Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

Abstract

Mathematical model development for multivariate decision-making problems (i.e., multiple parameter and response optimization problems) has received significant attention and has been investigated by many researchers and practitioners. Although many different optimization models and methods, including priority and weight allocation problems, have been proposed in the literature, there is significant room for improvement. The majority of existing optimization methods may have difficulties in determining reliable priorities and weights for practical industrial situations. In addition, because they often focus on tradeoffs only among multiple output responses, these methods may not incorporate the multiple priority and/or weight effects directly from input factors to output responses (i.e., quality characteristics). To address these problems, the primary objective of this research is to propose a new multi-objective optimization approach by integrating a game theory principle (i.e., the Stackelberg leadership game) into a robust parameter design model to determine the optimal factor settings. First, a multi-response robust design optimization (RDO) problem was formulated using a mean squared error model and response surface methodology. A Stackelberg leadership game is then integrated into this RDO problem, where multiple responses play the role of game participants. Second, the integrated RDO model using the Stackelberg game-based multi-response (SGMR) formulation approach is analyzed by decomposition into various sequential optimization models in terms of different leader–follower relationships. Finally, non-dominated solutions are obtained from the proposed model by evaluating the overall quality loss (OQL). A pharmaceutical numerical example was performed to demonstrate the proposed integrated model and to examine whether this model can determine the most efficient solutions when the relative importance among multiple responses is unidentified. In addition, a comparative study associated with the conventional multi-objective optimization methods and the newly proposed RDO model is presented, and the proposed RDO model provided significantly better solutions than the conventional methods in the relevant comparative study.