A Multi-objective Particle Swarm Optimizer Hybridized with Scatter Search

  • Luis V. Santana-Quintero
  • Noel Ramírez
  • Carlos Coello Coello
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4293)


This paper presents a new multi-objective evolutionary algorithm which consists of a hybrid between a particle swarm optimization (PSO) approach and scatter search. The main idea of the approach is to combine the high convergence rate of the particle swarm optimization algorithm with a local search approach based on scatter search. We propose a new leader selection scheme for PSO, which aims to accelerate convergence. Upon applying PSO, scatter search acts as a local search scheme, improving the spread of the nondominated solutions found so far. Thus, the hybrid constitutes an efficient multi-objective evolutionary algorithm, which can produce reasonably good approximations of the Pareto fronts of multi-objective problems of high dimensionality, while only performing 4,000 fitness function evaluations. Our proposed approach is validated using ten standard test functions commonly adopted in the specialized literature. Our results are compared with respect to a multi-objective evolutionary algorithm that is representative of the state-of-the-art in the area: the NSGA-II.


Pareto Front Multiobjective Optimization Scatter Search Nondominated Solution Multiobjective Evolutionary Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems, May 2002. Kluwer Academic Publishers, New York (2002)MATHGoogle Scholar
  2. 2.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)MATHGoogle Scholar
  3. 3.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  4. 4.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multiobjective Optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization. Theoretical Advances and Applications, pp. 105–145. Springer, USA (2005)Google Scholar
  5. 5.
    Eshelman, L.J., Schaffer, J.D.: Real-coded Genetic Algorithms and Interval-Schemata. In: Darrell Whitley, L. (ed.) Foundations of Genetic Algorithms 2, pp. 187–202. Morgan Kaufmann Publishers, California (1993)Google Scholar
  6. 6.
    Glover, F.: Heuristic for integer programming using surrogate constraints. Decision Sciences 8, 156–166 (1977)CrossRefGoogle Scholar
  7. 7.
    Glover, F.: Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). Discrete Applied Mathematics 49(1-3), 231–255 (1994)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    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, pp. 13–54. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers, California (2001)Google Scholar
  10. 10.
    Kursawe, F.: A Variant of Evolution Strategies for Vector Optimization. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 193–197. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  11. 11.
    Laguna, M., Martí, R.: Scatter Search: Methodology and Implementations in C. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  12. 12.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation 10(3), 263–282 (fall, 2002)CrossRefGoogle Scholar
  13. 13.
    Mostaghim, S., Teich, J.: Strategies for Finding Good Local Guides in Multi-objective Particle Swarm Optimization (MOPSO). In: 2003 IEEE SIS Proceedings, Indianapolis, USA, April 2003, pp. 26–33. IEEE Service Center, Los Alamitos (2003)Google Scholar
  14. 14.
    Reyes-Sierra, M., Coello Coello, C.A.: Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art. International Journal of Computational Intelligence Research 2(3), 287–308 (2006)MathSciNetGoogle Scholar
  15. 15.
    Van Veldhuizen, D.A.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering. Air Force Institute of Technology, Wright-Patterson AFB, Ohio (May 1999)Google Scholar
  16. 16.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (summer, 2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Luis V. Santana-Quintero
    • 1
  • Noel Ramírez
    • 1
  • Carlos Coello Coello
    • 1
  1. 1.CINVESTAV-IPN, Electrical Engineering DepartmentMéxico D.F.México

Personalised recommendations