Horsetail matching: a flexible approach to optimization under uncertainty*. Issue 4 (3rd April 2018)

• Record Type: Journal Article
• Authors: Cook, L. W.; Jarrett, J. P.
• Is Part Of: Engineering optimization. Volume 50:Issue 4(2018)
• Page Start: 549
• Page End: 567
• Publication Date: 2018-04-03
• Subjects: optimization under uncertainty -- horsetail matching -- robust optimization -- density matching -- probabilistic methods; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2017.1327581
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: It is important to design engineering systems to be robust with respect to uncertainties in the design process. Often, this is done by considering statistical moments, but over-reliance on statistical moments when formulating a robust optimization can produce designs that are stochastically dominated by other feasible designs. This article instead proposes a formulation for optimization under uncertainty that minimizes the difference between a design's cumulative distribution function and a target. A standard target is proposed that produces stochastically non-dominated designs, but the formulation also offers enough flexibility to recover existing approaches for robust optimization. A numerical implementation is developed that employs kernels to give a differentiable objective function. The method is applied to algebraic test problems and a robust transonic airfoil design problem where it is compared to multi-objective, weighted-sum and density matching approaches to robust optimization; several advantages over these existing methods are demonstrated.