ABSTRACT Many engineering design optimisation problems are multi-objective and subjected to multiple constraints. These problems may encounter uncertainties in their inputs, which may cause uncontrollable variations in the objectives and constraints. Multi-objective robust optimisation (MORO) approaches aim to obtain Pareto solutions with the least sensitivity to uncertainties. In this paper, an improved sequential MORO approach considering interval uncertainty reduction under mixed uncertainties (SMORO-IM) is proposed. Firstly, it adopts the efficient sequential optimisation framework based on the worst possible point constraint cuts. Secondly, a formulation for obtaining robust optimal solutions under mixed interval and probabilistic uncertainties is employed. In addition, considering that the interval uncertainties in inputs can be reduced at allowable cost, the cost of interval uncertainty reduction is defined as an extra objective function in the proposed approach, aiming at obtaining optimal solutions with different interval uncertainties. Two numerical examples and two engineering cases are used to illustrate the effectiveness of the proposed SMORO-IM approach. The objective and feasibility robustness of the obtained optimal solutions are verified by the Monte Carlo Method.

中文翻译：

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一种考虑混合不确定性下区间不确定性降低的改进序列多目标鲁棒优化方法

摘要 许多工程设计优化问题是多目标的，受到多重约束。这些问题的输入可能会遇到不确定性，这可能会导致目标和约束的不可控变化。多目标稳健优化 (MORO) 方法旨在获得对不确定性最不敏感的帕累托解决方案。在本文中，提出了一种考虑混合不确定性下区间不确定性降低的改进的顺序 MORO 方法（SMORO-IM）。首先，它采用基于最坏点约束削减的高效顺序优化框架。其次，采用了在混合区间和概率不确定性下获得稳健最优解的公式。此外，考虑到可以在允许的代价下降低输入中的区间不确定性，在所提出的方法中将区间不确定性降低的成本定义为一个额外的目标函数，旨在获得具有不同区间不确定性的最优解。两个数值例子和两个工程案例被用来说明所提出的 SMORO-IM 方法的有效性。蒙特卡罗方法验证了所得最优解的客观性和可行性鲁棒性。