Vehicle Route Optimization of Express Package Distribution Considering Time-dependent Vehicle Speed

WANG Yong; JIN Yan; WEI Yuanfan; WEI Yuanhan

doi:10.19554/j.cnki.1001-3563.2026.13.027

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Packaging Engineering ›› 2026, Vol. 47 ›› Issue (13) : 241-255. DOI: 10.19554/j.cnki.1001-3563.2026.13.027

Green Packaging and Circular Economy

Vehicle Route Optimization of Express Package Distribution Considering Time-dependent Vehicle Speed

WANG Yong^1,2, JIN Yan¹, WEI Yuanfan¹, WEI Yuanhan³

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Abstract

The work aims to incorporate the time-dependent vehicle speed into the vehicle route optimization for express package delivery to minimize total operational costs and the number of vehicles utilized in the distribution network. Firstly, a bi-objective optimization model was constructed subject to constraints including vehicle capacity, distribution centers, customer time windows and time-dependent vehicle speed conditions, with the objectives of minimizing the total operational cost of express parcel logistics distribution and minimizing the number of vehicles deployed. Secondly, an improved multi-objective particle swarm optimization algorithm based on spatiotemporal clustering (SC-IMOPSO) was proposed to solve the model. Heuristic population initialization and decoding mechanisms were introduced to improve the quality of initial solutions, an adaptive external archive mechanism was applied to enhance algorithm robustness, and a dynamic departure strategy and a multi-period vehicle-sharing strategy were integrated to improve algorithm search ability. Thirdly, the effectiveness of the proposed model and algorithm was validated through comparisons with CPLEX solver, multi-objective simulated annealing, multi-objective ant colony optimization, and multi-objective genetic algorithm. Finally, a case study was conducted to analyze key performance indicators. Sensitivity analyses were performed regarding different service period divisions and time-dependent vehicle speed segments. The optimized delivery network reduced total operating costs by 47.6% and the number of vehicles by 70.6%. Specifically, the optimization achieved superior performance when the time horizon^[8,20] was divided into four service periods and twelve time-dependent vehicle speed segments. The proposed model, algorithm, and configuration strategies provide effective methods for cost reduction and offer new theoretical insights and research directions for the time-dependent express package distribution vehicle route optimization.

Key words

time-dependent vehicle speed / express package distribution / vehicle route optimization / SC-IMOPSO algorithm / multi-period vehicle-sharing strategy

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WANG Yong, JIN Yan, WEI Yuanfan, WEI Yuanhan. Vehicle Route Optimization of Express Package Distribution Considering Time-dependent Vehicle Speed[J]. Packaging Engineering. 2026, 47(13): 241-255 https://doi.org/10.19554/j.cnki.1001-3563.2026.13.027

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