Solving uncapacitated multiple allocation p-hub center problem by Dijkstra’s algorithm-based genetic algorithm and simulated annealing

In the existing literature, there are a huge number of studies focused on p-hub median problems and inventing heuristic or metaheuristic algorithms for solving them. But such analogous body of literature does not exist for its counterpart problem; p-hub center problem. In fact, since p-hub center has been lately introduced and has a particular objective function, minimizing the maximum cost between origin-destination nodes, there are few studies investigating the problem and the challenges for solving it. In this study, after presenting a complete definition of the uncapacitated multiple allocation p-hub center problem (UMApHCP) two well-known metaheuristic algorithms are proposed to solve the problem for small scale and large scale standard data sets. These two algorithms are one single solution-based algorithm, Simulated Annealing (SA), and one population-based metaheuristic, Genetic Algorithm (GA). Because of the particular nature of the problem, Dijkstra’s algorithm has been incorporated in the fitness function calculation part of the proposed methods. The numerical results of running the GA and SA for standard test problems show that for smaller scale test problems, single solution-based SA shows greater performance versus GA but for larger scales of data sets the GA generally yield more desirable solutions.