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CivilComp Proceedings
ISSN 17593433 CCP: 97
PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON SOFT COMPUTING TECHNOLOGY IN CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING Edited by: Y. Tsompanakis, B.H.V. Topping
Paper 42
Hybrid Algorithms Based on Particle Swarm Optimization and the Powell Method for Global Optimization A.T. Beck and W.J.S. Gomes
Department of Structural Engineering, University of São Paulo, São Carlos SP, Brazil A.T. Beck, W.J.S. Gomes, "Hybrid Algorithms Based on Particle Swarm Optimization and the Powell Method for Global Optimization", in Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", CivilComp Press, Stirlingshire, UK, Paper 42, 2011. doi:10.4203/ccp.97.42
Keywords: global optimization, hybrid optimization algorithms, particle swarm optimization, Powell method, heuristic algorithms, test functions.
Summary
In this paper, two hybrid autoregulated optimization algorithms are developed, combining two proposed variations of the particle swarm optimization (PSO) [1] algorithm with a modified Powell algorithm [2]. The PSO algorithm is used to cover the entire search space, identifying the region of the global minimum, while the mathematical algorithm, starting from a point inside this region, quickly reaches the global minimum. This strategy increases reliability in comparison with mathematical methods, because it is more likely to reach the global minimum, and increases efficiency in comparison with pure heuristic algorithms.
One known drawback of heuristic algorithms is the necessity for userdefined, problemdependent algorithmic parameters. In the present paper, two variations of the PSO algorithm are proposed, in order to make the algorithm performance less sensitive to userdefined parameters. In these variations, the particles are divided into four groups, each group using one set of algorithmic parameters. In one, more simple algorithm, these parameters are kept constant during all iterations. This increases the diversity of the swarm movement as a whole, since each group shows different behavior moving in a slightly different form. This algorithm is not truly autoregulated, but it is shown to be more robust and less sensitive to userdefined parameters. The second is an autoregulated algorithm, where the PSO parameters are updated following predefined rules, in an attempt to find an "optimal" set of parameters during problem solution. The two PSO variations developed use literaturesuggested parameters, requiring no special parameter definition by the user. The two PSO variations proposed in this paper are shown to be less likely to remain trapped in regions of local minima, hence to be more reliable than the original or the constricted PSO algorithms. The hybrid algorithms developed herein are employed in the solution of seven test problems from the literature. They are shown to be reliable and to outperform nine out of ten algorithms from the literature, including the ant colony and simulated annealing algorithms, especially for test functions with several local minima. Comparing the two algorithms developed in this paper, the autoregulated PSO algorithm is shown to perform better than the algorithm with constant parameters. In addition to the excellent results obtained with the algorithms developed, the general ideas presented in this paper can be used to develop several other hybrid algorithms, combining other heuristics with other mathematical programming algorithms. References
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