A multi-objective evolutionary algorithm with constraint-compliant initialization for energy transport and urban logistics in Electric Vehicle Routing

Electric vehicles (EVs) offer a new opportunity to enhance the efficiency of both transportation logistics and energy distribution. Integrating these dual objectives introduces complex optimization challenges due to interdependent constraints. This paper addresses the Vehicle Routing Problem with Time Windows integrated with Energy Transport (VRPTW-ET), where a fleet of EVs is used to serve customer demands while simultaneously transporting energy to (dis)charging facilities. We formulate the problem as a multi-objective optimization problem and design an evolutionary algorithm based on NSGA-II, featuring constraint-aware initialization and problem-specific operators for routing, time windows, and energy logistics. Our approach operates under realistic simplification, including static energy demands and travel costs, which help isolate the core challenges of the problem. Experimental results on modified benchmarks show that the proposed integrated approach consistently outperforms decoupled baselines, achieving up to 30% reduction in energy costs and 20% fewer vehicles used. These findings demonstrate the effectiveness of coordinated logistics-energy strategies in promoting cost-efficient and sustainable urban mobility.