Globally convergent modifications of particle swarm optimization for unconstrained optimization

We focus on the solution of a class of unconstrained optimization problems, wherethe evaluation of the objective function is possibly costly and the use of exact algorithmsmay require a too large computational burden. Several real applications, includedin the latter class, claim for optimization methods where the derivatives of theobjective function are unavailable and/or the objective function must be treated as a'black-box'. Many design optimization [15] and shape optimization [11, 26] problemsbelong to the latter class; moreover, the derivatives computed with finite differencesmay be much inaccurate. Here, expensive simulations provide information to the optimizer,so that each function evaluation could require up to several CPU-hours. On theother hand, for continuously differentiable functions the use of heuristics may yieldinadequate and/or unsatisfactory results [17].We consider here the evolutionary Particle Swarm Optimization (PSO) algorithm [12].We introduce some globally convergent modifications of PSO by drawing our inspirationfrom [14], so that sequences of points are generated which admit stationary limitpoints for the objective function. The latter result is carried out for a generalized PSOscheme, where suitable ranges of the parameters are identified in order to possiblyavoid diverging trajectories for the particles [1]. © 2010 Nova Science Publishers, Inc. All rights reserved.