Evolução diferencial para problemas de otimização com restrições lineares

Abstract

Metaheuristics have been used to solve optimization problems. In particular, we can highlight the Differential Evolution(DE),which has been successfully applied insituations where the search space is continuous. Despite the advantages of those techniques, they require adjustments in order to deal with constraints, which commonly restrict the search space in real optimization problems. In this work, a change in the DE is proposed in order to deal with the linear equality constraints of the problem. The proposed method, here denoted by DELEqC, generates an initial population of candidate solutions, which are feasible with respect to the linear equality constraints, and generates new individuals without the standard crossover operation. The idea is to generate new solutions that are also feasible with respect to this kind of constraint. The proposed procedure for generating individuals and maintaining the feasibility of the population is straightforward when linear equality constraints are considered, but requires the use of slack variables when linear inequalities are present. If the optimization problem involves nonlinear constraints, their treatment is done here using an adaptive penalty method (APM), or by means of a selection scheme (DSS). The proposed procedure is applied to problems available in the literature and the results obtained are compared to those presented by other constraint handling techniques. The analysis of results indicates that the presented proposal found competitive solutions in relation to other specific techniques for the treatment of linear equality constraints and better than those achieved by strategies commonly adopted in metaheuristics.