Nondifferentiable Desirability Functions: Derivative Free Optimization with MATLAB/NOMAD

Year 2025, Volume: 7 Issue: 1, 28 - 39, 30.06.2025

Başak Öztürk

https://doi.org/10.47086/pims.1645638

Abstract

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.

Keywords

derivative free optimization , multi-response optimization , matlab

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