A Birnbaum-importance based genetic local search algorithm for component assignment problems
This paper considers the component assignment problem (CAP) of finding the optimal assignment of n available components to n positions in a system such that the system reliability is maximized. To solve the CAP, an important type of problems in reliability, we propose a Birnbaum-importance based genetic local search (BIGLS) algorithm in which a local search using the Birnbaum importance is embedded into the genetic algorithm. This paper presents comprehensive numerical tests to compare the performance of the BIGLS with a general genetic algorithm and a Birnbaum-importance based two-stage heuristic. The testing results show that the BIGLS is robust (with respect to its random operations) and effective, and outperforms two benchmark methods in terms of solution quality. It demonstrates the effectiveness of embedding the Birnbaum importance in the local search under the genetic evolutionary mechanism.
KeywordsGenetic algorithm Reliability Local search Component assignment problem Birnbaum importance
This work is supported in part by a National Science Foundation Project # CMMI-0825908.
- Birnbaum, Z. W. (1969). On the importance of different components in a multicomponent system. In P. R. Krishnaiah (Ed.), Multivariate analysis (Vol. 2, pp. 581–592). New York: Academic Press. Google Scholar
- Davis, L. (1991). Handbook of genetic algorithms. New York: Van Nostrand-Reinhold. Google Scholar
- Freisleben, B., & Merz, P. (1996). A genetic local search algorithm for solving symmetric and asymmetric traveling salesman problems. In Proceedings of the 1996 IEEE international conference on evolutionary computation (pp. 616–621). New York: IEEE Press. Google Scholar
- Grefenstette, J. J., Gopal, R., Rosmaita, B., & Cucht, D. V. (1985). Genetic algorithms for the traveling salesman problem. In Proceedings of the first international conference on genetic algorithms and their applications (pp. 160–168). Hillsdale: Erlbaum. Google Scholar
- Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading: Addison-Wesley. Google Scholar
- Goldberg, D. E., & Lingle, R. (1985). Alleles, loci, and the traveling salesman problem. In Proceedings of the first international conference on genetic algorithms and their applications (pp. 154–159). Hillsdale: Erlbaum. Google Scholar
- Kuo, W., & Zuo, M. J. (2002). Optimal reliability modeling: principles and applications. Hoboken: Wiley. Google Scholar
- Shingyoch, K., Yamamoto, H., Tsujimura, Y., & Akiba, T. (2010). Proposal of simulated annealing algorithms for optimal arrangement in a circular consecutive-k-out-of-n:F system. Qual Tech Quant Manag, 7, 395–405. Google Scholar
- Shingyoch, K., Yamamoto, H., Tsujimura, Y., & Kambayashi, Y. (2009). Improvement of ordinal representation scheme for solving optimal component arrangement problem of circular consecutive-k-out-of-n:F system. Qual Tech Quant Manag, 6, 11–22. Google Scholar
- Yao, Q., Zhu, X., & Kuo, W. (2011). Heuristics for component assignment problems based on the Birnbaum importance. AIIE Trans, 43, 633–646. Google Scholar
- Zhu, X., Yao, Q., & Kuo, W. (2012). Patterns of the Birnbaum importance in linear consecutive-k-out-of-n systems. AIIE Trans, 44, 277–290. Google Scholar
- Zuo, M. J., & Shen, J. (1992). System reliability enhancement through heuristic design. 1992 OMAE-Volume II, Safety and Reliability, ASME. pp. 301–304. Google Scholar