Abstract
The performance of the sequential metamodel based optimization procedure depends strongly on the chosen building blocks for the algorithm, such as the used metamodeling method and sequential improvement criterion. In this study, the effect of these choices on the efficiency of the robust optimization procedure is investigated. A novel sequential improvement criterion for robust optimization is proposed, as well as an improved implementation of radial basis function interpolation suitable for sequential optimization. The leave-one-out cross-validation measure is used to estimate the uncertainty of the radial basis function metamodel. The metamodeling methods and sequential improvement criteria are compared, based on a test with Gaussian random fields as well as on the optimization of a strip bending process with five design variables and two noise variables. For this process, better results are obtained in the runs with the novel sequential improvement criterion as well as with the novel radial basis function implementation, compared to the runs with conventional sequential improvement criteria and kriging interpolation.
Highlights
Engineering can be seen as a sequence of making choices, from fundamental design choices to defining design details
A striking example of the nonlinearity is the local minimum of the angle for the Jones criterion - RBFG0 run at a thickness of 0.52 mm (Fig. 11e), whereas the Jurecka criterion - RBFMQ0 optimum has a local maximum at the same thickness (Fig. 11g)
The only available criterion for sequential improvement in robust optimization was the Jurecka criterion. This criterion has some artifacts, such as that, when two points have the same prediction for the objective function value, the point with the largest prediction uncertainty is not always preferred as new sampling point
Summary
Engineering can be seen as a sequence of making choices, from fundamental design choices to defining design details. Nowadays engineers frequently use computational models to assess the effects of design choices and determine optimal designs. Many optimization methods have been developed to automate this process, each method being suitable to solve a specific type of problem in an efficient way. With these methods an optimal configuration of the design may be found. Such a design may malfunction in real-life due to variability of the model parameters. A specific branch of optimization research focuses on these problems: within robust optimization the goal is to find a design which fulfills the requirements even under the influence of parameter variations
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