<i>d</i>-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding <i>D</i>-Optimal Designs with Discrete and Continuous Factors and a Binary Response

Identifying optimal designs for generalized linear models with a binary response can be a challenging task, especially when there are both discrete and continuous independent factors in the model. Theoretical results rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions. In this paper we propose the <i>d</i>-QPSO algorithm, a modified version of quantum-behaved particle swarm optimization, to find a variety of <i>D</i>-optimal approximate and exact designs for experiments with discrete and continuous factors and a binary response. We show that the <i>d</i>-QPSO algorithm can efficiently find locally <i>D</i>-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigate robustness properties of the <i>d</i>-QPSO algorithm-generated designs to various model assumptions and provide real applications to design a bio-plastics odor removal experiment, an electronic static experiment, and a ten-factor car refueling experiment.

针对二元响应广义线性模型（generalized linear models）确定最优设计方案是一项极具挑战性的任务，尤其当模型中同时存在离散与连续自变量因子时。此类模型的理论研究成果极为有限，即便存在少量相关成果，通常也附带严苛的假设条件。本文提出一种改进型量子行为粒子群优化（quantum-behaved particle swarm optimization）算法——d-QPSO算法，用于为同时包含离散与连续因子、响应为二元变量的实验，求解多种D最优（D-optimal）近似设计与精确设计方案。研究表明，即便针对自变量因子数量较多的实验场景，d-QPSO算法仍可高效求解局部D最优设计方案；而当模型参数的名义值无法获取时，该算法亦能生成稳健的伪贝叶斯（pseudo-Bayesian）设计方案。此外，本文还探究了d-QPSO算法生成的设计方案对各类模型假设的稳健性，并为三项实际实验的设计提供了应用范例：生物塑料除臭实验、静电实验以及十因子汽车燃油实验。

搜集汇总

背景与挑战

背景概述

该数据集提供了一个名为“d-QPSO”的量子行为粒子群优化算法，用于在具有离散和连续因子及二元响应的实验中寻找D-最优近似和精确设计。它解决了广义线性模型中设计优化的挑战，并展示了算法在多个实际应用（如生物塑料气味去除实验）中的有效性，同时涵盖了医学、生物科学等多个类别。