Round-trip hub location problem

In this paper, we introduce a novel network design for the Hub Location Problem, inspired by the round-trip structure commonly used by transport service providers. Our design integrates spoke nodes assigned to a central hub node, creating round-trips where the hub node serves as the starting point, visits all assigned spoke nodes, and returns to the hub. To enhance transportation services and provide additional redundancy, we introduce a new type of nodes called runaway nodes to the network. The motivation for this research arises from two real-life cases encountered during consultancy projects, underscoring the necessity for an optimized network design in transportation services. To address the proposed problem, we introduce a mixed-integer linear programming (MIP) mathematical model. However, due to the problem's complexity, the feasibility of the MIP model is limited to small-scale instances. To tackle medium and large-scale instances, we introduce two hyper-heuristic approaches based on reinforcement learning. These hyper-heuristic approaches harness the power of reinforcement learning to guide the selection of low-level heuristics and improve solution quality. We conduct extensive computational experiments to evaluate the efficiency and effectiveness of the proposed approaches. The results of our experiments affirm the efficiency of the proposed hyper-heuristic approaches, showcasing their ability to discover high-quality solutions for the Hub Location Problem.