HDRA: An Hybrid Divine Religion Algorithm Integrating Ant Colony Optimization and Memetic Search for Sustainable Electric Vehicle Routing in Smart Cities

Description

The Electric Vehicle Routing Problem (EVRP) is a challenging NP-hard combinatorial optimization problem that has motivated the development of advanced heuristic and metaheuristic approaches. This study proposes HDRA, a hybrid metaheuristic framework that integrates the Divine Religion Algorithm (DRA) with Ant Colony Optimization (ACO) and Memetic Search (MS) operators. The proposed metaheuristic exploits the complementary strengths of these three approaches to achieve an effective balance between exploration and exploitation. Specifically, DRA is enhanced by incorporating ACO’s pheromone-based positive-feedback mechanism, which adaptively reinforces promising search regions and improves the exploitation capability of the algorithm. In addition, a memetic local-search operator is incorporated to intensify the refinement of candidate solutions through domain-specific neighborhood structures. This operator facilitates the propagation and refinement of heuristic knowledge, referred to as “memes,” among elite leaders and subordinate followers, thereby strengthening local exploitation and progressively improving solution quality. The resulting hybrid mechanism accelerates convergence toward high-quality solutions while maintaining sufficient search diversity to mitigate premature convergence and algorithmic stagnation. The performance of HDRA is evaluated on more than 35 EVRP test instances of varying scales and compared with three established metaheuristic algorithms: Simulated Annealing (SA), Grasshopper Optimization Algorithm (GOA), and Harris Hawks Optimization (HHO). The computational results demonstrate that HDRA consistently achieves lower routing costs across both small- and large-scale instances. On average, HDRA reduces the solution cost by 12.43% compared with SA, 6.77% compared with GOA, and 11.60% compared with HHO. These results demonstrate the effectiveness and scalability of the proposed hybrid framework for solving EVRP instances. Furthermore, by improving routing efficiency and potentially reducing travel distance, energy consumption, and associated emissions, the proposed approach can serve as a decision-support framework for intelligent and sustainable transportation systems, contributing to more efficient urban mobility while maintaining high service-level performance.

Steps to reproduce

Sustainable transportation; Electric vehicle routing problem; Hybrid metaheuristic; Divine religious algorithm; Ant Colony Optimization; Memetic Search

Institutions

• Qazvin Islamic Azad University

  Qazvin Province, Qazvin

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