stochastic-flow network [J]. Engineering Optimization,2013, 45(3): 265-285.
[12] BIRNBAUM Z W. On the importance of different components in a multicomponent system [R]. Seattle,Washington, USA: University of Washington, 1968.
[13] LIN F H, KUO W. Reliability importance and invariant optimal allocation [J]. Journal of Heuristics, 2002,8(2): 155-171.
[14] ZUO M, KUO W. Design and performance analysis of consecutive k-out-of-n:F system [J]. Naval Research Logistics, 1990, 37(2): 203-230.
[15] YAO Q Z, ZHU X Y, KUO W. Heuristics for component assignment problems based on the Birnbaum importance [J]. IIE Transactions, 2011, 43(9): 633-646.
[16] YAO Q Z, ZHU X Y, KUO W. A Birnbaumimportance based genetic local search algorithm for component assignment problems [J]. Annals of Operations Research, 2014, 212(1): 185-200.
[17] DORIGO M, MANIEZZO V, COLORNI A. The ant system: Optimization by a colony of cooperating agents [J]. IEEE Transactions on Systems, Man, and Cybernetics Part B (Cybernetics), 1996, 26(1): 29-41.
[18] MANIEZZO V. Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem [J]. INFORMS Journal on Computing,1998, 11(4): 358-369.