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Particle Swarm Optimization with a Simplex Strategy to Avoid Getting Stuck on Local Optimum

Heuristic methods, for global optimization, have been receiving much interest in the last years, among which Particle Swarm Optimization (PSO) algorithm can be highlighted. However, the application of heuristic methods can lead to premature convergence. In this work, the addition of a step on the PSO algorithm is proposed. This new step, based in Nelder–Mead simplex search method (NM), consists of repositioning the current particle with global best solution, not for a better position, but away from the current nearest local optimum, to avoid getting stuck on this local optimum. There are other PSO-NM algorithms, but the one we are proposing, has a different strategy. The proposed algorithm was also tested with the repositioning strategy in other particles beyond the current global best particle, depending on the repositioning probability. To evaluate the effectiveness of the proposed methods, and study its better parameters, were used various test functions, and for each test function, various number of particles were used in combination with various probabilities of particles repositioning. A thousand runs were performed for each case, resulting in more than two millions runs. The computational studies showed that the repositioning of of global best particle increases the percentage of success on reaching the global best solution, but better results can be obtained applying the repositioning strategy to other particles with repositioning probabilities between 1–5%.