A learning-based probabilistic tabu search for the uncapacitated single allocation hub location problem

In this paper, we develop a learning-based probabilistic tabu search to solve the uncapacitated single allocation hub location problem (USAHLP). In the proposed algorithm, a novel integer representation of solution is presented to maintain the feasibility of solution throughout the search and to simplify the calculation of the objective function value. Two randomized greedy construction procedures are adopted to obtain good initial solutions. Location improvement and allocation improvement procedures are utilized to enhance the exploitation ability. Furthermore, a new learning-based probabilistic tabu strategy is proposed to prevent the location improvement procedure from visiting the inferior solutions previously investigated. In the allocation improvement procedure, the difference between the value of the initial solution and its neighbor is applied to obtain the value of the neighbor for the purpose of reducing the running time. To verify the efficiency of the proposed algorithm, computational experiments are conducted on the benchmark instances for the USAHLP. Of all 76 instances, our algorithm is capable of attaining all the previous best known results and improving the best known results for five large instances in a reasonable time. The obtained results reveal that the proposed algorithm is competitive with the state-of-the-art heuristics.