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Dynamic system analysis and initial particles position in Particle Swarm Optimization

This paper focuses on a solution technique for global optimization problems, where the objective function value is possibly computed by the numerical solution of a PDE system. The nature of these optimization problems is that of a ‘blackbox’ type, where expensive simulations provide information to the optimizer, and each function evaluation could require several CPU-hours. The paper considers the evolutionary Particle Swarm Optimization (PSO) algorithm, for the minimization of a nonlinear function in the global optimization frameworks described. We reformulate the standard iteration of PSO [10], [3] into a linear dynamic system. Then, the latter is investigated in order to provide indications for the assessment of the initial particles position. We carry out our analysis on a generalized PSO iteration, which includes the standard one proposed in the literature. Therefore, our results perfectly apply to standard PSO too, without any modifications. In our scheme the path of any particle is possibly affected by the trajectories of all the other particles in the swarm. Our preliminary numerical experience, over a set of 35 standard test problems from the literature, confirms the theoretical analysis.