Abstract
This work introduces a hybrid PSO algorithm which includes perturbation operators to keep population diversity. A new neighborhood structure for Particle Swarm Optimization called Singly-Linked Ring is implemented. The approach proposes a neighborhood similar to the ring structure, but which has an innovative neighbors selection. The objective is to avoid the premature convergence into local optimum. A special technique to handle equality constraints with low side effects on the diversity is the main feature of this contribution. Two perturbation operators are used to improve the exploration, applying the modification only in the particle best population.We show through a number of experiments how, by keeping the selection pressure on a decreasing fraction of the population, COPSO can consistently solve a benchmark of constrained optimization problems.
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References
Angeline, P.J.: Evolutionary Optimization versus Particle Swarm Optimization: philosophy and performance differences. In: Porto, V.W., Waagen, D. (eds.) EP 1998. LNCS, vol. 1447, pp. 601–610. Springer, Heidelberg (1998)
Blackwell, T.M.: Particle swarms and population diversity. Soft Computing 9(11), 793–802 (2005)
Cagnina, L.C., Esquivel, S.C., Coello, C.A.: A particle swarm optimizer for constrained numerical optimization. In: Proceedings of the 9th International Conference - Parallel problem Solving from Nature, PPSN IX, pp. 910–919 (2006)
Carlisle, A., Dozier, G.: Adapting Particle Swarm Optimization to Dynamic Environments. In: Proceedings of the International Conference on Artificial Intelligence, ICAI 2000, pp. 429–434 (2000)
Coath, G., Halgamuge, S.K.: A comparison of Constraint-Handling Methods for the Application of Particle Swarm Optimization to Constrained Nonlinear Optimization Problems. In: Proceedings of the 2003 Congress on Evolutionary Computation, pp. 2419–2425. IEEE Press, Los Alamitos (2003)
Das, S., Konar, A., Chakraborty, U.K.: Improving particle swarm optimization with differentially perturbed velocity. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 177–184. ACM Press, New York (2005)
Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Appplied Mechanics and Engineering 186(2-4), 311–338 (2000)
Eberhart, R., Shi, Y.: Comparison between genetic algorithms and particle swarm optimization. In: Porto, V.W., Waagen, D. (eds.) EP 1998. LNCS, vol. 1447, pp. 611–616. Springer, Heidelberg (1998)
Eberhart, R., Dobbins, R., Simpson, P.: Computational Intelligence PC Tools. Academic Press Professional, London (1996)
Fogel, D.: An Introduction to Simulated Evolutionary Optimization. IEEE Transaction on Neural Networks 5(1), 3–14 (1994)
Hamida, S.B., Petrowski, A.: The need for improving the exploration operators for constrained optimization problems. In: Proceedings of the Congress on Evolutionary Computation, pp. 1176–1183. IEEE Press, Los Alamitos (2000)
He, S., Prempain, E., Wu, Q.H.: An Improved Particle Swarm Optimizer for Mechanical Design Optimization Problems. Engineering Optimization 36(5), 585–605 (2004)
Hernandez-Aguirre, A., Botello, S., Coello, C.: PASSSS: An implementation of a novel diversity strategy to handle constraints. In: Proceedings of the 2004 Congress on Evolutionary Computation CEC 2004, pp. 403–410. IEEE Press, Los Alamitos (2004)
Hernandez-Aguirre, A., Botello, S., Coello, C., Lizarraga, G., Mezura, E.: Handling constraints using multiobjective optimization concepts. International Journal for Numerical Methods in Engineering 59(13), 1989–2017 (2004)
Hernández, A., Muñoz, A., Villa, E., Botello, S.: COPSO: Constrained Optimization via PSO Algorithm. Technical Report of the Computer Sciences Department, Centro de Investigación en Matemáticas, Guanajuato, México (2007), http://www.cimat.mx/reportes/enlinea/I-07-04.pdf
Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Hu, X., Eberhart, R.: Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization. In: Proceedings of the 6th World Multiconference on Systemics, Cybernetics and Informatics, SCI 2002, p. IIIS (2002)
Hu, X., Eberhart, R., Shi, Y.: Engineering optimization with particle swarm. In: Proceedings of the IEEE Swarm Intelligence Symposium, pp. 53–57. IEEE Press, Los Alamitos (2003)
Kennedy, J.: The Particle Swarm: Social Adaptation of Knowledge. In: Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 303–308. IEEE Press, Los Alamitos (1997)
Kennedy, J.: Bare Bones Particle Swarms. In: IEEE Swarm Intelligence Symposium, pp. 80–87. IEEE Press, Los Alamitos (2003)
Kennedy, J., Eberhart, R.: The Particle Swarm: Social Adaptation in Information-Processing Systems. McGraw-Hill, London (1999)
Kennedy, J., Mendes, R.: Population Structure and Particle Swarm Performance. In: Proceedings of the 2002 Congress on Evolutionary Computation, pp. 1671–1676. IEEE Press, Los Alamitos (2002)
Krink, T., Vesterstrom, J.S., Riget, J.: Particle Swarm Optimization with Spatial Particle Extension. In: Proceedings of the 2002 Congress on Evolutionary Computation, pp. 1474–1479. IEEE Press, Los Alamitos (2002)
Liang, J., Runarsson, T., Mezura-Montes, E., Clerc, M., Suganthan, P., Coello, C., Deb, K.: Problem Definitions and Evaluation Criteria for the CEC 2006. Special Session on Constrained Real-Parameter Optimization, Technical Report (2006)
Lu, H., Chen, W.: Dynamic-objective particle swarm optimization for constrained optimization problems. Journal of Combinatorial Optimization 12(4), 408–418 (2006)
Lvbjerg, M., Rasmussen, T., Krink, T.: Hybrid particle swarm optimiser with breeding and subpopulations. In: Proceedings of the 2001 Genetic and Evolutionary Computation Conference (2001)
Mezura, E.: Alternatives to Handle Constraints in Evolutionary Optimization. CINVESTAV-IPN, D.F., Mexico (2004)
Mezura, E., Coello, C.: Identifying on-line behavior and some sources of difficulty in two competitive approaches for constrained optimization. In: Proceedings of the Conference on Evolutionary Computation, CEC 2005, pp. 56–63. IEEE Press, Los Alamitos (2005)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Germany (1994)
Muñoz, A., Hernández, A., Villa, E.: Constrained optimization via particle evolutionary swarm optimization algorithm (PESO). In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2005, pp. 209–216. Association for Computing Machinery (2005)
Parsopoulos, K., Vrahatis, M.: Particle swarm optimization method for constrained optimization problems. Intelligent Technologies - Theory and Application: New Trends in Intelligent Technologies 76, 214–220 (2002)
Parsopoulos, K., Vrahatis, M.: Unified Particle Swarm Optimization for Solving Constrained Engineering Optimization Problems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 582–591. Springer, Heidelberg (2005)
Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A practical approach to global optimization. Springer, Berlin (2005)
Runarsson, T.P., Yao, X.: Stochastic Ranking for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation 4(3), 284–294 (2000)
Runarsson, T.P., Yao, X.: Search Biases in Constrained Evolutionary Optimization. IEEE Transactions on Systems, Man and Cybernetics - Part C: Applications and Reviews 35(2), 233–243 (2005)
Settles, M., Soule, T.: Breeding Swarms: A GA/PSO Hybrid. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 161–168. ACM Press, New York (2005)
Storn, R.: System Design by Constraint Adaptation and Differential Evolution. IEEE Transactions on Evolutionary Computation 3(1), 22–34 (1999)
Storn, R., Price, K.: Differential Evolution - A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012, International Computer Science Institute (1995)
Toscano, G., Coello, C.: A Constraint-Handling Mechanism for Particle Swarm Optimization. In: Proceedings of the 2004 Congress on Evolutionary Computation, pp. 1396–1403. IEEE Press, Los Alamitos (2004)
van den Bergh, F.: An Analysis of Particle Swarm Optimizers. University of Pretoria, South Africa (2002)
Zhang, J., Xie, F.: DEPSO: Hybrid Particle Swarm with Differential Evolution Operator. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics, pp. 3816–3821. IEEE Press, Los Alamitos (2003)
Zhang, W., Xie, X., Bi, D.: Handling boundary constraints for numerical optimization by Particle Swarm flying in periodic search space. In: Proceedings of the 2004 Congress on Evolutionary Computation, pp. 2307–2311. IEEE Press, Los Alamitos (2004)
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Zavala, A.E.M., Aguirre, A.H., Diharce, E.R.V. (2009). Continuous Constrained Optimization with Dynamic Tolerance Using the COPSO Algorithm. In: Mezura-Montes, E. (eds) Constraint-Handling in Evolutionary Optimization. Studies in Computational Intelligence, vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00619-7_1
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DOI: https://doi.org/10.1007/978-3-642-00619-7_1
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