Almost all real-world and engineering problems involve multi-objective optimization of some sort that is often constrained. To solve these constrained multi-objective optimization problems, constrained multi-objective optimization evolutionary algorithms (CMOEAs) are enlisted. These CMOEAs require specific constraint handling techniques. This study aims to address and test the most successful constraint handling techniques, seven different penalty constraint techniques, as applied to the Non-dominated Sorting Genetic Algorithm II (NSGA-II). In this paper, NSGA-II is chosen because of its high popularity amongst evolutionary algorithms. Inverted Generational Distance and Hypervolume are the main metrics that are discussed to compare the constraint handling techniques. NSGA-II is applied on 13 constrained multi-objective problems known as CF1-CF10, C1-DTLZ1, C2-DTLZ2, and C3-DTLZ4. The result of IGD and HV values are compared and the feasibility proportions of each combination on each problem are shown. The results of simulation present interesting findings that have been presented at the end of paper as discussion and conclusion.

几乎所有现实世界和工程学问题都涉及某种经常受到限制的多目标优化。为了解决这些受约束的多目标优化问题，提出了受约束的多目标优化进化算法（CMOEA）。这些CMOEA需要特定的约束处理技术。本研究旨在解决和测试最成功的约束处理技术，即七种不同的惩罚约束技术，这些技术已应用于非支配排序遗传算法II（NSGA-II）。本文之所以选择NSGA-II，是因为它在进化算法中非常受欢迎。反向生成距离和超体积是讨论比较约束处理技术的主要指标。NSGA-II适用于13个受约束的多目标问题，称为CF1-CF10，C1-DTLZ1，C2-DTLZ2和C3-DTLZ4。比较了IGD和HV值的结果，并显示了每种组合在每个问题上的可行性比例。仿真结果提出了有趣的发现，这些发现已在论文结尾作为讨论和结论提出。