Annals of Operations Research

, Volume 212, Issue 1, pp 185–200 | Cite as

A Birnbaum-importance based genetic local search algorithm for component assignment problems

  • Qingzhu Yao
  • Xiaoyan Zhu
  • Way Kuo


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.


Genetic algorithm Reliability Local search Component assignment problem Birnbaum importance 



This work is supported in part by a National Science Foundation Project # CMMI-0825908.


  1. 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
  2. Davis, L. (1991). Handbook of genetic algorithms. New York: Van Nostrand-Reinhold. Google Scholar
  3. Fleurent, C., & Ferland, J. (1996). Genetic and hybrid algorithms for graph coloring. Ann Oper Res, 63, 437–463. CrossRefGoogle Scholar
  4. 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
  5. 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
  6. Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading: Addison-Wesley. Google Scholar
  7. 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
  8. Hartmann, S. (2001). Project scheduling with multiple modes: a genetic algorithm. Ann Oper Res, 102, 111–135. CrossRefGoogle Scholar
  9. Józefowska, J., Mika, M., Różycki, R., Waligóra, G., & Weglarz, J. (2001). Simulated annealing for multi-mode resource-constrained project scheduling. Ann Oper Res, 102, 137–155. CrossRefGoogle Scholar
  10. Kontoleon, J. M. (1979). Optimal link allocation of fixed topology networks. IEEE Trans Reliab, 28, 145–147. CrossRefGoogle Scholar
  11. Koulamas, C., Antony, S. R., & Jaen, R. (1994). A survey of simulated annealing applications to operations research problems. Omega—Int J Manag, 22, 41–56. CrossRefGoogle Scholar
  12. Kuo, W., & Zhu, X. (2012a). Relations and generalizations of importance measures in reliability. IEEE Trans Reliab, 61, 659–674. CrossRefGoogle Scholar
  13. Kuo, W., & Zhu, X. (2012b). Some recent advances on importance measures in reliability. IEEE Trans Reliab, 61, 344–360. CrossRefGoogle Scholar
  14. Kuo, W., & Zuo, M. J. (2002). Optimal reliability modeling: principles and applications. Hoboken: Wiley. Google Scholar
  15. Levitin, G., Rubinovitz, J., & Shnits, B. (2006). A genetic algorithm for robotic assembly line balancing. Eur J Oper Res, 168, 811–825. CrossRefGoogle Scholar
  16. Lim, M. H., Yuan, Y., & Omatu, S. (2000). Efficient genetic algorithms using simple gnens exchange local search policy for the quadratic assignment problem. Comput Optim Appl, 15, 249–268. CrossRefGoogle Scholar
  17. Lin, F. H., & Kuo, W. (2002). Reliability importance and invariant optimal allocation. J Heuristics, 8, 155–171. CrossRefGoogle Scholar
  18. Malon, D. (1984). Optimal consecutive-2-out-of-n:F component sequencing. IEEE Trans Reliab, 33, 414–418. CrossRefGoogle Scholar
  19. Pentico, D. W. (2007). Assignment problems: a golden anniversary survey. Eur J Oper Res, 176, 774–793. CrossRefGoogle Scholar
  20. 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
  21. 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
  22. Tseng, L.-Y., & Lin, Y.-T. (2009). A hybrid genetic local search algorithm for the permutation flowshop scheduling problem. Eur J Oper Res, 198, 84–92. CrossRefGoogle Scholar
  23. Yao, Q., Zhu, X., & Kuo, W. (2011). Heuristics for component assignment problems based on the Birnbaum importance. AIIE Trans, 43, 633–646. Google Scholar
  24. Zhu, X., & Kuo, W. (2008). Comments on “A hierarchy of importance indices”. IEEE Trans Reliab, 57, 529–531. CrossRefGoogle Scholar
  25. Zhu, X., & Kuo, W. (2012). Importance measures in reliability and mathematical programming. Ann Oper Res. doi: 10.1007/s10479-012-1127-0. Google Scholar
  26. 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
  27. Zuo, M. J., & Kuo, W. (1990). Design and performance analysis of consecutive-k-out-of-n structure. Nav Res Logist, 37, 203–230. CrossRefGoogle Scholar
  28. 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

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringUniversity of TennesseeKnoxvilleUSA
  2. 2.Revenue Analytics, Inc.AtlantaUSA
  3. 3.City University of Hong KongKowloonHong Kong

Personalised recommendations