In this study, we propose an improvement to the direct mating method, a constraint handling approach for multi-objective evolutionary algorithms, by hybridizing it with local mating. Local mating selects another parent from the feasible solution space around the initially selected parent. The direct mating method selects the other parent along the optimal direction in the objective space after the first parent is selected, even if it is infeasible. It shows better exploration performance for constraint optimization problems with coupling NSGA-II, but requires several individuals along the optimal direction. Due to the lack of better solutions dominated by the optimal direction from the first parent, direct mating becomes difficult as the generation proceeds. To address this issue, we propose a hybrid method that uses local mating to select another parent from the neighborhood of the first selected parent, maintaining diversity around good solutions and helping the direct mating process. We evaluate the proposed method on three mathematical problems with unique Pareto fronts and two real-world applications. We use the generation histories of the averages and standard deviations of the hypervolumes as the performance evaluation criteria. Our investigation results show that the proposed method can solve constraint multi-objective problems better than existing methods while maintaining high diversity.

翻译：在本研究中，我们通过将定向交配方法与局部交配进行混合，改进了多目标进化算法中处理约束问题的定向交配方法。局部交配从初始选定父代周围的可行解空间中选取另一父代。定向交配方法在选定第一个父代后，即使该父代不可行，也会沿目标空间中的最优方向选择另一个父代。该方法在耦合NSGA-II时对约束优化问题展现出更优的探索性能，但需要沿最优方向保持多个个体。由于缺乏被第一个父代的最优方向所支配的更好解，随着进化代数的增加，定向交配变得困难。为解决这一问题，我们提出一种混合方法，通过从第一个选定父代的邻域中选取另一个父代，维持优质解周围的多样性，并辅助定向交配过程。我们在三个具有独特帕累托前沿的数学问题和两个实际应用场景中对所提方法进行了评估，并使用超体积平均值与标准差的历史演化记录作为性能评价标准。研究结果表明，所提方法在保持高多样性的同时，能够比现有方法更有效地求解约束多目标优化问题。