Abstract
A variable neighborhood search (VNS) algorithm has been developed to solve the multiple objective redundancy allocation problems (MORAP). The single objective RAP is to select the proper combination and redundancy levels of components to meet system level constraints, and to optimize the specified objective function. In practice, the need to consider two or more conflicting objectives simultaneously increases nowadays in order to assure managers or designers’ demand. Amongst all system level objectives, maximizing system reliability is the most studied and important one, while system weight or system cost minimization are two other popular objectives to consider. According to the authors’ experience, VNS has successfully solved the single objective RAP (Liang and Chen, Reliab. Eng. Syst. Saf. 92:323–331, 2007; Liang et al., IMA J. Manag. Math. 18:135–155, 2007). Therefore, this study aims at extending the single objective VNS algorithm to a multiple objective version for solving multiple objective redundancy allocation problems. A new selection strategy of base solutions that balances the intensity and diversity of the approximated Pareto front is introduced. The performance of the proposed multi-objective VNS algorithm (MOVNS) is verified by testing on three sets of complex instances with 5, 14 and 14 subsystems respectively. While comparing to the leading heuristics in the literature, the results show that MOVNS is able to generate more non-dominated solutions in a very efficient manner, and performs competitively in all performance measure categories. In other words, computational results reveal the advantages and benefits of VNS on solving multi-objective RAP.
Similar content being viewed by others
References
Avanthay, C., Hertz, A., Zufferey, N.: A variable neighborhood search for graph coloring. Eur. J. Oper. Res. 151, 379–388 (2003)
Brimberg, J., Hansen, P., Mladenović, N., Taillard, É.: Improvements and comparison of heuristics for solving the multisource Weber problem. Oper. Res. 48, 444–460 (2000)
Bulfin, R.L., Liu, C.Y.: Optimal allocation of redundant components for large systems. IEEE Trans. Reliab. 34, 241–247 (1985)
Chen, T.-C., You, P.-S.: Immune algorithms-based approach for redundant reliability problems with multiple component choices. Comput. Ind. 56, 195–205 (2005)
Chen, Y.-C.: Redundancy allocation of series-parallel systems using variable neighbourhood search algorithms. Master Thesis, Yuan Ze University: Taiwan, ROC (in Chinese) (2005)
Chern, M.S.: On the computational complexity of reliability redundancy allocation in a series system. Oper. Res. Lett. 11, 309–315 (1992)
Coit, D.W., Liu, J.: System reliability optimization with k-out-of-n subsystems. Int. J. Reliab. Qual. Saf. Eng. 7, 129–143 (2000)
Coit, D.W., Smith, A.E.: Penalty guided genetic search for reliability design optimization. Comput. Ind. Eng. 30, 895–904 (1996a)
Coit, D.W., Smith, A.E.: Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Trans. Reliab. 45, 254–260 (1996b)
Coit, D.W., Smith, A.E.: Solving the redundancy allocation problem using a combined neural network/genetic algorithm approach. Comput. Oper. Res. 23, 515–526 (1996c)
Elegbede, C., Adjallah, K.: Availability allocation to repairable systems with genetic algorithms a multi-objective formulation. Reliab. Eng. Syst. Saf. 82, 319–330 (2003)
Fyffe, D.E., Hines, W.W., Lee, N.K.: System reliability allocation and a computational algorithm. IEEE Trans. Reliab. 17, 74–79 (1968)
Gagné, C., Gravel, M., Price, W.L.: Using metaheuristic compromise programming for the solution of multiple objective scheduling problems. J. Oper. Res. Soc. 56, 687–698 (2005)
Geiger, M.J.: Randomized variable neighborhood search for multi objective optimization. In: Proceedings of the 4th EU/ME Workshop: Design and Evaluation of Advanced Hybrid Meta-Heuristics, pp. 34–42. Nottingham, United Kingdom (2004)
Geiger, M.J.: Foundations of the Pareto iterated local search metaheuristic. In: Proceedings of the 18th International Conference on Multiple Criteria Decision Making, Chania, Greece (2006)
Ghare, P.M., Taylor, R.E.: Optimal redundancy for reliability in series systems. Oper. Res. 17, 838–847 (1969)
Hansen, P., Mladenović, N.: Variable neighborhood search for the P-median. Locat. Sci. 5, 207–226 (1997)
Hansen, P., Mladenović, N.: In: Variable Neighborhood Search. Handbook of Applied Optimization, pp. 221–234. Oxford University Press, New York (2002)
Hansen, P., Mladenović, N.: In: Variable Neighborhood Search. Handbook of Metaheuristics, pp. 145–184. Kluwer Academic, Amsterdam (2003)
Huang, Y.-C.: Optimization of the series-parallel system with the redundancy allocation problem using a hybrid ant colony algorithm. Master Thesis, Yuan Ze University: Taiwan, ROC (in Chinese) (2003)
Huang, Y.-C., Her, Z.-S., Liang, Y.-C.: Redundancy allocation using meta-heuristics. In: Proceedings of the 4th Asia-Pacific Conference on Industrial Engineering and Management System (APIEMS 2002), pp. 1758–1761. Taipei, Taiwan, ROC (2002)
Ishibuchi, H., Yoshida, T., Murata, T.: Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Trans. Evol. Comput. 7, 204–223 (2003)
Kulturel-Konak, S., Coit, D.W., Smith, A.E.: Efficiently solving the redundancy allocation problem using tabu search. IIE Trans. 35, 515–526 (2003)
Kulturel-Konak, S., Coit, D.W., Baheranwala, F.: Pruned Pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives. J. Heuristics 14, 335–357 (2008)
Kytöjoki, J., Nuortio, T., Bräysy, O., Gendreau, M.: An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Comput. Oper. Res. 34, 2743–2757 (2007)
Li, J.: A bound dynamic programming for solving reliability redundancy optimization. Microelectron. Reliab. 36, 1515–1520 (1996)
Liang, Y.-C.: Ant colony optimization approach to combinatorial problems. Ph.D. Dissertation, Auburn University: USA (2001)
Liang, Y.-C., Chen, Y.-C.: Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm. Reliab. Eng. Syst. Saf. 92, 323–331 (2007)
Liang, Y.-C., Smith, A.E.: Ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Trans. Reliab. 53, 417–423 (2004)
Liang, Y.-C., Wu, C.-C.: A variable neighbourhood descent algorithm for the redundancy allocation problem. Ind. Eng. Manag. Syst. 4, 109–116 (2005)
Liang, Y.-C., Lo, M.-H., Chen, Y.-C.: Variable neighborhood search for redundancy allocation problems. IMA J. Manag. Math. 18, 135–155 (2007)
Misra, K.B., Sharma, U.: An efficient algorithm to solve integer-programming problems arising in system-reliability design. IEEE Trans. Reliab. 40, 81–91 (1991)
Mladenović, N.: Abstracts of papers presented at optimization days: a variable neighborhood algorithm—a new metaheuristic for combinatorial optimization. Montréal (1995)
Nahas, N., Nourelfath, M., Ait-Kadi, D.: Coupling ant colony and the degraded ceiling algorithm for the redundancy allocation problem of series-parallel system. Reliab. Eng. Syst. Saf. 97, 211–222 (2007)
Nakagawa, Y., Miyazaki, S.: Surrogate constraints algorithm for reliability optimization problems with two constraints. IEEE Trans. Reliab. 30, 175–180 (1981)
Onishi, J., Kimura, S., James, R.J.W., Nakagawa, Y.: Solving the redundancy allocation problem with a mix of components using the improved surrogate constraint method. IEEE Trans. Reliab. 56, 94–101 (2007)
Ravi, V.: Optimization of complex system reliability by a modified great Deluge algorithm. Asia-Pac. J. Oper. Res. 21, 487–497 (2004)
Ravi, V., Murty, B.S.N., Reddy, P.J.: Nonequilibrium simulated annealing algorithm applied to reliability optimization of complex system. IEEE Trans. Reliab. 46, 233–239 (1997)
Ribeiro, C.C., Souza, M.C.: Variable neighborhood search for the degree-constrained minimum spanning tree problem. Discrete Appl. Math. 118, 43–54 (2002)
Salazar, D., Rocco, C.M., Galván, B.J.: Optimization of constrained multiple-objective reliability problems using evolutionary algorithms. Reliab. Eng. Syst. Saf. 91, 1057–1070 (2006)
Sasaki, M., Gen, M.: A method of fuzzy multi-objective nonlinear programming with GUB structure by hybrid genetic algorithm. Int. J. Smart Eng. Syst. Des. 5, 281–288 (2003)
Shelokar, P.S., Jayaraman, V.K., Kulkarni, B.D.: Ant algorithm for single and multiobjective reliability optimization problems. Qual. Reliab. Eng. Int. 18, 497–514 (2002)
Stummer, C., Sun, M.: New multiobjective metaheuristic solution procedures for capital investment planning. J. Heuristics 11, 183–199 (2005)
Taboada, H.A., Baheranwala, F., Coit, D.W., Wattanapongsakorn, N.: : Practical solutions for multi-objective optimization: an application to system reliability design problems. Reliab. Eng. Syst. Saf. 92(3), 314–322 (2007)
Tillman, F.A., Hwang, C.L., Kuo, W.: Determining component reliability and redundancy for optimum system reliability. IEEE Trans. Reliab. 26, 162–165 (1977)
Tillman, F.A., Hwang, C.L., Kuo, W.: Optimization of System Reliability. Marcel Dekker, New York (1985)
You, P.-S., Chen, T.-C.: An efficient heuristic for series—parallel redundant reliability problems. Comput. Oper. Res. 32, 2117–2127 (2005)
Zhao, J.-H., Liu, Z., Dao, M.-T.: Reliability optimization using multiobjective ant colony system approaches. Reliab. Eng. Syst. Saf. 92, 109–120 (2007)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liang, YC., Lo, MH. Multi-objective redundancy allocation optimization using a variable neighborhood search algorithm. J Heuristics 16, 511–535 (2010). https://doi.org/10.1007/s10732-009-9108-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-009-9108-4