A hybrid metaheuristic method for the deterministic and robust uncapacitated multiple allocation p-hub centre problem

This study considers the well-known uncapacitated multiple allocation p-hub centre problem (UMApHCP) and introduces its robust variant (UMApHCP-R) by involving flow variations with unknown distributions. As a solution method to both UMApHCP and UMAPHCP-R, a hybrid metaheuristic algorithm (HMA) is proposed, which successfully combines particle swarm optimisation and a local search heuristic. Constructive elements of the HMA are adapted to the considered problems and its parameters are experimentally adjusted. Experimental results obtained for the UMApHCP show the superiority of the proposed HMA over the existing methods from the literature on standard hub instances in the sense of solution quality or running times. The results obtained by the HMA on large-scale hub instances with up to 900 nodes are also presented. The analysis of the HMA results for the UMApHCP-R on selected problem instances shows the impact of flow variations on the objective function value. [Received 11 September 2016; Revised 23 March 2017; Accepted 7 July 2017]