Algoritmos evolutivos aplicados a problemas envolvendo funções computacionalmente custosas em domínios restritos

Abstract

The use of evolutionary algorithms in the optimization of real and complex engineering problems has proved to be quite efficient. However, since most of these problems are defined by expensive objective function and constraints, new modeling and constraint handling techniques have been proposed. In this scenario, this thesis proposes a constraint handling technique called Multiple Constraint Ranking (MCR) and a similarity-based surrogate algorithm. They assist evolutionary algorithms in the search for optimal solutions in optimization problems in which both objective function and constraints are costly. The MCR calculates the fitness of the solutions according to the sum of their positions in several queues, based on the values of the objective function, the violation in each constraint and the number of constraints violated. The similarity-based approach estimates the value of the objective function of a solution by a weighted average of the original objective function values of “neighboring” solutions by their distances. Such solutions are selected from a database, whose updating is based on the contribution of the solutions in the approximation process. Three algorithms are proposed: i) MCR coupled with a genetic algorithm; ii) differential evolution using similarity-based approximation; and, iii) differential evolution assisted by the MCR and the approximation. They were applied to complex problems suggested by the IEEE-CEC competitions and classical structural engineering problems. Their results were compared with relevant algorithms in the literature, where were proved the robustness of all of them.