Primal-dual algorithms for the Capacitated Single Allocation p-Hub Location Problem

The Hub Location Problems (HLP) have gathered great interest due to the complexity and to the many applications in industry such as aviation, public transportation, telecommunications, among others. The HLP have many variants regarding allocation (single or multiple) and capacity (uncapacitated or capacitated). This paper presents a variant of the HLP, encompassing single allocation with capacity constraints. The Capacitated Single Allocation p-Hub Location Problem (CSApHLP) objective consists on determine the set of p hubs in a network that minimizes the total cost of allocating all the non-hub nodes to the p hubs. In this work, it is proposed a sophisticated RAMP approach (PD-RAMP) to improve the results obtained previously by the simple version (Dual-RAMP). Thus, a parallel implementation is conducted to assess the effectiveness of a parallel RAMP model applied to the CSApHLP. The first algorithm, the sequential PD-RAMP, incorporates Dual-RAMP with a Scatter Search procedure to create a Primal-Dual RAMP approach. The second algorithm, the parallel PD-RAMP, also take advantage of the dual and primal, parallelizing the primal side of the problem and interconnecting both sides as it is expected in the RAMP sequential algorithm. The quality of the results carried out on a standard testbed shows that the PD-RAMP approach managed to improve the state-of-the-art algorithms for the CSApHLP.