Constraint-boundary-based Weight Allocation for Significant Input Variable Selection of HEB Constrained Optimization Problems

Abstract

Design optimization of high-dimensional expensive (computationally) black-box (HEB) problems has many challenges [1]. Especially, as the dimension of input variables increases, the design space increases exponentially, and the optimization costs tend to increase. The problem of high-dimensional input variables can be solved by using elastic net [2], one of the feature selection methods. That is, the size of design space is reduced by selecting the significant input variables in order of the significance of the input variables for a response. However, in the case of multiple responses like constrained optimization problems, since the significance of input variables for each response is different, it is necessary to calculate the variable selection measure through weight allocation according to the responses. Therefore, this study proposes constraint-boundary-based weight allocation (CBBWA). The more the response violates the constraint boundary, the higher weight is allocated to the significance of the response, and vice versa. By using the selected input variables through the CBBWA, design optimization is performed, and the proposed method is compared with the penalty function method [3] through the optimization results. Through the proposed method, it is expected that the significant input variables to obtain a feasible and improved design of the constrained optimization problems can be selected.