🤖 AI Summary
This study addresses the challenge of constructing D-optimal experimental designs for generalized linear models (GLMs) with mixed discrete-continuous factors, where the Fisher information matrix depends on unknown parameters and lacks closed-form solutions, rendering efficient computation difficult. To overcome this, the authors propose a penalty-based particle swarm optimization method (p-PSO) that reformulates the constrained optimization problem into an unconstrained one, enabling direct application of off-the-shelf PSO algorithms. The proposed penalty scheme is algorithm-agnostic and readily extensible to various black-box optimizers. Empirical results demonstrate that the method achieves superior computational efficiency and robustness, successfully generating D-optimal designs for GLMs with mixed factors and confirming the broad applicability of the penalty mechanism across diverse constrained optimization tasks.
📝 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.