Promising Infeasibility and Multiple Offspring Incorporated to Differential Evolution for Constrained Optimization

In this paper, we incorporate a diversity mechanism to the differential evolution algorithm to solve constrained optimization problems without using a penalty function. The aim is twofold: (1) to allow infeasible solutions with a promising value of the objective function to remain in the population and also (2) to increase the probabilities of an individual to generate a better offspring while promoting collaboration of all the population to generate better solutions. These goals are achieved by allowing each parent to generate more than one offspring. The best offspring is selected using a comparison mechanism based on feasibility and this child is compared against its parent. To maintain diversity, the proposed approach uses a mechanism successfully adopted with other evolutionary algorithms where, based on a parameter Sr a solution (between the best offspring and the current parent) with a better value of the objective function can remain in the population, regardless of its feasibility. The proposed approach is validated using test functions from a well-known benchmark commonly adopted to validate constraint-handling techniques used with evolutionary algorithms. The statistical results obtained by the proposed approach are highly competitive (based on quality, robustness and number of evaluations of the objective function) with respect to other constrainthandling techniques, either based on differential evolution or on other evolutionary algorithms, that are representative of the state-of-the-art in the area. Finally, a small set of experiments were made to detect sensitivity of the approach to its parameters.