TSP solution using an exact model based on the branch flow formulation and automatic cases generation via the Julia software

The traveling salesman problem (TSP) is a classical optimization problem with practical applications in logistics, transportation, and network design. This research proposes an efficient mixed-integer linear programming (MILP) model based on the branch flow formulation which prevents the formation of sub-tours during the solution process and guarantees valid optimal routes. Implemented in Julia with the JuMP optimization package and the HiGHS solver, the model achieves high computational efficiency. Unlike classical models, the branch flow formulation ensures a quadratic constraint growth, rather than an exponential one, significantly enhancing scalability. Benchmark tests on various instances (Eil51, Eil76, KroA100) demonstrate results comparable to state-of-the-art combinatorial optimizers, and six new TSP instances, ranging from 50 to 300 cities, validate the model’s performance. This scalable and robust approach is well-suited for real-world applications in supply chain management, network optimization, and urban planning, and it shows potential for future extensions to dynamic or multi-objective TSP variants.