By: Jianhua Xiao, Detian Kong, Zhiguang Cao, Jingyi Zhao,Deep reinforcement learning for the vehicle routing problem with route balancing,Transportation Research Part E:Logistics and Transportation Review.2026,208(04): 104632

ABSTRACT:The dynamic request vehicle routing problem has emerged as a key research focus, yet it continues to confront two major challenges. One significant issue is the highly time-dependent nature of urban travel speeds, which are influenced not only by recurrent congestion such as peak-hour traffic but also by non-recurrent congestion resulting from incidents like accidents or road work. Meanwhile, in the fiercely competitive market, achieving workload balance for delivery personnel is crucial fo maintaining workforce stability. Consequently, the dynamic request vehicle routing problem with workload balancing under time-dependent travel speeds (DRVRP-WT) has emerged as an urgent and significant research topic. Given the NP-hard nature of DRVRP-WT, developing computationally efficient solution methods is a key research challenge. We propose a novel multi-objective ant colony optimization algorithm with an adaptive objective bias mechanism (MOACO-AOB) to solve the DRVRP-WT problem. The proposed mechanism dynamically adjusts the optimization direction. Furthermore, we develop a local optimization strategy based on a hybrid time-dependent scheme to ensure timely responses to non-recurrent congestion. Extensive experiments on benchmark instances and case study demonstrate the effectiveness of the adaptive objective bias mechanism and the local optimization strategy in improving solution quality, and the proposed algorithm competes favorably with the algorithms documented in the literature.