Robust Optimization Of Multi-Response Surface Problems Using Desirability Function

This study copes with robust parameter optimization of product or process involving multiple independent quality characteristics. The purpose is to acquire robust optimal solutions which are insensitive to some pre-defined uncertainties. In this thesis, the response surface model is established to relate each response and design factors, and then the desirability function method is utilized to compromise all the responses. Using robust counterpart approach to measure robustness, we mainly deal with two types of uncertainty, i.e. tolerances bands on design factors and prediction errors of response surface models. The topics discussed in this paper are outlined as following.Firstly, we develop two intelligent algorithms, i.e. the genetic algorithm (GA) and the simulated annealing (SA) algorithm to find the maximum of overall desirability function. The pattern search (PS) algorithm is utilized to refine solutions found by GA and SA. Computational examples reveal that the intelligent algorithms have outperformed a single PS algorithm when the optimization problem is complex, but the PS algorithm can enchance the convergence precision of GA and SA. Thus, we propose to use the hybrid algorithm in this study rather than a single algorithm alone.Secondly, we present the robust counterpart for the desirability function method when the variations on input variables are considered. The GA post-hybridized with PS algorithm is employed to search for the robust optimum. The numerical example demonstrates that the proposed method can successfully find solutions lying in the robust feasible region. The so-obtained solutions are of more practical meanings since they are robust against production tolerances or manufacturing imprecision.Thirdly, we investigate the impact of (poor) model predictions on the desirability function. The Monte Carlo approach is used to simulate the distribution of desirability function and to give a statistical analysis of the simulated results. The case example shows that the traditional global optimum is more likely to have a high probabilistic risk, while the local optimum usually implys a new feasible operating region, which is helpful to guide for robust optimum solutions.Finally, we embed the uncertainty information of model predictions into the standard desirability function method. The GA combined with PS algorithm is used to find the robust optimum. The illustrated example indicates that the presented approach is very useful in indentifying solutions lying in the robust feasible region. It can also alleviate the impact of prediction errors a great deal on the desirability function. The found solutions are of more practical values because they are insensitive to model prediction errors.Although the examples illustrated in this thesis are motivated from the chemical or semiconductor industry, the procedures are quite general and are not restricted to these fields.