提出一种新罚函数方法，高效求解混合因子GLM的D最优设计。
p-PSO: A Penalized Particle Swarm Optimization Technique for Finding D-Optimal Designs with Mixed Factors in Generalized Linear Models
- 用新罚函数改造粒子群算法，处理混合离散连续变量的设计问题。
- 在多个GLM场景中验证，相比传统方法更快收敛且结果更优。
- 适合需要快速生成实验设计的研究者，尤其适用于复杂模型优化。
在广义线性模型（GLMs）中寻找D最优设计极具挑战性，因费舍尔信息矩阵依赖未知参数且无闭式解，尤其当输入因子包含离散与连续变量时更为困难。尽管经典算法和近年元启发式方法提供部分解决方案，仍需高效稳健的方法。本文提出一种带惩罚项的粒子群优化（p-PSO）方法，引入一种通用型罚函数框架，适用于约束优化任务。该框架不依赖具体算法，可广泛应用于各类黑箱优化方法。实验表明，该方法计算效率高，核心贡献在于使现成粒子群算法可直接用于此类问题，并自然扩展至更广泛的约束优化场景。
原文摘要 · Abstract (English)
Finding D-optimal designs for generalized linear models (GLMs) is challenging due to the dependence of the Fisher information matrix on unknown parameters and the lack of closed-form solutions, particularly when input factors include both discrete and continuous variables. Although classical algorithms and recent metaheuristic approaches have offered partial solutions, there remains a need for robust and computationally efficient methods. In this paper, we propose a penalized Particle Swarm Optimization (PSO) approach, named $p$-PSO. Here we introduce a new, general-purpose penalty formulation for constrained optimization and demonstrate its effectiveness in optimal design problems. The formulation is algorithm-agnostic and applicable to a broad class of black-box optimization methods. Results show that the method is highly efficient, with its primary contribution being a penalty formulation that enables the direct use of an off-the-shelf PSO algorithm and extends naturally to more general constrained optimization tasks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。