p-PSO: A Penalized Particle Swarm Optimization Technique for Finding D-Optimal Designs with Mixed Factors in Generalized Linear Models

Abstract: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.

Methodology (stat.ME); Machine Learning (cs.LG)

arXiv:2606.15962 [stat.ME]

(or arXiv:2606.15962v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2606.15962 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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