• A novel pathway to evaluate optimization algorithms utilizing statistics and ANN. • One-Way ANOVA, Tukey test, and ANN are used to choose the best procedure. • Statistically, the PSO algorithm surpasses all others, but the ANN is better. This study attempts to establish a novel statistical and ANN-based decision-making mechanism for appraising hybrid system optimization strategies. An operational strategy and optimization problem for a hybrid, off-grid PV-wind system based on Nickel Iron battery storage is established in this paper, and an objective function for the system under consideration is presented. Particle swarm optimization, hybrid firefly and harmony search algorithm (HFAHS), Cultural Algorithm, harmony search, and Simulated Annealing are all used to address the optimization issue. A new procedure for selecting the optimal efficient optimization algorithm based on the One-Way ANOVA, the Tukey test, and ANN has been suggested, which allows for effective comparative analysis of algorithms. In the proposed approach, there were just a few steps to determine which algorithm would be the most successful in addressing the specific problem. A comparison of meta-heuristic optimization techniques based on ANN for the optimality of the presented system has been done. Comparing statistical parameters and ANN (i.e., MAE, MAPE, RMSE, and R-squared) to other models verifies the proposed model's efficiency. PSO's R-squared was 99.7%, indicating more accurate predictions. Although the ANN is superior, the PSO algorithm surpasses all other statistically evaluated algorithms.