Using the Evolution Strategies' Self-adaptation Mechanism and Tournament Selection for Global Optimization

An approach based on a (μ+1)-ES and three simple tournament rules is proposed to solve global optimization problems. The proposed approach does not use a penalty function and does not require any extra parameters other than the original parameters of an evolution strategy. This approach is validated with respect to the state-of-the-art techniques in evolutionary constrained optimization using a well-known benchmark. The results obtained are very competitive with respect to the approaches against which our approach was compared. INTRODUCTION Having a strong theoretical background (Schwefel, 1995; Bäck, 1996; Beyer, 2000), Evolution Strategies (ES) have been found efficient in solving a wide variety of optimization problems (Asselmeyer, 1997). However, as other evolutionary Algorithms (EAs), ES lack an explicit mechanism to deal with constrained search spaces. Several approaches to incorporate constraints into the fitness function of an EA (Michalewicz, 1996; Coello, 2002) have been proposed. The most common approach used to incorporate the constraints of the problem to the fitness function of an EA is the use of penalty functions, where the amount of constraint violation is used to punish or “penalize” an infeasible solution so that feasible solutions are favored by the selection process. Without concerning their simplicity, they have many drawbacks from which the main one is that they require a careful fine tuning of the penalty factors that accurately estimates the degree of penalization to be applied so that we can approach efficiently the feasible region (Smith, 1997; Coello 2002). In this paper, we argue that the self-adaptation mechanism of a conventional evolution strategy combined with some (very simple) tournament rules based on feasibility can provide us with a highly competitive evolutionary algorithm for constrained optimization.