An efficient memetic algorithm for the uncapacitated single allocation hub location problem

Abstract

In this paper, we present a memetic algorithm (MA) for solving the uncapacitated single allocation hub location problem (USAHLP). Two efficient local search heuristics are designed and implemented in the frame of an evolutionary algorithm in order to improve both the location and allocation part of the problem. Computational experiments, conducted on standard CAB/AP hub data sets (Beasley in J Global Optim 8:429---433, 1996) and modified AP data set with reduced fixed costs (Silva and Cunha in Computer Oper Res 36:3152---3165, 2009), show that the MA approach is superior over existing heuristic approaches for the USAHLP. For several large-scale AP instances up to 200 nodes, the MA improved the best-known solutions from the literature until now. Numerical results on instances with 300 and 400 nodes introduced in Silva and Cunha (Computer Oper Res 36:3152---3165, 2009) show significant improvements in the sense of both solution quality and CPU time. The robustness of the MA was additionally tested on a challenging set of newly generated large-scale instances with 520---900 nodes. To the best of our knowledge, these are the largest USAHLP problem dimensions solved in the literature until now. In addition, in this paper, we report for the first time optimal solutions for 30 AP and modified AP instances.