Development of a D-Optimal Design-Based 0-1 Mixed-Integer Nonlinear Robust Parameter Design Optimization Model for Finding Optimum Design Factor Level Settings

Abstract

Information-based optimal experimental designs are effective offline quality improvement tools that provide insights into the information under complex engineering situations. In the literature, considerable attention has been focused on the regular design region-based experiments to generate design points for both qualitative and quantitative factors. However, there are several situations while some design points are infeasible due to the cost and resource-related restrictions. In such situations, an appropriate design should be selected to obtain feasible experimental design points. Therefore, this paper is three-fold. One, a D-optimal design is selected over other designs. Two, this paper is to develop models that interconnect experimental design as an information-gathering process in the early design phase with operations research in the optimization phase. To the best of our knowledge, there is not an optimization model for identifying optimum factor level settings by linking the D-optimal design concept to optimization. Thus, a 0-1 mixed-integer nonlinear programming model is proposed to obtain an optimal operating condition for both qualitative and quantitative factors. Relaxation and constraint enforcement concepts are also presented to solve the proposed optimization model. Besides, comparison studies of the proposed optimization model and counterparts are also conducted. Finally, the proposed methodology may have a potential impact to enhance complex engineering situations for both qualitative and quantitative factors in a linearly restricted experimental design region.