Abstract
In this paper we present a multi-start particle swarm optimization algorithm for the global optimization of a function subject to bound constraints. The procedure consists of three main steps. In the initialization phase, an opposition learning strategy is performed to improve the search efficiency. Then a variant of the adaptive velocity based on the differential operator enhances the optimization ability of the particles. Finally, a re-initialization strategy based on two diversity measures for the swarm is act in order to avoid premature convergence and stagnation. The strategy uses the super-opposition paradigm to re-initialize particles in the swarm. The algorithm has been evaluated on a set of 100 global optimization test problems. Comparisons with other global optimization methods show the robustness and effectiveness of the proposed algorithm.
Similar content being viewed by others
References
Ali M.M., Khompatraporn C., Zabinsky Z.B.: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J. Glob. Optim. 31, 635–672 (2005)
Angeline, P.: Evolutionary optimization versus particle swarm optimization: philosophy and performance differences. In: IEEE Press (Ed.) Proceedings of the Seventh Annual Conference on Evolutionary Programming, EP VII, vol. 1447. Lecture Notes in Computer Science, pp. 601–610 (1998)
Bartz-Beielstein T.: Experimental Research in Evolutionary Computation—The New Experimentalism. Springer, Berlin (2006)
Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: Proceedings of the 2007 IEEE Swarm Intelligence Symposium (SIS 2007), pp. 120–127 (2007)
Clerc, M.: The swarm and the queen: towards a deterministic adaptive particle swarm optimization. In: Proceedings of the Congress of Evolutionary Computation, vol. 3, pp. 1951–1957. Washington, DC (1999)
Das, S., Abraham, A., Konar, A.: Particle swarm optimization and differential evolution algorithms: technical analysis, applications and hybridization perspectives. In: Liu, Y., Sun, A., Loh, H.T., Lu, W.F., Lim, E.P. (eds.) Studies in Computational Intelligence (SCI), vol. 116, pp. 1–38. Springer, Berlin (2008)
Das, S., Konar, A., Chakraborty, U.K.: Particle swarm optimization with a differentially perturbed velocity. In: ACM-SIGEVO Proceedings of GECCO ’05, pp. 991–998. Washington, DC, USA (2005)
de Carvalho D.F., Bastos-Filho C.J.A.: Clan particle swarm optimization. Int. J. Intell. Comput. Cybern. 2(2), 197–227 (2009)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micromachine and Human Science, pp. 39–43. Nagoya, Japan (1995)
Eberhart, R.C., Shi, Y.: Comparison between genetic algorithms and particle swarm optimization. In: IEEE Press (Ed.) Proceedings of the Seventh Annual Conference on Evolutionary Programming, EP VII, vol. 1447. Lecture Notes in Computer Science, pp. 601–610 (1998)
Eberhart, R.C., Shi, Y.: Particle swarm optimization: developments, applications and resources. In: Proceedings of the IEEE Congress of Evolutionary Computation, pp. 81–86. Seoul, Korea (2001)
Evers, G.: An automatic regrouping mechanism to deal with stagnation in particle swarm optimization. Master’s thesis, Electrical Engeneering Department, The University of Texas-Pan American, Edinburg, TX (2009)
Finkel, D.E.: DIRECT: optimizaion algorithm user guide. North Carolina State University. http://www4.ncsu.edu/~definkel/research/index.html (2003)
Habibi, J., Zonouz, S.A., Saneei, M.: A hybrid PS-based optimization algorithm for solving traveling salesman problem. In: IEEE Symposium on Frontiers in Networking with Applications (FINA 2006), pp. 18–20. Vienna, Austria (2006)
Jabeen, H., Jalil, Z., Baig, A.R.: Opposition based initialization in particle swarm optimization (O-PSO). In: GECCO (Companion), pp. 2047–2052 (2009)
Jiao B., Lian Z., Gu X.: A dynamic inertia weight particle swarm optimization algorithm. Chaos Solitons Fractals 37, 698–705 (2008)
Kennedy, J.: Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: IEEE Press (Ed.) Proceedings of the 1999 Congress of Evolutionary Computation, vol. 3, pp. 1931–1938 (1999)
Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948. Piscataway, NJ (1995)
Krink, T., Vesterstrøm, J., Riget, J.: Particle swarm optimization with spatial particle extension. In: IEEE Press (Ed.) Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002, vol. 2, pp. 1474–1479 (2002)
Lopes, H.S., Coelho, L.S.: Particle swarm optimization with fast local search for the blind traveling salesman problem. In: Proceedings of Fifth International Conference on Hybrid Intelligent Systems (HIS’05), pp. 245–250. Rio de Janeiro, Brazil (2005)
Lu H., Chen W.: Self-adaptive velocity particle swarm optimization for solving constrained optimization problems. J. Glob. Optim. 31, 427–445 (2008)
Mishra, S.: Some new test functions for global optimization and performance of repulsive particle swarm method. MPRA Paper 2718, North-Eastern Hill University, Department of Economics, Shillong, India (2006)
Pant, M., Radha, T., Singh, V.P.: A simple diversity guided particle swarm optimization. In: IEEE Congress on Evolutionary Computation (CEC 2007), pp. 3294–3299. Singapore (2007)
Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution algorithms. In: IEEE Congress on Evolutionary Computation, pp. 7363–7370 (2006)
Rahnamayan S., Tizhoosh H.R., Salama M.M.A.: A novel population initialization method for accelerating evolutionary algorithms. Comput. Math. Appl. 53, 1605–1614 (2007)
Rahnamayan S., Tizhoosh H.R., Salama M.M.A.: Opposition versus randomness in soft computing techniques. Appl. Soft Comput. 8(2), 906–918 (2008)
Riget, J., Vesterstrøm, J.S.: A diversity-guided particle swarm optimizer—the ARPSO. Technical Report 2000-02, EVALife, Department of Computer Science, Aarhus, Denmark (2002)
Shahzad, F., Baig, A.R., Masood, S., Kamran, M., Naveed, N.: Opposition-based swarm optimization with velocity clamping (OVCPSO). In: Yu, W., Sanchez, E.N. (eds.) Advances in Computational Intelligence, volume 116/2009 of AISC. pp. 339–348. Springer, Berlin (2009)
Shi, Y., Eberhart, R.C.: Parameter selection in particle swarm optimization. In: Evolutionary Programming VII, vol. 1447. Lecture Notes in Computer Science, pp. 591–600. Springer, Berlin (1998)
Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: IEEE Press (Ed.) Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 69–73. Piscataway, NJ, USA (1998)
Shi Y., Eberhart R.C.: Monitoring of particle swarm optimization. Frontiers Comput. Sci. China. 3(1), 31–37 (2009)
Singh S.K., Borah M.: A comparative performance of swarm intelligence optimization method and evolutionary optimization method on some noisy numerical benchmark test problems. Int. J. Comput. Appl. Math. 4(1), 1–9 (2009)
Tizhoosh H.R.: Opposition-based reinforcement learning. J. Adv. Comput. Intell. Intell. Inf. 10(4), 578–585 (1998)
Tizhoosh, H.R., Hamid, R.: Opposition-based learning: a new scheme for machine intelligence. In: CIMCA ’05: Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, vol. 1 (CIMCA-IAWTIC’06), pp. 695–701. IEEE Computer Society, Washington, DC, USA (2005)
Tizhoosh, H.R., Ventresca, M., Rahnamayan, S.: Oppositional Concepts in Computational Intelligence, vol. 155 of Studies in Computational Intelligence, chapter Opposition-Based Computing, pp. 11–28. Springer, Berlin (2008)
Trelea I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003)
van den Bergh, F.: An analysis of particle swarm optimizers. Ph.D. thesis, Faculty of Natural and Agricultural Science, University of Pretoria, South Africa (2001)
van den Bergh, F., Engelbrecht, A.: A new locally convergent particle swarm optimizer. In: IEEE Press (Ed.) Proceedings of the IEEE Conference on Systems, Man, and Cybernetics, vol. 3, pp. 96–101 (2002)
Vaz A.I., Vicente L.N.: A particle swarm pattern search method for bound constrained global optimization. J. Glob. Optim. 33(2), 197–219 (2007)
Ventresca S., Rahnamayan S., Tizhoosh H.R.: A note on “Opposition versus randomness in soft computing techniques” [Appl. Soft Comput] 8(2) (2008) 906–918. Appl. Soft Comput. 10, 956–957 (2010)
Wang, H., Liu, Y., Zeng, S.: Opposition-based particle swarm optimization algorithm with Cauchy mutation. In: IEEE Congress on Evolutionary Computation (CEC 2007), pp. 4750–4756. Singapore (2007)
Muñoz Zavala, A.E., Aguirre, A.H., Villa Diharce, E.R.: Constrained optimization via particle evolutionary swarm optimization algorithm (PESO). In: GECCO ’05: Proceedings of the 2005 conference on Genetic and evolutionary computation, pp. 209–216. Washington, DC, USA (2005)
Muñoz Zavala A.E., Aguirre A.H., Villa Diharce E.R., Botello Rionda S.: Constrained optimization with an improved particle swarm optimization algorithm. Int. J. Intell. Comput. Cybern. 1(3), 425–453 (2008)
Zhan Z.H., Zhang J., Li Y., Chung H.S.H.: Adaptive particle swarm optimization. IEEE Trans. Syst. Man Cybern. 39(6), 1362–1381 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaucic, M. A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization. J Glob Optim 55, 165–188 (2013). https://doi.org/10.1007/s10898-012-9913-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-012-9913-4