Hub location problem in round-trip service applications

In this paper, we introduce a new hub-and-spoke structure for service networks based on round-trips as practiced by some transport providers. This problem is variant of Uncapacitated Hub Location Problem wherein the spoke nodes allocated to hub node form (cycles) starting from and ending node. motivated two real-life practices in logistics runaway connections with their associated economies scale were foreseen increase redundancy network. We propose mixed integer linear programming mathematical model exponential number constraints. addition separation routines separating among constraints, hyper-heuristic reinforcement learning its comparable counterpart variable neighborhood search. Our extensive computational experiments confirm efficiency proposed approaches.