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

arXiv: https://arxiv.org/abs/2606.15962 · HTML: https://mlsanity.com/paper/2606.15962/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 53 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Builds on (most cited first, 1 of 1)

- [ForLion: A New Algorithm for D-optimal Designs under General Parametric Statistical Models with Mixed Factors](https://mlsanity.com/paper/2309.09367/) (2023)

## Abstract (arXiv)

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.