An Improved Central Force Optimization Algorithm for Multimodal Optimization

This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient

An Improved Central Force Optimization Algorithm for Multimodal Optimization

This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient

A new approach to particle swarm optimization algorithm

Particularly interesting group consists of algorithms that implement co-evolution or co-operation in natural environments, giving much more powerful implementations. The main aim is to obtain the algorithm which operation is not influenced by the environment. An unusual look at optimization algorithms made it possible to develop a new algorithm and its metaphors define for two groups of algorithms. These studies concern the particle swarm optimization algorithm as a model of predator and prey. New properties of the algorithm resulting from the co-operation mechanism that determines the operation of algorithm and significantly reduces environmental influence have been shown. Definitions of functions of behavior scenarios give new feature of the algorithm. This feature allows self controlling the optimization process. This approach can be successfully used in computer games. Properties of the new algorithm make it worth of interest, practical application and further research on its development. This study can be also an inspiration to search other solutions that implementing co-operation or co-evolution.Angeline, P. (1998). Using selection to improve particle swarm optimization. In Proceedings of the IEEE congress on evolutionary computation, Anchorage (pp. 84–89).Arquilla, J., & Ronfeldt, D. (2000). Swarming and the future of conflict, RAND National Defense Research Institute, Santa Monica, CA, US.Bessaou, M., & Siarry, P. (2001). A genetic algorithm with real-value coding to optimize multimodal continuous functions. Structural and Multidiscipline Optimization, 23, 63–74.Bird, S., & Li, X. (2006). Adaptively choosing niching parameters in a PSO. In Proceedings of the 2006 genetic and evolutionary computation conference (pp. 3–10).Bird, S., & Li, X. (2007). Using regression to improve local convergence. In Proceedings of the 2007 IEEE congress on evolutionary computation (pp. 592–599).Blackwell, T., & Bentley, P. (2002). Dont push me! Collision-avoiding swarms. In Proceedings of the IEEE congress on evolutionary computation, Honolulu (pp. 1691–1696).Brits, R., Engelbrecht, F., & van den Bergh, A. P. (2002). Solving systems of unconstrained equations using particle swarm optimization. In Proceedings of the 2002 IEEE conference on systems, man, and cybernetics (pp. 102–107).Brits, R., Engelbrecht, A., & van den Bergh, F. (2002). A niching particle swarm optimizer. In Proceedings of the fourth asia-pacific conference on simulated evolution and learning (pp. 692–696).Chelouah, R., & Siarry, P. (2000). A continuous genetic algorithm designed for the global optimization of multimodal functions. Journal of Heuristics, 6(2), 191–213.Chelouah, R., & Siarry, P. (2000). Tabu search applied to global optimization. European Journal of Operational Research, 123, 256–270.Chelouah, R., & Siarry, P. (2003). Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima function. European Journal of Operational Research, 148(2), 335–348.Chelouah, R., & Siarry, P. (2005). A hybrid method combining continuous taboo search and Nelder–Mead simplex algorithms for the global optimization of multiminima functions. European Journal of Operational Research, 161, 636–654.Chen, T., & Chi, T. (2010). On the improvements of the particle swarm optimization algorithm. Advances in Engineering Software, 41(2), 229–239.Clerc, M., & Kennedy, J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), 58–73.Fan, H., & Shi, Y. (2001). Study on Vmax of particle swarm optimization. In Proceedings of the workshop particle swarm optimization, Indianapolis.Gao, H., & Xu, W. (2011). Particle swarm algorithm with hybrid mutation strategy. Applied Soft Computing, 11(8), 5129–5142.Gosciniak, I. (2008). Immune algorithm in non-stationary optimization task. In Proceedings of the 2008 international conference on computational intelligence for modelling control & automation, CIMCA ’08 (pp. 750–755). Washington, DC, USA: IEEE Computer Society.He, Q., & Wang, L. (2007). An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engineering Applications of Artificial Intelligence, 20(1), 89–99.Higashitani, M., Ishigame, A., & Yasuda, K., (2006). Particle swarm optimization considering the concept of predator–prey behavior. In 2006 IEEE congress on evolutionary computation (pp. 434–437).Higashitani, M., Ishigame, A., & Yasuda, K. (2008). Pursuit-escape particle swarm optimization. IEEJ Transactions on Electrical and Electronic Engineering, 3(1), 136–142.Hu, X., & Eberhart, R. (2002). Multiobjective optimization using dynamic neighborhood particle swarm optimization. In Proceedings of the evolutionary computation on 2002. CEC ’02. Proceedings of the 2002 congress (Vol. 02, pp. 1677–1681). Washington, DC, USA: IEEE Computer Society.Hu, X., Eberhart, R., & Shi, Y. (2003). Engineering optimization with particle swarm. In IEEE swarm intelligence symposium, SIS 2003 (pp. 53–57). Indianapolis: IEEE Neural Networks Society.Jang, W., Kang, H., Lee, B., Kim, K., Shin, D., & Kim, S. (2007). Optimized fuzzy clustering by predator prey particle swarm optimization. In IEEE congress on evolutionary computation, CEC2007 (pp. 3232–3238).Kennedy, J. (2000). Stereotyping: Improving particle swarm performance with cluster analysis. In Proceedings of the 2000 congress on evolutionary computation (pp. 1507–1512).Kennedy, J., & Mendes, R. (2002). Population structure and particle swarm performance. In IEEE congress on evolutionary computation (pp. 1671–1676).Kuo, H., Chang, J., & Shyu, K. (2004). A hybrid algorithm of evolution and simplex methods applied to global optimization. Journal of Marine Science and Technology, 12(4), 280–289.Leontitsis, A., Kontogiorgos, D., & Pange, J. (2006). Repel the swarm to the optimum. Applied Mathematics and Computation, 173(1), 265–272.Li, X. (2004). Adaptively choosing neighborhood bests using species in a particle swarm optimizer for multimodal function optimization. In Proceedings of the 2004 genetic and evolutionary computation conference (pp. 105–116).Li, C., & Yang, S. (2009). A clustering particle swarm optimizer for dynamic optimization. In Proceedings of the 2009 congress on evolutionary computation (pp. 439–446).Liang, J., Suganthan, P., & Deb, K. (2005). Novel composition test functions for numerical global optimization. In Proceedings of the swarm intelligence symposium [Online]. Available: .Liang, J., Qin, A., Suganthan, P., & Baskar, S. (2006). Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Transactions on Evolutionary Computation, 10(3), 281–295.Lovbjerg, M., & Krink, T. (2002). Extending particle swarm optimizers with self-organized criticality. In Proceedings of the congress on evolutionary computation, Honolulu (pp. 1588–1593).Lung, R., & Dumitrescu, D. (2007). A collaborative model for tracking optima in dynamic environments. In Proceedings of the 2007 congress on evolutionary computation (pp. 564–567).Mendes, R., Kennedy, J., & Neves, J. (2004). The fully informed particle swarm: simpler, maybe better. IEEE Transaction on Evolutionary Computation, 8(3), 204–210.Miranda, V., & Fonseca, N. (2002). New evolutionary particle swarm algorithm (EPSO) applied to voltage/VAR control. In Proceedings of the 14th power systems computation conference, Seville, Spain [Online] Available: .Parrott, D., & Li, X. (2004). A particle swarm model for tracking multiple peaks in a dynamic environment using speciation. In Proceedings of the 2004 congress on evolutionary computation (pp. 98–103).Parrott, D., & Li, X. (2006). Locating and tracking multiple dynamic optima by a particle swarm model using speciation. In IEEE transaction on evolutionary computation (Vol. 10, pp. 440–458).Parsopoulos, K., & Vrahatis, M. (2004). UPSOA unified particle swarm optimization scheme. Lecture Series on Computational Sciences, 868–873.Passaroand, A., & Starita, A. (2008). Particle swarm optimization for multimodal functions: A clustering approach. Journal of Artificial Evolution and Applications, 2008, 15 (Article ID 482032).Peram, T., Veeramachaneni, K., & Mohan, C. (2003). Fitness-distance-ratio based particle swarm optimization. In Swarm intelligence symp. (pp. 174–181).Sedighizadeh, D., & Masehian, E. (2009). Particle swarm optimization methods, taxonomy and applications. International Journal of Computer Theory and Engineering, 1(5), 1793–8201.Shi, Y., & Eberhart, R. (2001). Particle swarm optimization with fuzzy adaptive inertia weight. In Proceedings of the workshop particle swarm optimization, Indianapolis (pp. 101–106).Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. In Proceedings of IEEE International Conference on Evolutionary Computation (pp. 69–73). Washington, DC, USA: IEEE Computer Society.Thomsen, R. (2004). Multimodal optimization using crowding-based differential evolution. In Proceedings of the 2004 congress on evolutionary computation (pp. 1382–1389).Trojanowski, K., & Wierzchoń, S. (2009). Immune-based algorithms for dynamic optimization. Information Sciences, 179(10), 1495–1515.Tsoulos, I., & Stavrakoudis, A. (2010). Enhancing PSO methods for global optimization. Applied Mathematics and Computation, 216(10), 2988–3001.van den Bergh, F., & Engelbrecht, A. (2004). A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8, 225–239.Wolpert, D., & Macready, W. (1997). No free lunch theorems for optimization. IEEE Transaction on Evolutionary Computation, 1(1), 67–82.Xie, X., Zhang, W., & Yang, Z. (2002). Dissipative particle swarm optimization. In Proceedings of the congress on evolutionary computation (pp. 1456–1461).Yang, S., & Li, C. (2010). A clustering particle swarm optimizer for locating and tracking multiple optima in dynamic environments. In IEEE Trans. on evolutionary computation (Vol. 14, pp. 959–974).Kuo, H., Chang, J., & Liu, C. (2006). Particle swarm optimization for global optimization problems. Journal of Marine Science and Technology, 14(3), 170–181