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Design Optimization Using Multiple Dominance Relations
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2020-03-11 , DOI: 10.1002/nme.6316
Laurence W. Cook 1 , Karen E. Willcox 2 , Jerome P. Jarrett 3
Affiliation  

A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs that are optimal with respect to a binary relation within the set of designs that are optimal with respect to another binary relation. We then propose a method of finding such designs in a single optimization by defining an overall ranking function to use in optimizers, reducing the cost required to solve this formulation. In a design under uncertainty problem, our method obtains the most robust design that is not stochastically dominated faster than a multi-objective optimization. In a car suspension design problem, our method obtains superior designs according to a k-optimality condition than previously suggested multi-objective approaches to this problem. In an airfoil design problem, our method obtains designs closer to the true lift/drag Pareto front using the same computational budget as a multi-objective optimization.

中文翻译:

使用多重支配关系进行设计优化

工程设计中的一个挑战是从许多感兴趣的数量中选择合适的目标和约束,同时确保优化既有意义又易于计算。我们提出了一种优化公式,它可以考虑比现有公式更多的兴趣量,而不会降低问题的易处理性。该公式在相对于另一个二元关系最优的设计集合中搜索相对于一个二元关系最优的设计。然后,我们提出了一种通过定义在优化器中使用的整体排名函数来在单个优化中找到此类设计的方法,从而降低解决此公式所需的成本。在不确定性问题下的设计中,我们的方法获得了最稳健的设计,该设计不会比多目标优化更快地随机支配。在汽车悬架设计问题中,我们的方法根据 k 最优条件获得了比之前针对该问题建议的多目标方法更好的设计。在翼型设计问题中,我们的方法使用与多目标优化相同的计算预算来获得更接近真实升力/阻力帕累托前沿的设计。
更新日期:2020-03-11
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