Analysis of Variance on Weighted Design Improvement Space Considering Feasible Region for Efficient Variable Screening of Design Optimization

Abstract

As the design optimization problem becomes increasingly complex, the complexity of the design and the number of input variables are increasing. This acts as a cause of increasing the cost and time required for design optimization. In particular, the number of input variables means the dimension of the design optimization problem, and the increase in the number of input variables exponentially increases the cost and time required. In order to perform efficient design optimization, a variable screening method that reduces the number of input variables is used. However, previous variable screening methods are performed in terms of system response change rather than design optimization. Therefore, in this study, a variable screening method using design optimization information is proposed in the process of analyzing the significance of input variables with the goal of performing variable screening considering design optimization. This study aims to perform efficient variable screening for design optimization problems. To accomplish this, design optimization information must be reflected in the variable screening process. In this regard, this study approached the problems of the previous method from the following two points of view. First, the direction of response change does not coincide with the direction of design improvement. Second, the influence of constraints is not reflected in response-based analysis. This study proposes the following two methods to perform efficient variable screening for design optimization by overcoming the problems of previous methods. First, the direction of design improvement is derived from the design optimization formulation, and the analyzing significance of input variables on the derived direction is proposed. Second, in order to reflect the influence of constraints in the design optimization process, this study proposes weighting for responses by evaluating the extent of the infeasible domain of constraints. By integrating the two proposed methods, this study performs variable screening by analyzing the significance of input variables for weighted responses on the direction of design improvement. In addition, this study proposes a fixing rule for further performance improvement through the screened input variables. Although the input variable is screened for low significance may still have a little influence on the response. Therefore, the screened input variable is fixed to a value with high potential for improvement in the current data without additional design process or experiment through a fixing rule. The usefulness of proposed method was verified through mathematical examples. The proposed screening method provided different screening results as the constraint boundary was changed, and the efficiency of variable screening was confirmed in the design optimization result. In addition, a more improved optimal design was obtained through fixing rule. Then, the proposed method was applied to the vehicle body design optimization problem. Likewise, different screening results were derived whenever the constraint boundaries were changed, and it was confirmed that the proposed method screened more efficiently than the previous methods. Through this study, it is expected that more efficient and effective optimal designs can be obtained than previous response-based variable screening in high-dimensional design optimization problems.