A deep reinforcement learning-enhanced metaheuristic approach for a multi-objective sustainable hub location-routing problem

This study presents a novel approach to addressing the multi-objective sustainable hub Location-routing problem, an NP-hard optimization challenge that balances economic efficiency and environmental sustainability. The model integrates constraints on transportation fleet availability and routing while minimizing CO2 emissions and total transportation costs. A deep reinforcement learning-enhanced metaheuristic approach, combining archived multi-objective simulated annealing with deep Q networks (DQN) using both replay and no-replay mechanisms, is proposed to solve large-scale instances. Comprehensive experiments conducted on CAB and AP datasets demonstrate the superiority of the proposed method in generating high-quality Pareto front solutions. Notably, the DQN-enhanced approaches, particularly those leveraging experience replay, achieve superior Pareto front coverage and solution quality compared to traditional metaheuristics and the no-replay variant. These findings highlight the potential of combining deep reinforcement learning with metaheuristic optimization for advancing sustainable logistics.