Comparative multi-objective optimization of Flux-Switching Generator using GWO, PSO, NSGA-II, and MODE

The transition toward sustainable energy systems demands electrical generators that are highly efficient, reliable, and durable. Among emerging topologies, Flux-Switching Generators (FSGs) offer considerable potential. Nevertheless, without a systematic design methodology, FSGs may suffer from excessive torque ripple and reduced efficiency. This study presents a comprehensive multi-objective optimization of an FSG using four meta-heuristic algorithms: Gray Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Differential Evolution (MODE). The objective is to minimize total loss, active material volume, and torque ripple, while treating the average electromagnetic torque magnitude as a competing objective. To ensure a fair comparison, each algorithm is executed in 10 independent runs with identical population sizes and iteration limits, and equal weighting is assigned to all objective functions. Because GWO and PSO minimize a scalarized weighted cost whereas NSGA-II and MODE rely on Pareto dominance, all four designs are compared through a common normalized cost. The optimal designs obtained from each method are further validated through Finite Element Analysis (FEA), which indicates that bulk saturation is markedly reduced with respect to the preliminary design, the cores operating predominantly at about 1.4–1.6 T, while high flux-density regions remain confined to localized tooth-tip and magnet-interface areas. Notably, although the optimized designs operate at a lower torque magnitude, they attain a higher power density and efficiency than the preliminary machine, indicating that the framework yields more compact and efficient generators. Statistical evaluation based on the Friedman test and Holm-corrected pairwise Wilcoxon tests indicates that the four algorithms are statistically equivalent in solution quality; nevertheless, GWO attains the best mean rank, the lowest mean and minimum cost, and roughly half the computation time of the other methods, and is therefore identified as the most practical and efficient approach for FSG optimization.