Deterministic parameter control in differential evolution with combined variants for constrained search spaces

Abstract

This chapter presents an empirical comparison of six deterministic parameter control schemes based on a sinusoidal behavior that are incorporated into a differential evolution algorithm called “Differential Evolution with Combined Variants” (DECV) to solve constrained numerical optimization problems. Besides, the feasibility rules and the ε-constrained method are adopted as constraint-handling techniques. Two parameters are considered in this work, F (related with the mutation operator) and CR (related with the crossover operator). Two DECV versions (rand-best) and (best-rand) are assessed. From the above elements, 24 different variants are tested in 36 well-known benchmark problems (in 10 and 30 dimensions). Two performance measures used in evolutionary constrained optimization (successful percentage and average number of evaluations in successful runs) are adopted to evaluate the performance of each variant. Five experiments are proposed to compare (1) those variants with the feasibility rules, (2) those variants with the ε-constrained method, (3) the most competitive variants from the previous two experiments, (4) the convergence plots of those most competitive variants and (5) the significant statistical differences of feasible final results among variants. The obtained results suggest that an increasing oscillation of F and CR values, starting around 0.5 and then moving between 0 and 1, is suitable for the (rand-best) DECV variant. In contrast, a decreasing oscillation of both parameter values is suitable for the (best-rand) DECV variant. The convergence behavior observed in the most competitive variants indicates the convenience of the increasing oscillation of both parameters, coupled with the rand-best DECV version, to promote a faster convergence. The ε-constrained method showed to be more competitive with this type of parameter control than the feasibility rules. Finally, no significant differences among variants were observed based on final feasible results.