Development of a bi-objective 0-1 mixed-integer nonlinear response surface-based robust design optimization model for unbalanced experimental data

•A modified exchange algorithm is developed for the I-optimality criterion.•A model construction scheme is proposed with a weighted least squares method.•A bi-objective 0-1 mixed-integer nonlinear robust design model is proposed.•A nonlinear branch and bound method with the depth-first search is proposed.•The effectiveness of the proposed methodology is shown in the case study. The purpose of this paper is to develop a model to obtain the optimum operating conditions under special engineering situations. These special situations are: (1) both qualitative and quantitative input variables are considered, (2) a specific number of design points is required, (3) the experimental design space is irregular due to physical constraints, and (4) the unbalanced experimental data is collected due to resource limitations and focusing on certain treatment combinations. Although such situations may occur in many processes, there has been little research on this subject. To address these research gaps, first, an I-optimal experimental design is selected to construct a design matrix by using a modified exchange algorithm. Second, a weighted least squares method is presented to deal with the unbalanced experimental data. Third, a bi-objective 0-1 mixed-integer nonlinear programming-based robust design model and its solution procedures are proposed to obtain optimum settings of both qualitative and quantitative variables. Finally, a case study, along with the comparative study, is presented.