Multi-Objective Optimization with Desirability and Morris-Mitchell Criterion

Abstract: Existing experimental designs in industry are often unplanned, biased, and lack optimal space-filling properties, making them unrepresentative of the input space. This article presents an approach to improve such designs by increasing coverage quality while simultaneously optimizing experimental results. We utilize the intensified Morris-Mitchell criterion, a size-invariant extension of the standard criterion, to quantify and improve input space coverage for existing designs. Using the Python package spotdesirability, we define a multi-objective desirability function that combines predictions from surrogate models (Random Forest) with the Morris-Mitchell improvement into a single score. This approach is demonstrated using a case study from compressor development, optimizing two performance objectives alongside the space-filling criterion. The Python package spotoptim is used for the optimization, and infill-point plots are introduced to visualize the placement of new design points relative to existing ones. This methodology effectively balances the exploration-exploitation trade-off in multi-objective optimization.