The optimization of large-scale multibody systems is a numerically challenging task, in particular when considering multiple conflicting criteria at the same time. In this situation, we need to approximate the Pareto set of optimal compromises, which is significantly more expensive than finding a single optimum in single-objective optimization. To prevent large costs, the usage of surrogate models, constructed from a small but informative number of expensive model evaluations, is a very popular and widely studied approach. The central challenge then is to ensure a high quality (that is, near-optimality) of the solutions that were obtained using the surrogate model, which can be hard to guarantee with a single pre-computed surrogate. We present a back-and-forth approach between surrogate modeling and multi-objective optimization to improve the quality of the obtained solutions. Using the example of an expensive-to-evaluate multibody system, we compare different strategies regarding multi-objective optimization, sampling and also surrogate modeling, to identify the most promising approach in terms of computational efficiency and solution quality.

翻译：大规模多体系统的优化是一项数值计算上的挑战性任务，特别是在同时考虑多个相互冲突的准则时。在这种情况下，我们需要近似最优折衷的帕累托集，这比在单目标优化中寻找单个最优解要昂贵得多。为了防止高昂的计算成本，利用由少量但信息量大的昂贵模型评估构建的代理模型，是一种非常流行且被广泛研究的方法。此时的核心挑战在于确保使用代理模型获得的解具有高质量（即接近最优性），而这在仅使用单个预先计算的代理模型时往往难以保证。我们提出了一种在代理建模与多目标优化之间来回迭代的方法，以提高所得解的质量。通过一个评估成本高昂的多体系统实例，我们比较了多目标优化、采样以及代理建模方面的不同策略，以在计算效率和求解质量方面确定最有前景的方法。