The rapid expansion of express delivery volume necessitates the development of logistics centers and the optimization of parcel transportation routes between cities within an extensive express transportation network. This study addresses the intercity express transportation network optimization problem (IETNP), which integrates the hub location problem with the multi-commodity flow problem. An integer linear programming model is introduced to represent the IETNP. To leverage the decomposable structure of the IETNP model, an improved Alternating direction method of multipliers (ADMM)-based algorithm is developed for solving the IETNP. A novel dual decomposition strategy is proposed to mitigate the negative effects of numerous coupling constraints on achieving high-quality upper-bound solutions. This strategy, incorporating penalty-term-reduction and multiplier-replacement methods, diminishes the number of penalty terms and the search space, thus enhancing computational efficiency while maintaining solution quality. A Lagrangian relaxation (LR)-based algorithm is employed to generate lower-bound solutions that assess the quality of the upper-bound solutions. Auxiliary constraints are integrated into the dualized formulation to enhance these lower-bound solutions. The effectiveness and efficiency of the improved ADMM-based algorithm are validated using over 100 artificial instances with 10–500 nodes and a realistic instance involving 338 cities. Comparative analysis with an off-the-shelf solver and existing ADMM- and LR-based algorithms reveals that the improved ADMM-based algorithm reduced the upper-bound values by 11.44% on average and by up to 22.09%.

中文翻译：

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基于ADMM的改进城际快速交通网络优化方法：一种新颖的对偶分解策略，部分保留耦合约束


快递量的快速增长，需要在广阔的快递运输网络中建设物流中心，优化城市之间的包裹运输线路。本研究解决了城际快速交通网络优化问题（IETNP），该问题将枢纽选址问题与多商品流问题相结合。引入整数线性规划模型来表示 IETNP。为了利用 IETNP 模型的可分解结构，开发了一种改进的基于乘子交替方向法 (ADMM) 的算法来求解 IETNP。提出了一种新颖的对偶分解策略，以减轻众多耦合约束对实现高质量上限解决方案的负面影响。该策略结合了惩罚项减少和乘数替换方法，减少了惩罚项的数量和搜索空间，从而在保持解质量的同时提高了计算效率。采用基于拉格朗日松弛 (LR) 的算法来生成评估上限解质量的下限解。辅助约束被集成到对偶公式中以增强这些下限解。使用 100 多个具有 10-500 个节点的人工实例和涉及 338 个城市的实际实例验证了改进的基于 ADMM 的算法的有效性和效率。与现成求解器和现有基于 ADMM 和 LR 的算法的比较分析表明，改进的基于 ADMM 的算法将上限值平均降低了 11.44%，最高降低了 22.09%。