Multi-Objective Optimization and Hyperparameter Tuning With Desirability Functions

The desirability-function approach is a widely adopted method for optimizing multiple-response processes. Kuhn (2016) implemented the packages desirability and desirability2 in the statistical programming language R, but no comparable packages exists for Python. The goal of this article is to provide an introduction to the desirability function approach using the Python package spotdesirability, which is available as part of the sequential parameter optimization framework. After a brief introduction to the desirability function approach, three examples are given that demonstrate how to use the desirability functions for (i) classical optimization, (ii) surrogate-model based optimization, and (iii) hyperparameter tuning. An extended Morris-Mitchell criterion, which allows the computation of the search-space coverage, is proposed and used in a fourth example to handle the exploration-exploitation trade-off in optimization. Finally, infill-diagnostic plots are introduced as a tool to visualize the locations of the infill points with respect to already existing points.