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TOWARD THE USE OF PARETO PERFORMANCE SOLUTIONS AND PARETO ROBUSTNESS SOLUTIONS FOR MULTI-OBJECTIVE ROBUST OPTIMIZATION PROBLEMS

机译:面向多目标鲁棒优化问题的帕累托性能解决方案和帕累托鲁棒性解决方案的使用

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For Multi-Objective Robust Optimization Problem (MO-ROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a M0R0P into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions ((Pp) and the Pareto Robustness Solutions (Pr). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (Pp(Pp)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (Pp(Pp)). Further more, the intersection of PrPp) and Pp(Pr) can represent the intersection of Pr and PP well. Then the designer can choose good solutions by comparing the results of Pr(Pp) and Pp(Pr). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.
机译:对于多目标鲁棒优化问题(MO-ROP),获得最优且鲁棒的设计解决方案很重要。为了找到这些解决方案,通常,设计人员需要在优化之前设置性能函数(PF)的变化阈值,或者在原始PF上添加不确定性影响,以生成新的Pareto鲁棒前沿。在本文中,我们将M0R0P分为两个多目标优化问题(MOOP)。一种是原始的MOOP,另一种是我们将原始PF的健壮对等物稳健性函数(RF)作为优化目标。分别解决这两个MOOP之后,提出了两组解决方案,分别是帕累托性能解决方案((Pp)和帕累托鲁棒性解决方案(Pr)。对这两组进行进一步开发,我们可以得到两种类型的解决方案,分别是帕累托性能解决方案(Pp(Pp))中的帕累托鲁棒性解决方案,以及帕累托鲁棒性解决方案(Pp(Pp))中的帕累托性能解决方案。此外,PrPp)和Pp(Pr)的交集可以表示交集的Pr和PP很好。然后,设计人员可以通过比较Pr(Pp)和Pp(Pr)的结果来选择好的解决方案。借助这种方法,我们可以找到最佳且鲁棒的解决方案,而无需设置PF的变化阈值,也不会丢失初始的Pareto前沿。最后,一个示例性的例子突出了本文的贡献。

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