Initial Particles Position for PSO, in Bound Constrained Optimization

We consider the solution of bound constrained optimizationproblems, where we assume that the evaluation of the objective functionis costly, its derivatives are unavailable and the use of exact derivativefreealgorithms may imply a too large computational burden. There isplenty of real applications, e.g. several design optimization problems [1,2],belonging to the latter class, where the objective function must be treatedas a 'black-box' and automatic differentiation turns to be unsuitable.Since the objective function is often obtained as the result of a simulation,it might be affected also by noise, so that the use of finite differences maybe definitely harmful.In this paper we consider the use of the evolutionary Particle SwarmOptimization (PSO) algorithm, where the choice of the parameters isinspired by [4], in order to avoid diverging trajectories of the particles,and help the exploration of the feasible set. Moreover, we extend theideas in [4] and propose a specific set of initial particles position for thebound constrained problem.