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On the Complexity of the Uncapacitated Single Allocation p-Hub Median Problem with Equal Weights
(2007)
The Super-Peer Selection Problem is an optimization problem in network topology construction. It may be cast as a special case of a Hub Location Problem, more exactly an Uncapacitated Single Allocation p-Hub Median Problem with equal weights. We show that this problem is still NP-hard by reduction from Max Clique.
In this paper, a new mixed integer mathematical programme is proposed for the application of Hub Location Problems (HLP) in public transport planning. This model is among the few existing ones for this application. Some classes of valid inequalities are proposed yielding a very tight model. To solve instances of this problem where existing standard solvers fail, two approaches are proposed. The first one is an exact accelerated Benders decomposition algorithm and the latter a greedy neighborhood search. The computational results substantiate the superiority of our solution approaches to existing standard MIP solvers like CPLEX, both in terms of computational time and problem instance size that can be solved. The greedy neighborhood search heuristic is shown to be extremely efficient.