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<p>The School Bus Routing Problem (SBRP) is a complex vehicle routing problem involving multiple operational constraints, including vehicle capacities, time windows, service times, and workload balance. This paper proposes a hybrid optimization framework that integrates a reinforcement learning–based Neural Constructor with a Large Neighborhood Search (LNS) improvement phase. The Neural Constructor generates feasible and high-quality initial routing plans by learning structural properties of the problem, while LNS systematically enhances these solutions through adaptive neighborhood exploration. Computational experiments based on real-world data demonstrate that the proposed method significantly improves key logistical performance indicators compared to baseline planning solutions. On average, total travel distance is reduced by 11.5%, service time by 10.5%, and fleet utilization increases from 74.9% to 82.6%, while workload imbalance is reduced by 37%. All operational constraints are strictly satisfied. Sensitivity analyses show that neighborhood size and vehicle capacity are the most influential parameters, confirming the robustness and stability of the approach across different problem configurations. The results indicate that combining learning-based construction with local search constitutes an effective and computationally efficient strategy for solving large-scale and realistic SBRP instances, offering strong potential for practical deployment in school transportation systems.</p>

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The Urban Bus Routing Problem: Toward a Hybrid Deep Learning and Adaptive Metaheuristic Approach

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Sayda Ben Sghaier

摘要

The School Bus Routing Problem (SBRP) is a complex vehicle routing problem involving multiple operational constraints, including vehicle capacities, time windows, service times, and workload balance. This paper proposes a hybrid optimization framework that integrates a reinforcement learning–based Neural Constructor with a Large Neighborhood Search (LNS) improvement phase. The Neural Constructor generates feasible and high-quality initial routing plans by learning structural properties of the problem, while LNS systematically enhances these solutions through adaptive neighborhood exploration. Computational experiments based on real-world data demonstrate that the proposed method significantly improves key logistical performance indicators compared to baseline planning solutions. On average, total travel distance is reduced by 11.5%, service time by 10.5%, and fleet utilization increases from 74.9% to 82.6%, while workload imbalance is reduced by 37%. All operational constraints are strictly satisfied. Sensitivity analyses show that neighborhood size and vehicle capacity are the most influential parameters, confirming the robustness and stability of the approach across different problem configurations. The results indicate that combining learning-based construction with local search constitutes an effective and computationally efficient strategy for solving large-scale and realistic SBRP instances, offering strong potential for practical deployment in school transportation systems.