Multiobjective optimization is increasingly used in engineering to design new systems and to identify design tradeoffs. Yet, design problems often have objective functions and constraints that are expensive and highly nonlinear. Combinations of these features lead to poor convergence and diversity loss with common algorithms that have not been specifically designed for constrained optimization. Constrained benchmark problems exist, but they do not necessarily represent the challenges of engineering problems. In this article, a framework to design electro-mechanical actuators, called multiobjective design of actuators (MODAct), is presented and 20 constrained multiobjective optimization test problems are derived from the framework with a specific focus on constraints. The full source code is made available to ease its use. The effects of the constraints are analyzed through their impact on the Pareto front as well as on the convergence performance. A constraint landscape analysis approach is followed and extended with three new metrics to characterize the search and objective spaces. The features of MODAct are compared to existing test suites to highlight the differences. In addition, a convergence analysis using NSGA-II, NSGA-III, and C-TAEA on MODAct and existing test suites suggests that the design problems are indeed difficult due to the constraints. In particular, the number of simultaneously violated constraints in newly generated solutions seems key in understanding the convergence challenges. Thus, MODAct offers an efficient framework to analyze and handle constraints in future optimization algorithm design.

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设计中的现实约束多目标优化基准问题

在工程中越来越多地使用多目标优化来设计新系统并确定设计折衷方案。然而，设计问题通常具有昂贵且高度非线性的客观功能和约束。这些功能的组合导致收敛性差和分集丢失，而通用算法尚未针对约束优化进行专门设计。存在受约束的基准问题，但是它们不一定代表工程问题的挑战。在本文中，提出了一种用于设计机电执行器的框架，称为执行器多目标设计（MODAct），并从该框架中导出了20个受约束的多目标优化测试问题，并特别关注约束。提供了完整的源代码以简化其使用。通过约束对帕累托前沿和收敛性能的影响来分析约束的影响。遵循约束态势分析方法，并使用三个新指标进行扩展，以表征搜索空间和目标空间。将MODAct的功能与现有测试套件进行比较，以突出差异。此外，在MODAct和现​​有测试套件上使用NSGA-II，NSGA-III和C-TAEA进行的收敛性分析表明，由于约束条件，设计问题确实很困难。特别是，新生成的解决方案中同时违反的约束的数量似乎是理解融合挑战的关键。因此，MODAct提供了一个有效的框架来分析和处理未来优化算法设计中的约束。