Enhancing constrained MOEA/D with direct mating using hybrid mating strategies and diverse crossover methods

Abstract The direct mating strategy, which is a constraint-handling method in multi-objective evolutionary algorithms, selects a second parent on the basis of the optimal direction in the objective space, disregarding feasibility. This approach, although effective in early generations, encounters difficulties as solutions better than the current Pareto solutions become scarce, reducing diversity and hindering exploration. Herein, we introduce a hybrid approach that combines direct mating with newly proposed local mating strategies, aiming to generate offspring around the Pareto optimal solutions to improve the solution search performance via a direct mating strategy. Our method addresses the limitations of conventional direct mating, thereby improving its applicability to real-world design problems. Our hybrid strategy employs local mating to select an additional parent close to the initially chosen parent, preserving solution diversity and effectively exploring the solution space. This enhances the effectiveness of direct mating across all generations. In addition, we introduce two types of crossover methods, i.e., simulated binary crossover and differential evolution, for parents selected by direct and local mating, respectively. The synergy among these techniques facilitates a robust search process that can efficiently yield superior solutions. We evaluated the proposed approach using three mathematical problems with distinct Pareto fronts and two practical applications, including an aerospace design problem. The performances of these methods were assessed on the basis of the averages and standard deviations of the hypervolume and inverted generational distance metrics across multiple solution attempts to determine the average performances and the dependencies on initial population variance. The obtained results demonstrate that the hybrid method significantly outperforms the existing methods in the case of constrained multi-objective optimization. Specifically, the hybrid method yielded higher average hypervolumes and lower dependency on initial population variance than the existing methods. The hybrid method also yielded a lower average and less dependency on initial population variance in the inverted generational distance compared to existing methods. This result suggests that the proposed method can obtain high-quality non-dominated solutions, regardless of the initial population.