Extending the Speed-Constrained Multi-objective PSO (SMPSO) with Reference Point Based Preference Articulation

  • Antonio J. NebroEmail author
  • Juan J. Durillo
  • José García-Nieto
  • Cristóbal Barba-González
  • Javier Del Ser
  • Carlos A. Coello Coello
  • Antonio Benítez-Hidalgo
  • José F. Aldana-Montes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11101)


The Speed-constrained Multi-objective PSO (SMPSO) is an approach featuring an external bounded archive to store non-dominated solutions found during the search and out of which leaders that guide the particles are chosen. Here, we introduce SMPSO/RP, an extension of SMPSO based on the idea of reference point archives. These are external archives with an associated reference point so that only solutions that are dominated by the reference point or that dominate it are considered for their possible addition. SMPSO/RP can manage several reference point archives, so it can effectively be used to focus the search on one or more regions of interest. Furthermore, the algorithm allows interactively changing the reference points during its execution. Additionally, the particles of the swarm can be evaluated in parallel. We compare SMPSO/RP with respect to three other reference point based algorithms. Our results indicate that our proposed approach outperforms the other techniques with respect to which it was compared when solving a variety of problems by selecting both achievable and unachievable reference points. A real-world application related to civil engineering is also included to show up the real applicability of SMPSO/RP.


Multi-objective optimization SMPSO Decision making Reference point 



This work has been partially funded by Grants TIN2017-86049-R (Spanish Ministry of Education and Science) and P12-TIC-1519 (Plan Andaluz de Investigación, Desarrollo e Innovación). Cristóbal Barba-González is supported by Grant BES-2015-072209 (Spanish Ministry of Economy and Competitiveness). José García-Nieto is the recipient of a Post-Doctoral fellowship of “Captación de Talento para la Investigación” Plan Propio at Universidad de Málaga. Javier Del Ser thanks the Basque Government for its funding support through the EMAITEK program. Carlos A. Coello Coello is supported by CONACyT project no. 221551.


  1. 1.
    Coello Coello, C., Lamont, G., van Veldhuizen, D.: Multi-Objective Optimization Using Evolutionary Algorithms, 2nd edn. Wiley, Hoboken (2007)zbMATHGoogle Scholar
  2. 2.
    Coello Coello, C.: Handling preferences in evolutionary multiobjective optimization: a survey. In: Proceedings of the IEEE Conference on Evolutionary Computation, ICEC, vol. 1, pp. 30–37 (2000)Google Scholar
  3. 3.
    Nebro, A., Durillo, J., García-Nieto, J., Coello Coello, C., Luna, F., Alba, E.: SMPSO: a new PSO-based metaheuristic for multi-objective optimization. In: IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making, MCDM 2009, pp. 66–73. IEEE Press (2009)Google Scholar
  4. 4.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  5. 5.
    Durillo, J.J., Nebro, A.J.: jMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760–771 (2011)CrossRefGoogle Scholar
  6. 6.
    Ruiz, A., Saborido, R., Luque, M.: A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm. J. Glob. Optim. 62(1), 101–129 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Branke, J.: MCDA and multiobjective evolutionary algorithms. In: Greco, S., Ehrgott, M., Figueira, J. (eds.) Multiple Criteria Decision Analysis. ISOR, vol. 233, pp. 977–1008. Springer, New York (2016). Scholar
  8. 8.
    Li, L., Wang, Y., Trautmann, H., Jing, N., Emmerich, M.: Multiobjective evolutionary algorithms based on target region preferences. Swarm Evol. Comput. 40, 196–215 (2018)CrossRefGoogle Scholar
  9. 9.
    Wierzbicki, A.P.: Reference point approaches. In: Gal, T., Stewart, T.J., Hanne, T. (eds.) Multicriteria Decision Making. ISOR, vol. 21, pp. 237–275. Springer, Boston (1999). Scholar
  10. 10.
    Molina, J., Santana, L., Hernández-Díaz, A., Coello Coello, C., Caballero, R.: g-dominance: Reference point based dominance for multiobjective metaheuristics. Eur. J. Oper. Res. 197(2), 685–692 (2009)CrossRefGoogle Scholar
  11. 11.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)Google Scholar
  12. 12.
    Sierra, M.R., Coello Coello, C.A.: Improving PSO-based multi-objective optimization using crowding, mutation and \(\epsilon \)-dominance. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 505–519. Springer, Heidelberg (2005). Scholar
  13. 13.
    Durillo, J., Nebro, A., Coello Coello, C., Garcia-Nieto, J., Luna, F., Alba, E.: A study of multiobjective metaheuristics when solving parameter scalable problems. IEEE Trans. Evol. Comput. 14(4), 618–635 (2010)CrossRefGoogle Scholar
  14. 14.
    Clerc, M., Kennedy, J.: The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6(1), 58–73 (2002)CrossRefGoogle Scholar
  15. 15.
    Nebro, A.J., Durillo, J.J., Vergne, M.: Redesigning the jMetal multi-objective optimization framework. In: Proceedings of the Companion of the Conference on Genetic and Evolutionary Computation (GECCO), pp. 1093–1100 (2015)Google Scholar
  16. 16.
    Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)CrossRefGoogle Scholar
  17. 17.
    Deb, K., Sundar, J., Ubay, B., Chaudhuri, S.: Reference point based multi-objective optimization using evolutionary algorithm. Int. J. Comput. Intell. Res. 2(6), 273–286 (2006)MathSciNetGoogle Scholar
  18. 18.
    Allmendinger, R., Li, X., Branke, J.: Reference point-based particle swarm optimization using a steady-state approach. In: Li, X., et al. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 200–209. Springer, Heidelberg (2008). Scholar
  19. 19.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar
  20. 20.
    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. AI&KP, pp. 105–145. Springer, London (2005). Scholar
  21. 21.
    Huband, S., Barone, L., While, L., Hingston, P.: A scalable multi-objective test problem toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 280–295. Springer, Heidelberg (2005). Scholar
  22. 22.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRefGoogle Scholar
  23. 23.
    Derrac, J., García, S., Molina, D., Herrera, F.: A practical tutorial on the use of non-parametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011)CrossRefGoogle Scholar
  24. 24.
    Zavala, G., Nebro, A.J., Luna, F., Coello Coello, C.: Structural design using multi-objective metaheuristics. Comparative study and application to a real-world problem. Struct. Multidiscip. Optim. 53(3), 545–566 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Antonio J. Nebro
    • 1
    Email author
  • Juan J. Durillo
    • 2
  • José García-Nieto
    • 1
  • Cristóbal Barba-González
    • 1
  • Javier Del Ser
    • 3
    • 4
    • 5
  • Carlos A. Coello Coello
    • 6
  • Antonio Benítez-Hidalgo
    • 1
  • José F. Aldana-Montes
    • 1
  1. 1.Dept. de Lenguajes y Ciencias de la ComputaciónUniversidad de MálagaMálagaSpain
  2. 2.Leibniz Supercomputing CentreMunichGermany
  3. 3.TECNALIA Research and InnovationDerioSpain
  4. 4.University of the Basque Country (UPV/EHU)BilbaoSpain
  5. 5.Basque Center for Applied Mathematics (BCAM)BilbaoSpain
  6. 6.Computer Science DepartmentCINVESTAV-IPN (Evolutionary Computation Group)Ciudad de MéxicoMexico

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