Abstract. A stochastic algorithm that computes box-shaped solution spaces for nonlinear, high-dimensional and noisy problems with uncertain input parameters has been proposed in [35]. This paper studies in detail the quality of the results and the e ciency of the algorithm. Appropriate benchmark problems are specified and compared with exact solutions that were derived analytically. The speed of convergence decreases as the number of dimensions increases. Relevant mechanisms are identified that explain how the number of dimensions a↵ects the performance. The optimal number of sample points per iteration is determined in dependence of the preference for fast convergence or a large volume.

Key parameters may be used to turn a bad design into a good design with comparatively little effort. The proposed method identifies key parameters in high-dimensional nonlinear systems that are subject to uncertainty. A numerical optimization algorithm seeks a solution space on which all designs are good, that is, they satisfy a specified design criterion. The solution space is box-shaped and provides target intervals for each parameter. A bad design may be turned into a good design by moving its key parameters into their target intervals. The solution space is computed so as to minimize the effort for design work: its shape is controlled by particular constraints such that it can be reached by changing only a small number of key parameters. Wide target intervals provide tolerance against uncertainty, which is naturally present in a design process, when design parameters are unknown or cannot be controlled exactly. In a simple two-dimensional example problem, the accuracy of the algorithm is demonstrated. In a high-dimensional vehicle crash design problem, an underperforming vehicle front structure is improved by identifying and appropriately changing a relevant key parameter.

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