New Ideas in Applying Scatter Search to Multiobjective Optimization

  • Antonio J. Nebro
  • Francisco Luna
  • Enrique Alba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3410)


This paper elaborates on new ideas of a scatter search algorithm for solving multiobjective problems. Our approach adapts the well-known scatter search template for single objective optimization to the multiobjective field. The result is a simple and new metaheuristic called SSMO, which incorporates typical concepts from the multiobjective optimization domain such as Pareto dominance, crowding, and Pareto ranking. We evaluate SSMO with both constrained and unconstrained problems and compare it against NSGA-II. Preliminary results indicate that scatter search is a promising approach for multiobjective optimization.


Pareto Front Multiobjective Optimization Scatter Search Nondominated Solution Multiobjective Problem 
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  1. 1.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)CrossRefGoogle Scholar
  2. 2.
    Knowles, J., Corne, D.: The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Multiobjective Optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, Piscataway, NJ, pp. 9–105. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  3. 3.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report 103, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (2001)Google Scholar
  4. 4.
    Coello, C.A., Toscano, G.: Multiobjective Optimization Using a Micro-Genetic Algorithm. In: GECCO-2001, pp. 274–282 (2001)Google Scholar
  5. 5.
    Glover, F., Laguna, M., Martí, R.: Fundamentals of Scatter Search and Path Relinking. Control and Cybernetics 29, 653–684 (2000)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Beausoleil, R.P.: MOSS: Multiobjective Scatter Search Applied to Nonlinear Multiple Criteria Optimization. To appear in the European Journal of Operational Research (2004)Google Scholar
  7. 7.
    Caballero, R., Laguna, M., Molina, J., Martí, R.: SSPMO: A Scatter Search Procedure for Non-Linear Multiobjective Optimization. Submitted to INFORMS Journal on Computing (2004)Google Scholar
  8. 8.
    da Silva, C.G., Clímaco, J., Figueira, J.: A Scatter Search Method for the Bi-Criteria Multi-Dimensional {0,1}-Knapsack Problem using Surrogate Relaxation. Journal of Mathematical Modelling and Algorithms 3, 183–208 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Glover, F.: A Template for Scatter Search and Path Relinking. In: Hao, J.-K., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds.) AE 1997. LNCS, vol. 1363. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Glover, F., Laguna, M., Martí, R.: Scatter Search. In: Ghosh, A., Tsutsui, S. (eds.) Advances in Evolutionary Computing: Theory and Applications. Springer, Heidelberg (2003)Google Scholar
  11. 11.
    Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, Dordrecht (2002)zbMATHGoogle Scholar
  12. 12.
    Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)zbMATHGoogle Scholar
  13. 13.
    Schaffer, J.D.: Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In: Grefensttete, J. (ed.) First International Conference on Genetic Algorithms, Hillsdale, NJ, pp. 93–100 (1987)Google Scholar
  14. 14.
    Fonseca, C.M., Flemming, P.J.: Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms - Part II: Application Example. IEEE Transactions on System, Man, and Cybernetics 28, 38–47 (1998)CrossRefGoogle Scholar
  15. 15.
    Kursawe, F.: A Variant of Evolution Strategies for Vector Optimization. In: Schwefel, H., Männer, R. (eds.) Parallel Problem Solving for Nature, pp. 193–197. Springer, Berlin (1990)Google Scholar
  16. 16.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. IEEE Transactions on Evolutionary Computation 8, 173–195 (2000)Google Scholar
  17. 17.
    Osyczka, A., Kundo, S.: A New Method to Solve Generalized Multicriteria Optimization Problems Using a Simple Genetic Algorithm. Structural Optimization 10, 94–99 (1995)CrossRefGoogle Scholar
  18. 18.
    Tanaka, M., Watanabe, H., Furukawa, Y., Tanino, T.: GA-Based Decision Support System for Multicriteria Optimization. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, vol. 2, pp. 1556–1561 (1995)Google Scholar
  19. 19.
    Srinivas, N., Deb, K.: Multiobjective Function Optimization Using Nondominated Sorting Genetic Algorithms. Evolutionary Computation 2, 221–248 (1995)CrossRefGoogle Scholar
  20. 20.
    Kurpati, A., Azarm, S., Wu, J.: Constraint Handling Improvements for Multi-Objective Genetic Algorithms. Structural and Multidisciplinary Optimization 23, 204–213 (2002)CrossRefGoogle Scholar
  21. 21.
    Montgomery, D.C.: Design and Analysis of Experiments, 3rd edn. John Wiley, New York (1991)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Antonio J. Nebro
    • 1
  • Francisco Luna
    • 1
  • Enrique Alba
    • 1
  1. 1.Departamento de Lenguajes y Ciencias de la ComputaciónE.T.S. Ingeniería InformáticaMálagaSpain

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