IHG-GPSO: An Improved Hybrid Gaussian Particle Swarm Optimization with Nonlinear Inertia Weight and Directed Differential Experience for Global Optimization

This paper proposes an Improved Hybrid Gaussian Particle Swarm Optimization (IHG-GPSO) algorithm for high-dimensional global optimization. Four synergistic mechanisms are integrated: a nonlinear cosine–sine inertia weight to smoothly transition from exploration to exploitation, a memoryless random experience learning term that retains the experience-guided optimization paradigm of global PSO (GPSO) and improved PSO (IPSO) while eliminating historical optimum storage, a best-directed differential experience term inspired by differential evolution that tightens the swarm around the current global best, and a stagnation-triggered Gaussian mutation to restore population diversity without perturbing elite solutions. The proposed algorithm is evaluated on 12 classical benchmark functions at 30, 50, and 100 dimensions under a budget of 105 fitness evaluations, and on the CEC2017 test suite with 29 functions at 10, 30, and 50 dimensions, against PSO, GPSO, IPSO, CLPSO, CMA-ES, and L-SHADE over 30 independent runs (20 independent runs for the classical functions at D=100). Wilcoxon rank-sum tests at α=0.05 show that IHG-GPSO is statistically superior or equivalent to PSO, GPSO, and IPSO on the 12 classical functions, with no case of statistical inferiority on that suite; comparisons with the contemporary optimizers CLPSO, CMA-ES, and L-SHADE show that IHG-GPSO outperforms PSO, GPSO, and IPSO on all 12 functions, while CLPSO retains an edge on selected highly multimodal functions (Rastrigin, Schwefel 2.26, Penalized 1) and CMA-ES/L-SHADE remain superior on selected unimodal cases. On CEC2017, IHG-GPSO is again the most accurate PSO-family method, attaining the best Friedman average rank among PSO, GPSO, and IPSO at all three dimensions (3.638, 3.862, and 3.621 at D = 10, 30, 50, respectively), while L-SHADE, CLPSO, and CMA-ES occupy the top of the overall ranking on most functions; statistically significant losses against them are confined to a subset of shifted and rotated problems. Convergence curves and boxplot analysis confirm faster convergence and higher stability than the PSO-family baselines, while the algorithm maintains O(TND) time complexity and O(ND) memory complexity, making it a lightweight and effective solver for high-dimensional optimization tasks.