New Hybrid Matheuristic Solves Chinese Postman Problem with Load Costs

A team of researchers from Vietnam—Thieu Khang Nguyen, Thu Huong Dang, and Truong-Son Hy—has introduced a hybrid optimizer for the Chinese Postman Problem with load-dependent costs (CPP-LC), a routing problem where travel expenses vary with vehicle payload and energy use. Published on arXiv (2607.22542), their framework combines metaheuristic search with mathematical programming to efficiently explore and exploit the solution space. Specifically, it couples local search with reduced mixed-integer linear programming (MILP) models, and incorporates an Ant Colony Optimization (ACO) algorithm for larger instances. The approach is designed to reflect real-world logistics scenarios, such as delivery fleets where fuel consumption increases with heavier loads.

Extensive benchmarking shows the hybrid framework consistently yields high-quality solutions, outperforming prior methods in solution quality while keeping computational time competitive. The authors note that hybridizing metaheuristics with exact optimization is especially effective for load-dependent routing problems. Their implementation is open-source, allowing logistics engineers and researchers to adapt it for practical route optimization. This work advances both the theory of arc routing and applications for sustainable last-mile delivery, as load-aware planning can reduce fuel costs and emissions.