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arXiv · 2512.21989

Multi-Objective Optimization with Desirability and Morris-Mitchell Criterion

Thomas Bartz-Beielstein·Eva Bartz·Alexander Hinterleitner·Christoph Leitenmeier·Ihab Abd El Hussein
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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.

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Thomas Bartz-Beielstein, Eva Bartz, Alexander Hinterleitner, Christoph Leitenmeier, Ihab Abd El Hussein. 2025-12-26. Multi-Objective Optimization with Desirability and Morris-Mitchell Criterion. https://arxiv.org/abs/2512.21989

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