On the Computational Effectiveness of Multiple Objective Metaheuristics

  • Andrzej Jaszkiewicz
Part of the Advances in Soft Computing book series (AINSC, volume 12)

Abstract

The paper describes a technique for comparison of computational effectiveness of two approaches to generation of approximately Pareto-optimal solutions with the use of metaheuristics. In the on-line generation approach the approximately Pareto-optimal solutions are generated during the interactive process, e.g. by optimization of some scalarizing functions. In the off-line generation approach, the solutions are generated prior to the interactive process with the use of multiple objective metaheuristics. The results of experiment on travelling salesperson instances indicate that in the case of some multiple objective metheuristics the off-line generation approach may be computationally effective alternative to the on-line generation of approximately Pareto-optimal solutions.

Keywords

Multiple objective optimization metaheuristics scalarizing functions interactive methods computational effectiveness 

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Bibliography

  1. [1]
    Borges P.C., Hansen P.H. (1998), A basis for future successes in multiobjective combinatorial optimization. Technical Report, Department of Mathematical Modelling, Technical University of Denmark,1MM-REP-1998–8.Google Scholar
  2. [2]
    Czyzak P., Jaszkiewicz A. (1998), Pareto simulated annealing–a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7, 34–47.CrossRefGoogle Scholar
  3. [3]
    Finkel R.A. and Bentley J.L. (1974), Quad Trees, A data structure for retrieval on composite keys. Acta Informatica, 4, 1–9.CrossRefGoogle Scholar
  4. [4]
    Fonseca C.M., Fleming P.J. (1993), Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In S. Forrest (Ed.), Genetic Algorithms: Proceedings of 5 31 International Conference, San Mateo, CA, Morgan Kaufmann, 416–423.Google Scholar
  5. [5]
    Freisleben B., Merz P. (1996), A genetic local search algorithm for travelling salesman problem. In H.-M. Voigt, W. Ebeling, I. Rechenberg, II.-P. Schwefel (eds.), Proceedings of the 4` h Conference on Parallel Problem Solving fram Nature- PPSN IV, 890–900.CrossRefGoogle Scholar
  6. [6]
    Gandibleux, X., Mezdaoui N., Fréville A. (1996). A tabu search procedure to solve multiobjective combinatorial optimization problems, In R. Caballero, R. Steuer (Eds.), Proceedings volume ofMOPGP `96,, Springer-Verlag.Google Scholar
  7. [7]
    Habenicht W. (1982), Quad Trees, A datastructure for discrete vector optimization problems Lecture Notes in Economics and Mathematical Systems, 209, 136–145.CrossRefGoogle Scholar
  8. [8]
    Hansen M. (1997), Tabu search for multiobjective optimization: MOTS, presented at the 13th MCDM conference, Cape Town, South Africa, January 6–10.Google Scholar
  9. [9]
    Horn. J., Nafpliotis N. (1994). A niched Pareto genetic algorithm for multiobjective optimization. Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, vol. 1, IEEE, New York, 82–87.CrossRefGoogle Scholar
  10. [10]
    Hwang C.-L. and Masud A.S.M. (1979). Mutiple Objective Decision Making - Methods and Applications, Springer, Berlin.CrossRefGoogle Scholar
  11. [11]
    Hwang C.-L., Paidy S.R., Yoon K. and Masud A.S.M. (1980), Mathematical programming with multiple objectives: A tutorial. Comput. Oper. Res., 7, 5–31.CrossRefGoogle Scholar
  12. [12]
    Jaszkiewicz A. (1998). Genetic local search for multiple objective combinatorial optimization. Research report, Institute of Computing Science, Poznan University of Technology, RA-014/98, pp. 23.Google Scholar
  13. [13]
    Jaszkiewicz A., Slowinski R. (1997). The LBS-Discrete Interactive Procedure for Multiple-Criteria Analysis of Decision Problems. In: J. Climaco (red.) Multicriteria Analysis. Proceedings of the XIth International Conference on MCDM, 1–6, August 1994, Coimbra, Portugal, Springer-Verlag, Berlin–Heidelberg, 320–330.Google Scholar
  14. [14]
    Köksalan M., Karwan M.H. and Zionts S. (1988). An Approach for Solving Discrete Alternative Multiple Criteria Problems Involving Ordinal Criteria. Naval Research Logistics, 35, 6, 625–642.CrossRefGoogle Scholar
  15. [15]
    Korhonen P. (1988). A Visual Reference Direction Approach to Solving Discrete Multiple Criteria Problems. EJOR, 34, 2, 152–159.CrossRefGoogle Scholar
  16. [16]
    Korhonen P. Wallenius J. and Zionts S. (1984). Solving the Discrte Multiple Criteria Problem Using Convex Cones. Management Science, 30, 11, 1336–1345.CrossRefGoogle Scholar
  17. [17]
    Lotfi V., Stewart T.J. and Zionts S. (1992). An aspiration-level interactive model for multiple criteria decision making. Comput. Ops. Res., 19, 677–681.CrossRefGoogle Scholar
  18. [18]
    Malakooti B. (1989). Theories and an Exact Interactive Paired-COmparison Approach for Discrete Multiple Criteria Problems IEEE Transactions on Systems, Man, and Cybernetics, 19, 2, 365–378.CrossRefGoogle Scholar
  19. [19]
    Merz P., Freisleben B., Genetic Local Search for the TSP: New Results, hi Proceedings of the 1997 IEEE International Conference on Evolutionary Computation, IEEE Press, 159–164, 1997.Google Scholar
  20. [20]
    Reinelt G. (1991). TSPLIB — a traveling salesman problem library. ORSA Journal of Computing, 3, 4, 376–384.CrossRefGoogle Scholar
  21. [21]
    Schaffer J.D. (1985). Multiple objective optimization with vector evaluated genetic algorithms. In: J.J. Grefenstette (ed.), Genetic Algorithms and Their Applications: Proceedings of the Third International Conference on Genetic Algorithms, Lawrence Erlbaum, Hillsdale, NJ, 93–100.Google Scholar
  22. [22]
    Serafmi P (1994). Simulated annealing for multiple objective optimization problems. In: Tzeng G.H., Wang H.F., Wen V.P., Yu P.L. (eds), Multiple Criteria Decision Making. Expand and Enrich the Domains of Thinking and Application, Springer Verlag, 283–292.Google Scholar
  23. [23]
    Shin W.S. and Ravindran A. (1991). Interactive multiple objective optimization: survey I–continuous case, Comput. Oper. Res., 18, 97–114.CrossRefGoogle Scholar
  24. [24]
    Srinivas N., Deb K. (1994). Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2, 2, 221–248.CrossRefGoogle Scholar
  25. [25]
    Steuer R.E. (1986). Multiple Criteria Optimization - Theory, Computation and Application, Wiley, New York.Google Scholar
  26. [26]
    Sun M., Steuer R. E. (1996). htterQuad: An Interactive Quad Tree Based Procedure for Solving the Discrete Alternative Multiple Criteria Problem. European Journal of Operational Research, 89, No. 3, 462–472.Google Scholar
  27. [27]
    Taner O.V. and Köksalan M.M. (1991). Experiments and an Improved Method for Solving the Discrete Alternative Multiple-Criteria Problem. Journal of the Operational Research Society, 42, 5, 383–392.Google Scholar
  28. [28]
    Ulungu E.L. and Teghem J. (1994). Multiobjective Combinatorial Optimization Problems: A Survey. Journal of Multi-Criteria Decision Analysis, 3, 83–101.CrossRefGoogle Scholar
  29. [29]
    Ulungu E.L., Teghem J., Fortemps Ph., Tuyttens (1999). MOSA method: a toll for solving multiobjective combinatorial optimization problems. Journal of Multi-Criteria Decision Analysis, 8, 221–236.CrossRefGoogle Scholar
  30. [30]
    Wierzbicki A.P. (1980), The use of reference objective in Multiobjective Optimization. In: Fandel G. and Gal T. (eds.) Multiple Criteria Decision Making, Theory and Application, Springer-Verlag, Berlin, 468–486.Google Scholar
  31. [31]
    Wierzbicki A.P. (1986), On the completeness and constructiveness of parametric characterization to vector optimization problems. OR Spektrum, 8, 73–87.CrossRefGoogle Scholar
  32. [32]
    Zionts S. (1981). A Multiple Criteria Method for Choosing among Discrete Alternatives. EJOR, 7, 1, 143–147CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Andrzej Jaszkiewicz
    • 1
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland

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