HDRADE: A Hybrid Divine Religion Algorithm Integrated with Differential Evolution for Efficient Electric Vehicle Routing

The Electric Vehicle Routing Problem (EVRP) is a central challenge in intelligent transportation, given its NP-hard nature and the substantial computational burden of exact approaches. To address this problem, researchers have increasingly turned to heuristic and metaheuristic methods to accelerate solution discovery. In this paper, we tackle EVRP with a novel hybrid metaheuristic: the Hybrid Divine Religions Algorithm Improved by Differential Evolution (HDRADE). The framework of HDRADE combines the Divine Religion Algorithm (DRA), a concept inspired by human behavioral tendencies and social dynamics, with the robust search operators of Differential Evolution (DE). To further enhance performance, we introduce a blacklist mechanism within DRA: penalized individuals are removed from subsequent steps (selection, mutation, and crossover), which helps mitigate bias and promotes diversity. The extended DRA is then integrated with DE’s mutation and crossover operators to yield an adaptive and balanced search process. The empirical results across more than 35 test cases show that HDRADE outperforms Harmony Search (HS), the Grasshopper Optimization Algorithm (GOA), and Harris Hawks Optimization (HHO) on both small- and large-scale instances, achieving an average cost reduction of 18.7% and faster run times than GOA. In addition to improving optimization performance, the proposed HDRADE supports sustainable logistics and eco-efficient transportation by reducing energy consumption, minimizing charging-related costs, and promoting intelligent green routing decisions in electric vehicle networks. Overall, HDRADE demonstrates a compelling balance among solution quality, convergence speed, robustness, and sustainability-oriented performance, making it a promising candidate for solving complex EVRP instances in smart transportation environments.