An adaptive penalty scheme to solve constrained structural optimization problems by a Craziness based Particle Swarm Optimization

Abstract

The use of Evolutionary Algorithms (EAs) to solve optimization problems has been increasing. One of the most used techniques is Particle Swarm Optimization (PSO), which is considered robust, efficient and competitive in comparison with other bio-inspired algorithms. EAs were originally designed to solve unconstrained optimization problems. However, the most significant problems, particularly those from real world optimization, present constraints. It is not trivial to define a strategy to handle constraints and, in general, penalty functions containing parameters to be set by the user and it may affect the search considerably. This paper consists of a combination of the Craziness based Particle Swarm Optimization (CRPSO) with an adaptive penalty technique, called Adaptive Penalty Method (APM), to solve constrained optimization problems. A CRPSO is adopted here in order to avoid premature convergence using a new velocity expression and an operator called “craziness velocity”. APM and its variants were applied in other EAs, originally in a Genetic Algorithm, which demonstrated its robustness. APM deals with inequality and equality constraints, and it is free of parameters to be defined by the user. In order to assess the applicability and performance of the algorithm, several structural engineering optimization problems traditionally found in the literature are used in the computational experiments.