Fuzzy probability based randomness is utilized for polymorphic uncertain design and a priori parameters in design optimization tasks. Methods for the algorithmic interface between optimization and polymorphic uncertainty analysis are introduced. Uncertain design vectors are incorporated by affine transformation from deterministic design vectors. Multiple uncertainty reducing measures are discussed, which are required for the evaluation and comparability of fitness in optimization.

Nested uncertainty reducing measures are mandatory for polymorphic uncertain objectives. The inherence of multiple nested objectives is pointed out, which leads to inherence of multi-objective optimization in single-objective optimization problems with polymorphic uncertain parameters.

In this contribution, a framework is presented considering polymorphic uncertain a priori and design parameters in a multi-objective optimization. A parameter based geometric design optimization of a steel hook is investigated. Several uncertainty reducing measures are evaluated for optimization of performance and robustness.

Fuzzy design parameters are considered with respect to geometry and, therefore, an automated geometry regeneration and remeshing method is propagated. Material characteristics are modeled with stochastic a priori parameters. The load conditions are assumed to be a priori polymorphic uncertain. Pareto optimality is evaluated depending on the surrogate formulation of uncertainty reducing measures.

基于模糊概率的随机性用于多态不确定性设计和设计优化任务中的先验参数。介绍了优化和多态不确定性分析之间算法接口的方法。通过确定性设计向量的仿射变换将不确定的设计向量并入。讨论了减少不确定性的多种措施，这对于优化的适用性进行评估和可比性是必需的。

嵌套的不确定性降低措施对于多态不确定性目标是强制性的。指出了多个嵌套目标的内在性，从而导致了具有多态不确定参数的单目标优化问题中的多目标优化的固有性。

在此贡献中，提出了一种框架，该框架考虑了多态不确定性的先验和多目标优化中的设计参数。研究了基于参数的钢钩几何设计优化。评估了几种降低不确定性的措施，以优化性能和鲁棒性。

关于几何形状考虑了模糊的设计参数，因此，传播了一种自动的几何形状再生和重新网格化方法。使用随机先验参数对材料特性进行建模。假定负载条件是先验多态不确定性。根据不确定性降低措施的替代公式评估帕累托最优性。