Nondifferentiable Desirability Functions: Derivative Free Optimization with MATLAB/NOMAD

Nondifferentiable Desirability functions are one of the most preferred multi-response optimiza- tion methods in nonlinear robust parameter design. Their nondifferentiability makes the optimization prob- lem hard to solve and researchers and scientists look for new softwares and new desirability function structures to overcome this problem. In this study, we suggest a new implementation of derivative free mash adaptive direct search algorithm (MADS) with MATLAB/NOMAD to nondifferentiable desirability functions. For doing this, we need to model the optimization problem of desirability functions as a mixed- integer nonlinear optimization program (MINLP) by introducing a new binary variable to the model. This integer shows the side of the two-sided desirability function which is active. Hence, the model of our problem becomes nondifferentiable nonconvex MINLP. We show our implementation on three well-known optimization problem from the multi-response optimization literature. We finally conclude with an outlook and future research projects.