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This paper proposes a new variant of the PSO algorithm named Complex Neighborhood Particle Swarm Optimizer (CNPSO) for solving global optimization problems. In the CNPSO, the neighborhood of the particles is organized through a complex network which is modified during the search process. This evolution of the topology seeks to improve the influence of the most successful particles and it is fine tuned for maintaining the scale-free characteristics of the network while the optimization is being performed. The use of a scale-free topology instead of the usual regular or global neighborhoods is intended to bring to the search procedure a better capability of exploring promising regions without a premature convergence, which would result in the procedure being easily trapped in a local optimum. The performance of the CNPSO is compared with the standard PSO on some well-known and high-dimensional benchmark functions, ranging from multimodal to plateau-like problems. In all the cases the CNPSO outperformed the standard PSO.