An Application of Infinite Programming on Desirability Functions

Abstract

When assessing the quality of a system or product, it is necessary to take all responses into account and optimize them in a concurrent manner to find the factor levels that satisfy the overall system, process, or product properties to solve the robust design problem. This problem can be solved as a multi-response optimization problem. There are many methods suggested to solve this problem based on different disciplines like multi-objective optimization. In this study, we improve the theory of nondifferentiable desirability functions' optimization for which the so-called gradient-based methods are not useful. In this study, we propose an infinite programming approach for nondifferentiable desirability functions including more than one nondifferentiable point. We employed DNLP model of GAMS/BARON which is a nondifferentiable solver, however, the solution of more than one nondifferentiable point problem is resulted as infeasible. We also tested MATLAB/NOMAD which is a derivative-free solver for MINLP problems, however, MATLAB/NOMAD also did not succeed and could not solve this nondifferentiable problem. Lastly, we use a genetic algorithm that is implemented under MATLAB and it also cannot find a feasible solution. We use an example that is solved by different desirability functions approaches before and show that the desirability functions approach with more than one nondifferentiable point is a good alternative to the ones in the literature. We present the conclusion and future studies at the end of the paper.