ILS-based algorithms for the profit maximizing uncapacitated hub network design problem with multiple allocation.

This study addresses a hub network design problem to maximize net profit. This problem considers an incomplete hub network with multiple allocation that does not impose capacity constraints, does not allow direct connections between non-hub nodes, and accepts the demand to be partially met, being satisfied only when profitable. To tackle this problem, which is NP-hard, we propose two heuristic algorithms based on the Iterated Local Search (ILS) metaheuristic, a standard ILS algorithm, and an Enhanced ILS algorithm, which increases the perturbation level only after a few unsuccessful attempts at improvement. Both algorithms use Random Variable Neighborhood Descent in the local search. Computational experiments were performed using benchmark instances for hub location problems, and statistical analyzes of the algorithms were presented. Numerical results confirm that both algorithms yield good-quality solutions with an acceptable runtime. In particular, the proposed algorithms obtain the optimal solution for most instances with up to 150 nodes, which have known optimal solutions. Furthermore, the proposed algorithms were able to handle instances with up to 500 nodes.