A metaheuristic approach for the multi-objective sustainable vehicle routing problem

Abstract This study introduces the Multi-Objective Sustainable Vehicle Routing Problem (MOSVRP) with time windows, designed for congested urban networks. The model simultaneously addresses economic, environmental, and social sustainability by minimizing costs and emissions while maximizing customer satisfaction through enhanced service at pickup nodes. To manage the complexity of large-scale urban routing, we propose a novel Voronoi diagram-based network shrinking procedure that significantly reduces computational effort. More specifically, the model incorporates time-dependent traffic patterns to capture realistic urban conditions. For the solution, we propose a tailored metaheuristic, the enhanced Multi-Objective Volleyball Premier League (MOVPL) algorithm, which incorporates reference point guidance, disruption operators, and adaptive weight adjustment. This hybrid approach effectively balances conflicting objectives and improves solution diversity. Applied to Tehran’s urban freight network, the proposed method demonstrates superior performance across all metrics compared to benchmark algorithms and exact methods. Results show notable reductions in fuel consumption and travel distance, alongside improved service equity. Furthermore, the framework offers a scalable and transferable solution for sustainable logistics in other urban contexts.