Initial Particles Position for PSO, in Bound Constrained Optimization

Abstract

Abstract. We consider the solution of bound constrained optimization problems, where we assume that the evaluation of the objective function is costly, its derivatives are unavailable and the use of exact derivativefree algorithms may imply a too large computational burden. There is plenty of real applications, e.g. several design optimization problems [1,2], belonging to the latter class, where the objective function must be treated as 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 may be definitely harmful.In this paper we consider the use of the evolutionary Particle Swarm Optimization (PSO) algorithm, where the choice of the parameters is inspired by [4], in order to avoid diverging trajectories of the particles, and help the exploration of the feasible set. Moreover, we extend the ideas in [4] and propose a specific set of initial particles position for the bound constrained problem.

Multi-disciplinary, community-oriented design of low-noise aircraft: the COSMA project

“…All the modules are dynamically linked to the multi-objective optimization engine, in charge of the search for the extrema of the objective functions. The optimization core implements two evolutionary global search methods: an original deterministic Particle Swarm Optimization (PSO) method [16] and the classic Multi-Objective Genetic Algorithm (MOGA) [17]. The interested reader can find additional details about the analysis methods adopted in FRIDA in [18,19].…”

“…The approach was based on the measure of the matching of the noise produced by the configuration under analysis with a previously defined weakly annoying sound [16]. The method has been applied here using the target sounds as reference sounds.…”

“…The method has been applied here using the target sounds as reference sounds. As in [16], the measure of the matching level, I M , has been defined as the L 2 -norm of the difference of the spectra of current and target sound, Sc and S t , evaluated over the duration of the event, T, and the frequency range of interest, F − f .…”

Dense Orthogonal Initialization for Deterministic PSO: ORTHOinit+

“…There are several convergence studies on PSO in the literature, focusing on the role of PSO control parameters, as for instance swarm size, inertia weight, acceleration coefficients, velocity clamping, as well as particles' initialization. All these studies reveal that PSO parameters must be confined to specific subsets of values, in order to avoid diverging trajectories, and some of them provide necessary conditions for the trajectories convergence (see for instance [2][3][4][5][6], along with [7][8][9][10]). Improper initializations of PSO parameters may yield divergent or even cyclic behavior.…”

“…Earlier studies (see for instance [7][8][9]) show that coupling proper control parameters with an efficient particles initialization may give strong synergies and improve the algorithm effectiveness. On this guideline, here we want to propose a novel particles initialization, for DPSO, showing the following two features:…”