Modified Differential Evolution for Constrained Optimization

In this paper, we present a Differential-Evolution based approach to solve constrained optimization problems. The aim of the approach is to increase the probability of each parent to generate a better offspring. This is done by allowing each solution to generate more than one offspring but using a different mutation operator which combines information of the best solution in the population and also information of the current parent to find new search directions. Three selection criteria based on feasibility are used to deal with the constraints of the problem and also a diversity mechanism is added to maintain infeasible solutions located in promising areas of the search space. The approach is tested in a set of test problems proposed for the special session on Constrained Real Parameter Optimization. The results obtained are discussed and some conclusions are established.

I. Introduction

Evolutionary Algorithms (EAs) have been successfully applied to solve optimization problems [1], [2]. However, in their original versions, EAs lack a mechanism to deal with the constraints of a problem. Therefore, several approaches have been proposed to incorporate information of feasibility into the EAs' fitness function. The most popular approach is the use of penalty functions [3]. The aim of penalty functions is to decrease the fitness value of those infeasible individuals (which do not satisfy the constraints of the problem). In this way, feasible solutions will have more probabilities to be selected and the EA will approach the feasible region of the search space. However, the main drawback of penalty functions if that they require the definition of penalty factors. These factors will determine the degree of penalization. If the penalty value is very high, the feasible region will be approached mostly at random and the feasible global optimum will be hard to get. On the other hand, if the penalty is too low, the probability of not reaching the feasible region will be high. Therefore, the penalty factors must be carefully tuned as they are problem-dependent [4].