Gaussian-Process-Augmented Particle Swarm Optimization (GP-PSO): Taxonomy, Survey, and Practitioner Guidance

High‐fidelity engineering simulations-Computational Fluid Dynamics, Finite‐Element Analysis and system‐dynamics models-impose prohibitive costs on optimization via traditional metaheuristics. Particle Swarm Optimization (PSO) and Gaussian Processes (GPs) have each shown promise, but canonical PSO suffers from premature convergence and excessive iterations when evaluations are noisy or expensive, and GP‐PSO integrations lack a unifying framework. In this review, we introduce a three‐axis taxonomy (1) surrogate‐integration strategy (e.g. fitness‐function replacement vs. augmentation), (2) acquisition (infill) function (e.g. Expected Improvement vs. Upper Confidence Bound), and (3) fidelity paradigm (e.g. single‐ vs. multi‐fidelity)-to classify and compare recent methods. We survey advances in deep‐kernel and neural‐augmented GPs, sparse‐GP approximations, adaptive retraining mechanisms, and hybrid/transfer‐learning extensions. Benchmark results on synthetic test suites and three real‐world applications (aerodynamic shape design, structural health monitoring, chemical‐process tuning) demonstrate 30–70 % fewer costly evaluations and 20–50 % faster convergence compared to PSO baselines, while maintaining or improving solution quality. From these studies, we distill practitioner guidelines for kernel and acquisition‐function selection, fidelity‐level choices, and reproducibility best practices-emphasizing shared code repositories and hyperparameter logs. Finally, we outline future directions in online surrogate updates, convergence theory under uncertainty, physics‐informed kernels, and standardized community benchmarks.