Mauro Innocente

Particle Swarm Optimization: Fundamental Study and its Application to Optimization and to Jetty Scheduling Problems

The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature. While particle swarm optimizers share such advantages, they outperform evolutionary algorithms in that they require lower computational cost and easier implementation, involving no operator design and few coefficients to be tuned. However, even marginal variations in the settings of these coefficients greatly influence the dynamics of the swarm. Since this paper does not intend to study their tuning, general-purpose settings are taken from previous studies, and virtually the same algorithm is used to optimize a variety of notably different problems. Thus, following a review of the paradigm, the algorithm is tested on a set of benchmark functions and engineering problems taken from the literature. Later, complementary lines of code are incorporated to adapt the method to combinatorial optimization as it occurs in scheduling problems, and a real case is solved using the same optimizer with the same settings. The aim is to show the flexibility and robustness of the approach, which can handle a wide variety of problems.

Pseudo-Adaptive Penalization to Handle Constraints in Particle Swarm Optimizers

The penalization method is a popular technique to provide particle swarm optimizers with the ability to handle constraints. The downside is the need of penalization coefficients whose settings are problem-specific. While adaptive coefficients can be found in the literature, a different adaptive scheme is proposed in this paper, where coefficients are kept constant. A pseudo-adaptive relaxation of the tolerances for constraint violations while penalizing only violations beyond such tolerances results in a pseudo-adaptive penalization. A particle swarm optimizer is tested on a suite of benchmark problems for three types of tolerance relaxation: no relaxation; self-tuned initial relaxation with deterministic decrease; and self-tuned initial relaxation with pseudo-adaptive decrease. Other authors’ results are offered as frames of reference.

Individual and social behaviour in particle swarm optimizers

Three basic factors govern the individual behaviour of a particle: the inertia from its previous displacement; the attraction to its own best experience; and the attraction to a given neighbour’s best experience. The importance awarded to each factor is controlled by three coefficients: the inertia; the individuality; and the sociality weights. The social behaviour is ruled by the structure of the social network, which defines the neighbours that are to inform of their experiences to a given particle. This paper presents a study of the influence of different settings of the coefficients as well as of the combined effect of different settings and different neighbourhood topologies on the speed and form of convergence.