Design-target-based optimization using input variable selection and penalty-Lagrange multiplier for high-dimensional design problems

Abstract

Design optimization of high-dimensional, computationally-expensive, and black-box problems has many challenges to resolve. Owing to the enormously high computational costs, obtaining the optimum design that has the minimum or maximum objective function value while satisfying constraints requires elaborated approaches. Instead, this paper suggests that if a design that satisfies a design target demanded by designers or decision makers can be obtained with low computational costs, the design could be quite useful for practitioners. To minimize the computational costs while obtaining the design, we aim to select the minimum number of significant input variables of a high-dimensional problem. Accordingly, a new design optimization problem for input variable selection, which is named design-target-based optimization (DTBO), is proposed to achieve it. The input variable selection is performed based on the selection measure that is calculated by the significance of input variables and the weights of each response. In the viewpoint of obtaining the design by minimally selecting the significant input variables, it is crucial to allocate weights appropriately by considering the status of constraints whether they are violated, active or inactive. Therefore, a penalty-Lagrange multiplier (PLM) method is also proposed for the DTBO to allocate weights adaptively. The performance and effectiveness of the DTBO for solving high-dimensional design problems are demonstrated by examining two numerical examples and the design of the body-in-white of a vehicle. We anticipate that the DTBO with the PLM method can obtain a practical design satisfying the design target efficiently.