Computing Experiment-Constrained D-Optimal Designs

TL;DR

This paper introduces scalable algorithms for generalized D-optimal experimental design with nonlinear models and constraints, combining convex relaxation and local search to improve efficiency and scalability over existing methods.

Contribution

It develops a novel approach integrating convex relaxation with pricing-based local search for constrained D-optimal design, handling nonlinear models and large candidate sets.

Findings

Algorithms outperform commercial software in efficiency

Effective handling of arbitrary constraints in design space

Scalable solutions for large, nonlinear experimental design problems

Abstract

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing for nonlinear relationships in factor levels. We develop scalable algorithms suitable for cases where the number of candidate experiments grows exponentially with the factor dimension, focusing on both first- and second-order models under design constraints. Particularly, our approach integrates convex relaxation with pricing-based local search techniques, which can provide upper bounds and performance guarantees. Unlike traditional local search methods, such as the ``Fedorov exchange" and its variants, our method effectively accommodates arbitrary side constraints in the design space. Furthermore, it yields both a feasible solution and an upper bound on the optimal value derived from the convex relaxation. Numerical results highlight the efficiency and scalability of our algorithms, demonstrating superior performance compared to the state-of-the-art commercial software, JMP