Multi-Objective Optimization with Desirability and Morris-Mitchell Criterion
Abstract
Industrial experimental designs frequently lack optimal space-filling properties, rendering them unrepresentative. This study presents a comprehensive methodology to refine existing designs by enhancing coverage quality while optimizing experimental outcomes. We discuss and analyse variants of the Morris-Mitchell criterion to quantify and improve spatial distributions. Based on potential theory, we analyze monotonicity properties and limitations of the Morris-Mitchell criteria. Practically, we implement a multi-objective optimization framework utilizing the Python packages spotdesirability and spotoptim. This framework uses desirability functions to combine surrogate-model predictions with space-filling enhancements into a unified score. Demonstrated through data from a compressor development case study, this approach optimizes performance objectives alongside design coverage. To facilitate implementation, we introduce novel infill-point diagnostics that visually guide the sequential placement of design points. This integrated methodology successfully bridges spatial theory with engineering application, balancing the crucial exploration and exploitation trade-off.
Cite
@article{arxiv.2512.21989,
title = {Multi-Objective Optimization with Desirability and Morris-Mitchell Criterion},
author = {Thomas Bartz-Beielstein and Eva Bartz and Alexander Hinterleitner and Christoph Leitenmeier and Ihab Abd El Hussein},
journal= {arXiv preprint arXiv:2512.21989},
year = {2026}
}