Multi-Objective Optimization with Desirability and Morris-Mitchell Criterion

TL;DR

This paper introduces a multi-objective optimization framework that enhances experimental design coverage and performance, using desirability functions and Morris-Mitchell criteria, demonstrated on compressor data.

Contribution

It develops a novel methodology combining space-filling criteria with desirability functions, implemented via Python packages, to improve experimental design in engineering applications.

Findings

Improved design coverage using Morris-Mitchell variants.

Unified optimization of performance and coverage with desirability functions.

Visual diagnostics for sequential design point placement.

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.