Abstract
Particle Swarm Optimization (PSO) is a bio-inspired metaheuristic that has been successfully adopted for single- and multi-objective optimization. Several studies show that the way in which particles are connected with each other (the swarm topology) influences PSO’s behavior. A few of these studies have focused on analyzing the influence of swarm topologies on the performance of Multi-objective Particle Swarm Optimizers (MOPSOs) using problems with two or three objectives. However, to the authors’ best knowledge such studies have not been done so far for many-objective optimization problems. This paper provides an analysis of the influence of the ring, star, lattice, wheel, and tree topologies on the performance of SMPSO (a well-known Pareto-based MOPSO) using many-objective problems. Based on these results, we also propose two MOPSOs that use a combination of topologies: SMPSO-SW and SMPSO-WS. Our experimental results show that SMPSO-SW is able to outperform SMPSO in most of the test problems adopted.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Although many-objective problems are those having more than 3 objectives, our experiments include test problems with 3 objectives to allow a more clear visualization of the effect of dimensionality increase in objective function space.
- 2.
Without loss of generality, we will assume only minimization problems.
References
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). (CEC 2002)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)
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, London (2005). https://doi.org/10.1007/1-84628-137-7_6
Figueiredo, E.M.N., Ludermir, T.B., Bastos-Filho, C.J.A.: Many objective particle swarm optimization. Inf. Sci. 374, 115–134 (2016)
Han, H., Lu, W., Zhang, L., Qiao, J.: Adaptive gradient multiobjective particle swarm optimization. IEEE Trans. Cybern. 48(11), 3067–3079 (2018)
Hardin, D., Saff, E.: Discretizing manifolds via minimum energy points. Not. Am. Math. Soc. 51(10), 1186–1194 (2004)
Kennedy, J.: Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC 1999), vol. 3, pp. 1931–1938, July 1999
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks (ICNN 1995), vol. 4, pp. 1942–1948 (1995)
Lin, Q., et al.: Particle swarm optimization with a balanceable fitness estimation for many-objective optimization problems. IEEE Trans. Evol. Comput. 22(1), 32–46 (2018)
McNabb, A., Gardner, M., Seppi, K.: An Exploration of topologies and communication in large particle swarms. In: 2009 IEEE Congress on Evolutionary Computation (CEC 2009), pp. 712–719, May 2009
Mendes, R.: Population topologies and their influence in particle swarm performance. Ph.D. thesis, Departamento de Informática, Escola de Engenharia, Universidade do Minho, April 2004
Nebro, A.J., Durillo, J.J., García-Nieto, J., Coello Coello, C.A., Luna, F., Alba, E.: SMPSO: a new PSO-based metaheuristic for multi-objective optimization. In: 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM 2009), pp. 66–73, March 2009
Pan, A., Wang, L., Guo, W., Wu, Q.: A diversity enhanced multiobjective particle swarm optimization. Inf. Sci. 436, 441–465 (2018)
Taormina, R., Chau, K.: Neural network river forecasting with multi-objective fully informed particle swarm optimization. J. Hydroinf. 17(1), 99–113 (2014)
Valencia-Rodríguez, D.C., Coello Coello, C.A.: A study of swarm topologies and their influence on the performance of multi-objective particle swarm optimizers. In: Bäck, T., et al. (eds.) PPSN 2020. LNCS, vol. 12270, pp. 285–298. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58115-2_20
Valencia-Rodríguez, D.C.: Estudio de topologías cumulares y su impacto en el desempeño de un optimizador mediante cúmulos de partículas para problemas multiobjetivo. Master’s thesis, Departamento de Computación, CINVESTAV-IPN, México, October 2019, http://delta.cs.cinvestav.mx/~ccoello/tesis/tesis-valencia.pdf.gz
Yamamoto, M., Uchitane, T., Hatanaka, T.: An experimental study for multi-objective optimization by particle swarm with graph based archive. In: Proceedings of SICE Annual Conference (SICE 2012), pp. 89–94, August 2012
Zhu, Q., et al.: An external archive-guided multiobjective particle swarm optimization algorithm. IEEE Trans. Cybern. 49(9), 2794–2808 (2017)
Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology (ETH), Zurich, Suiza, November 1999
Acknowledgements
The first author acknowledges support from CONACyT and CINVESTAV-IPN to pursue graduate studies in Computer Science. The second author acknowledges support from CONACyT grant no. 1920 and from a SEP-Cinvestav grant (application no. 4).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Valencia-Rodríguez, D.C., Coello Coello, C.A. (2021). The Influence of Swarm Topologies in Many-Objective Optimization Problems. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-72062-9_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-72061-2
Online ISBN: 978-3-030-72062-9
eBook Packages: Computer ScienceComputer Science (R0)