ForLion: A New Algorithm for D-optimal Designs under General Parametric Statistical Models with Mixed Factors

TL;DR

The paper introduces ForLion, an efficient algorithm for designing D-optimal experiments with mixed factors under general parametric models, reducing experimental settings and costs while maintaining high efficiency.

Contribution

It presents a novel algorithm, ForLion, that efficiently searches for locally optimal designs with mixed factors, guaranteeing optimality and outperforming existing methods.

Findings

Reduces the number of experimental settings by 25%.

Improves design efficiency by 17.5% on average.

Demonstrates superiority through real-life experiments and simulations.

Abstract

In this paper, we address the problem of designing an experimental plan with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for locally optimal approximate designs under the D-criterion. The algorithm performs an exhaustive search in a design space with mixed factors while keeping high efficiency and reducing the number of distinct experimental settings. Its optimality is guaranteed by the general equivalence theorem. We present the relevant theoretical results for multinomial logit models (MLM) and generalized linear models (GLM), and demonstrate the superiority of our algorithm over state-of-the-art design algorithms using real-life experiments under MLM and GLM. Our simulation studies show that the ForLion algorithm could reduce the number of experimental settings by 25% or improve the relative efficiency of the designs by 17.5% on average. Our algorithm can help the experimenters reduce the time cost, the usage of experimental devices, and thus the total cost of their experiments while preserving high efficiencies of the designs.