Constrained multiobjective optimization problems (CMOPs) involve both conflicting objective functions and various constraints. Due to the presence of constraints, CMOPs' Pareto-optimal solutions are very likely lying on constraint boundaries. The experience from the constrained single-objective optimization has shown that to quickly obtain such an optimal solution, the search should surround the boundary of the feasible region from both the feasible and infeasible sides. In this article, we extend this idea to cope with CMOPs and, accordingly, we propose a novel constrained multiobjective evolutionary algorithm with bidirectional coevolution, called BiCo. BiCo maintains two populations, that is: 1) the main population and 2) the archive population. To update the main population, the constraint-domination principle is equipped with an NSGA-II variant to move the population into the feasible region and then to guide the population toward the Pareto front (PF) from the feasible side of the search space. While for updating the archive population, a nondominated sorting procedure and an angle-based selection scheme are conducted in sequence to drive the population toward the PF within the infeasible region while maintaining good diversity. As a result, BiCo can get close to the PF from two complementary directions. In addition, to coordinate the interaction between the main and archive populations, in BiCo, a restricted mating selection mechanism is developed to choose appropriate mating parents. Comprehensive experiments have been conducted on three sets of CMOP benchmark functions and six real-world CMOPs. The experimental results suggest that BiCo can obtain quite competitive performance in comparison to eight state-of-the-art-constrained multiobjective evolutionary optimizers.

中文翻译：

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通过双向协同处理约束多目标优化问题。

受约束的多目标优化问题（CMOP）涉及相互矛盾的目标函数和各种约束。由于存在约束，CMOP的帕累托最优解很可能位于约束边界上。受约束的单目标优化的经验表明，为了快速获得这样的最优解，搜索应该从可行和不可行的方面围绕可行区域的边界。在本文中，我们将这一思想扩展为应对CMOP，因此，我们提出了一种新颖的双向约束约束多目标进化算法，称为BiCo。BiCo保留两个人口，即：1）主要人口和2）档案人口。要更新主要人口，约束支配原理配备了NSGA-II变体，可将种群移动到可行区域，然后将种群从搜索空间的可行侧引向Pareto前沿（PF）。在更新档案种群时，依次执行非主导排序程序和基于角度的选择方案，以在不可行区域内将种群驱向PF，同时保持良好的多样性。结果，BiCo可以从两个互补方向接近PF。此外，为了协调主要种群和档案种群之间的相互作用，在BiCo中，开发了一种受限的交配选择机制来选择合适的交配父母。已经对三组CMOP基准功能和六个实际CMOP进行了全面的实验。