AI 中文总结
针对具有负载相关成本的中国邮递员问题，提出混合优化框架，结合元启发式搜索与数学规划，包括局部搜索与简化MILP模型，还开发ACO算法，实验表明该框架能高效获高质量解，优于现有方法。
AI 中文摘要
具有负载相关成本的中国邮递员问题（CPP-LC）出现在现实世界的物流和运输系统中，其中旅行成本取决于车辆负载和能源消耗。在这项工作中，我们提出了一种混合优化框架，将元启发式搜索与数学规划相结合，以有效地解决CPP-LC。所提出的方法将局部搜索过程与简化的混合整数线性规划（MILP）模型相结合，以平衡探索和强化搜索。此外，我们开发了一种蚁群优化（ACO）算法来提高在大型实例上的可扩展性。在基准数据集上进行的大量实验表明，所提出的框架始终能获得高质量的解决方案，在解决方案质量方面优于现有方法，同时保持有竞争力的计算效率。这些结果突出了混合优化策略在实际应用中解决复杂的、负载相关的路由问题的有效性。我们的实现可通过此https URL公开获取。
英文摘要
The Chinese Postman Problem with load-dependent costs (CPP-LC) arises in real-world logistics and transportation systems where travel costs depend on vehicle load and energy consumption. In this work, we propose a hybrid optimization framework that integrates metaheuristic search with mathematical programming to efficiently solve CPP-LC. The proposed method combines local search procedures with reduced mixed-integer linear programming (MILP) models to balance exploration and intensification. In addition, we develop an Ant Colony Optimization (ACO) algorithm to enhance scalability on large instances. Extensive experiments on benchmark datasets demonstrate that the proposed framework consistently achieves high-quality solutions and outperforms existing approaches in solution quality, while maintaining competitive computational efficiency. These results highlight the effectiveness of hybrid optimization strategies for complex, load-dependent routing problems in practical applications. Our implementation is publicly available at https://github.com/HySonLab/MatCPP
