At present, black-box and simulation-based optimization problems with multiple objective functions are becoming increasingly common in the engineering context. In many cases, the functional relationships that define the objective and constraints are only known as black-boxes, cannot be differentiated accurately, and may be subject to unexpected failures. Directional direct search techniques, in particular the direct multisearch (DMS) methodology, may be applied to identify Pareto fronts for such problems. In this work, we propose a mechanism for adaptively selecting search directions in the DMS framework, with the goal of reducing the number of black-box evaluations required during the optimization. Our method relies on the concept of simplex derivatives in order to define search directions that are optimal for a local, linear model of the objective function. We provide a detailed description of the resulting algorithm and offer several practical recommendations for efficiently solving the associated subproblems. The overall performance in an academic context is assessed via a standard benchmark. Through a realistic case study, involving the bi-objective design optimization of a mechatronic quarter-car suspension, the performance of the novel method in a multidisciplinary engineering setting is tested. The results show that our method is competitive with standard implementations of DMS and other state-of-the-art multi-objective direct search methods.

目前，具有多个目标函数的黑盒和基于仿真的优化问题在工程环境中变得越来越普遍。在很多情况下，定义目标和约束的函数关系仅被称为黑盒，无法准确区分，并且可能会出现意外故障。定向直接搜索技术，特别是直接多重搜索 (DMS) 方法，可用于识别此类问题的帕累托前沿。在这项工作中，我们提出了一种在 DMS 框架中自适应选择搜索方向的机制，目的是减少优化过程中所需的黑盒评估次数。我们的方法依赖于单纯形导数的概念来定义对局部最优的搜索方向，目标函数的线性模型。我们提供了结果算法的详细描述，并提供了一些实用的建议，以有效地解决相关的子问题。学术环境中的整体表现通过标准基准进行评估。通过涉及机电一体化四分之一汽车悬架的双目标设计优化的现实案例研究，测试了该新方法在多学科工程环境中的性能。结果表明，我们的方法与 DMS 的标准实现和其他最先进的多目标直接搜索方法具有竞争力。学术环境中的整体表现通过标准基准进行评估。通过一个现实的案例研究，涉及机电一体化四分之一汽车悬架的双目标设计优化，在多学科工程环境中测试了新方法的性能。结果表明，我们的方法与 DMS 的标准实现和其他最先进的多目标直接搜索方法具有竞争力。学术环境中的整体表现通过标准基准进行评估。通过一个现实的案例研究，涉及机电一体化四分之一汽车悬架的双目标设计优化，在多学科工程环境中测试了新方法的性能。结果表明，我们的方法与 DMS 的标准实现和其他最先进的多目标直接搜索方法具有竞争力。