Hybrid Improved DRA-DE

Here introduces an innovative hybrid metaheuristic known as the Hybrid Algorithm of Divine Religions with Differential Evolution (HDRADE), aimed at addressing NP-hard problems. It achieves this by merging the evolutionary socio-economic approach with the robust mutation and intersection mechanisms inherent in differential evolution (DE), thereby facilitating a balanced and adaptive search process. In this enhanced algorithm, in addition to elements such as miracles and reward-penalty, a blacklist operator has been incorporated. This operator ensures that during the follower qualification stages, penalized followers (infidels) are blacklisted and subsequently excluded from the selection, mutation, or combination processes in later stages of the algorithm. The blacklist is updated at each stage to mitigate any bias towards religious missions within any school. The suggested algorithm's performance is compared to that of eight popular metaheuristic techniques, including the Sine–Cosine Algorithm (SCA), Tunicate Swarm Algorithm (TSA), Moth–flame Optimization (MFO), Gray Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Fire Hawk Optimization (FHO), Smell Agent Optimization (SAO), and Divine Religions Algorithm (DRA). We assess the suggested algorithm by utilizing twenty-three standard benchmarks from the CEC-BC-2019 collection. Furthermore, key metrics such as accuracy, convergence, efficiency, and cost have been analyzed based on the criteria of best cost, cost, and standard deviation.