Skip to main content
SpringerLink
Log in

Combinatorial Reliability Optimization

  • Chapter
Handbook of Reliability Engineering

5.5 Summary

This chapter considers various combinatorial reliability optimization problems with multiple resource constraints or multiple-choice constraints incorporated for a variety of different system structures, including series systems, mixed series-parallel systems, and general systems.

Each of the problems is known as an NP-hard problem. This provided us with the motivation to develop various solution approaches, including optimal solution approaches, continuous relaxation approaches, and heuristic approaches, based on various problem-dependent solution properties. In particular, owing to the combinatorial nature of the problems, this chapter focuses on some combinatorial solution approaches, including the branch-and-bound method, the partial enumeration method, the dynamic programming method, and the greedy-type heuristic method, which can give integer optimal or heuristic solutions.

These days, metaheuristic approaches, including the simulated annealing method, the tabu search method, the neural network approach, and genetic algorithms, have been getting popular for combinatorial optimization. However, not many applications of those approaches have been made to the combinatorial reliability optimization problems yet. Thus, those approaches are not discussed here.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Valiant LG. The complexity of enumeration and reliability problems. SIAM J Comput 1979;8:410–21.

    Article  MATH  MathSciNet  Google Scholar 

  2. Satyanarayana A, Wood RK. A linear-time algorithm for computing K-terminal reliability in series-parallel networks. SIAM J Comput 1985;14:818–32.

    Article  MathSciNet  Google Scholar 

  3. Chern CS. On the computational complexity of reliability redundancy allocation in a series system. Oper Res Lett 1992;11:309–15.

    Article  MATH  MathSciNet  Google Scholar 

  4. Malon DM. When is greedy module assembly optimal? Nav Res Logist 1990;37:847–54.

    MATH  MathSciNet  Google Scholar 

  5. Tillman IA, Hwang CL, Kuo W. Optimization techniques for system reliability with redundancy: a review. IEEE Trans Reliab 1977;R-36:148–55.

    MathSciNet  Google Scholar 

  6. Tillman FA, Liittschwager JM. Integer programming formulation of constrained reliability problems. Manage Sci 1967;13:887–99.

    Google Scholar 

  7. Misra KB. A method of solving redundancy optimization problems. IEEE Trans Reliab 1971;R-20:117–20.

    Google Scholar 

  8. Lawler EL, Bell MD. A method of solving discrete optimization problems. Oper Res 1966;14:1098–112.

    Google Scholar 

  9. Ghare PM, Talyer RE. Optimal redundancy for reliability in series systems. Oper Res 1969;17:838–47.

    Google Scholar 

  10. Sung CS, Lee HK. A branch-and-bound approach for spare unit allocation in a series system. Eur J Oper Res 1994;75:217–32.

    Article  Google Scholar 

  11. Kuo E, Lin HH, Xu Z, Zhang W. Reliability optimization with the Lagrange-multiplier and branch-and-bound technique. IEEE Trans Reliab 1987;R-36:624–30.

    Google Scholar 

  12. Lawler EL, Wood DE. Branch-and-bound method: a survey. Oper Res 1966;14:699–719.

    MathSciNet  Google Scholar 

  13. Balas E. A note on the branch-and-bound principle. Oper Res 1968;16:442–5.

    MATH  Google Scholar 

  14. McLeavey DW. Numerical investigation of optimal parallel redundancy in series systems. Oper Res 1974;22:1110–7.

    MATH  Google Scholar 

  15. McLeavey DW, McLeavey JA. Optimization of system reliability by branch-and-bound. IEEE Trans Reliab 1976;R-25:327–9.

    Google Scholar 

  16. Luus R. Optimization of system reliability by a new nonlinear programming procedure. IEEE Trans Reliab 1975;R-24:14–6.

    Google Scholar 

  17. Aggarwal AK, Gupta JS, Misra KB. A new heuristic criterion for solving a redundancy optimization problem. IEEE Trans Reliab 1975;R-24:86–7.

    Google Scholar 

  18. Bellman R, Dreyfus S. Dynamic programming and the reliability of multicomponent devices. Oper Res 1958;6:200–6.

    MathSciNet  Google Scholar 

  19. Kettelle JD. Least-cost allocation of reliability investment. Oper Res 1962;10:249–65.

    Google Scholar 

  20. Woodhouse CF. Optimal redundancy allocation by dynamic programming. IEEE Trans Reliab 1972;R-21:60–2.

    Google Scholar 

  21. Sharma J, Venkateswaran KV. A direct method for maximizing the system reliability. IEEE Trans Reliab 1971;R-20:256–9.

    Google Scholar 

  22. Gopal D, Aggarwal KK, Gupta JS. An improved algorithm for reliability optimization. IEEE Trans Reliab 1978;R-27:325–8.

    Google Scholar 

  23. Misra KB. A simple approach for constrained redundancy optimization problem. IEEE Trans Reliab 1972;R-21:30–4.

    Google Scholar 

  24. Nakagawa Y, Nakashima K. A heuristic method for determining optimal reliability allocation. IEEE Trans Reliab 1977;R-26:156–61.

    Google Scholar 

  25. Kuo W, Hwang CL, Tillman FA. A note on heuristic methods in optimal system reliability. IEEE Trans Reliab 1978;R-27:320–324.

    Google Scholar 

  26. Nakagawa Y, Miyazaki S. An experimental comparison of the heuristic methods for solving reliability optimization problems. IEEE Trans Reliab 1981;R-30:181–4.

    Google Scholar 

  27. Burton RM, Howard GT. Optimal system reliability for a mixed series and parallel structure. J Math Anal Appl 1969;28:370–82.

    MathSciNet  Google Scholar 

  28. Cho YK. Redundancy optimization for a class of reliability systems with multiple-choice resource constraints. Unpublished PhD Thesis, Department of Industrial Engineering, KAIST, Korea, 2000; p.66–75.

    Google Scholar 

  29. Aggarwal KK. Redundancy optimization in general systems. IEEE Trans Reliab 1976;R-25: 330–2.

    Google Scholar 

  30. Shi DH. A new heuristic algorithm for constrained redundancy-optimization in complex system. IEEE Trans Reliab 1987;R-36:621–3.

    Google Scholar 

  31. Ravi V, Murty BSN, Reddy PJ. Nonequilibrium simulated annealing-algorithm applied to reliability optimization of complex systems. IEEE Trans Reliab 1997;46:233–9.

    Article  Google Scholar 

  32. Sung CS, Cho YK. Reliability optimization of a series system with multiple-choice and budget constraints. Eur J Oper Res 2000;127:159–71.

    Article  MathSciNet  Google Scholar 

  33. Chern CS, Jan RH. Reliability optimization problems with multiple constraints. IEEE Trans Reliab 1986;R-35:431–6.

    Google Scholar 

  34. Sung CS, Cho YK. Branch-and-bound redundancy optimization for a series system with multiple-choice constraints. IEEE Trans Reliab 1999;48:108–17.

    Google Scholar 

  35. Sasaki G, Okada T, Shingai S. A new technique to optimize system reliability. IEEE Trans Reliab 1983;R-32:175–82.

    Google Scholar 

  36. Murphee EL, Fenves S. A technique for generating interpretive translators for problem oriented languages. BIT 1970:310–23.

    Google Scholar 

Download references

Authors
  1. C. S. Sung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. K. Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. H. Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Rutgers University, Piscataway, New Jersey, USA

    Hoang Pham PhD

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag London Limited

About this chapter

Cite this chapter

Sung, C.S., Cho, Y.K., Song, S.H. (2003). Combinatorial Reliability Optimization. In: Pham, H. (eds) Handbook of Reliability Engineering. Springer, London. https://doi.org/10.1007/1-85233-841-5_5

Download citation

  • DOI: https://doi.org/10.1007/1-85233-841-5_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-453-6

  • Online ISBN: 978-1-85233-841-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation