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A Meta-heuristic with Orthogonal Experiment for the Set Covering Problem

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Journal of Mathematical Modelling and Algorithms

Abstract

This paper reports an evolutionary meta-heuristic incorporating fuzzy evaluation for some large-scale set covering problems originating from the public transport industry. First, five factors characterized by fuzzy membership functions are aggregated to evaluate the structure and generally the goodness of a column. This evaluation function is incorporated into a refined greedy algorithm to make column selection in the process of constructing a solution. Secondly, a self-evolving algorithm is designed to guide the constructing heuristic to build an initial solution and then improve it. In each generation an unfit portion of the working solution is removed. Broken solutions are repaired by the constructing heuristic until stopping conditions are reached. Orthogonal experimental design is used to set the system parameters efficiently, by making a small number of trials. Computational results are presented and compared with a mathematical programming method and a GA-based heuristic.

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References

  1. Aickelin, U.: An indirect genetic algorithm for set covering problems, J. Oper. Res. Soc.53 (2002), 1118–1126.

    Google Scholar 

  2. Beasley, J. E.: A Lagrangian heuristic for set covering problems, Naval Res. Logist.37 (1990), 151–164.

    Google Scholar 

  3. Beasley, J. E.: OR-Library: Distribution test problems by electronic mail, J. Oper. Res. Soc.41 (1990), 1069–1072.

    Google Scholar 

  4. Beasley, J. E. and Chu, P. C.: A genetic algorithm for the set covering problem, European J. Oper. Res.94 (1996), 392–404.

    Google Scholar 

  5. Caprara, A., Fischetti, M. and Toth, P.: A heuristic method for the set covering problem, Oper. Res.47 (1999), 730–743.

    Google Scholar 

  6. Dénes, J. and Keedwell, A. D.: Latin Square and Their Applications, English Universities Press Limited, Budapest, 1974.

    Google Scholar 

  7. Garey, M. R. and Johnson, D. S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.

    Google Scholar 

  8. Fores, S., Proll, L. and Wren, A.: TRACS II: A hybrid IP/heuristic driver scheduling system for public transport, J. Oper. Res. Soc.53 (2002), 1093–1100.

    Google Scholar 

  9. Haddadi, S.: Simple Lagrangian heuristic for the set covering problem, European J. Oper. Res.97 (1997), 200–204.

    Google Scholar 

  10. Karmarkar, N.: A new polynomial-time algorithm for linear programming, Combinatorica4 (1984), 373–395.

    Google Scholar 

  11. Kling, R. M. and Banerjee, P.: ESP: A new standard cell placement package using simulated evolution, in Proceedings of the 24th ACM/IEEE Design Automation Conference, 1987, pp. 60–66.

  12. Kwan, R. S. K, Kwan, A. S. K. and Wren, A.:Evolutionary driver scheduling with relief chains, Evolutionary Computation9 (2001), 445–460.

    Google Scholar 

  13. 2001 IEEE Congress on Evolutionary Computation, IEEE Press}, 2001, pp. 1115–1122.

  14. Li, J. and Kwan, R. S. K.: A fuzzy theory based evolutionary approach for driver scheduling, in L. Spector et al. (eds), Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufman, 2001, pp. 1152–1158.

  15. Li, J. and Kwan, R. S. K.: A fuzzy genetic algorithm for driver scheduling, European J. Oper. Res.147 (2003), 334–344.

    Google Scholar 

  16. Ohlsson, M., Peterson, C. and Söberderg, B.: An efficient mean field approach to the set covering problem,European J. Oper. Res.133 (2001), 583–599.

    Google Scholar 

  17. Sen, S.: Minimal cost set covering using probabilistic methods in Proceedings of the 1993 ACM Symposium on Applied Computing: States of the Art and Practice, 1993, pp. 157–164.

  18. Slavík, P.: A tight analysis of the greedy algorithm for set cover, in ACM Symposium on Theory of Computing, 1996, pp. 435–441.

  19. Solar, M., Parada, V. and Urrutia, R.: A parallel genetic algorithm to solve the set-covering problem, Comput. Oper. Res.29 (2002), 1221–1235.

    Google Scholar 

  20. Srinivasan, A.: Improved approximations of packing and covering problems, in ACM Symposium on Theory of Computing, 1995, pp. 268–276.

  21. Taguchi, G.: System of Experimental Design, Vols. 1 and 2, UNIPUB/Kraus International Publications, New York, 1987.

    Google Scholar 

  22. The triplex design group of Chinese Association of Statistics: Orthogonal Method and Triplex Design, Science Press, Beijing, 1987.

  23. Zadeh, L. A.: Fuzzy sets, Inform. Control8 (1965), 338–353.

    Google Scholar 

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Authors and Affiliations

  1. School of Computer Science & Information Technology, The University of Nottingham, Nottingham, NG8 1BB, U.K.

    Jingpeng Li

  2. School of Computing, University of Leeds, Leeds, LS2 9JT, U.K.

    Raymond S. K. Kwan

Authors
  1. Jingpeng Li
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  2. Raymond S. K. Kwan
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Li, J., Kwan, R.S.K. A Meta-heuristic with Orthogonal Experiment for the Set Covering Problem. Journal of Mathematical Modelling and Algorithms 3, 263–283 (2004). https://doi.org/10.1023/B:JMMA.0000038619.69509.bf

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  • DOI: https://doi.org/10.1023/B:JMMA.0000038619.69509.bf

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