Abstract
Hub Location Problems are complex combinatorial optimization problems that raised a lot of interest in the literature and have a huge number of practical applications, going from the telecommunications, airline transportation among others. In this paper we propose a primal-dual algorithm to solve the Uncapacitated Multiple Allocation Hub Location Problem (UMAHLP). RAMP algorithm combines information of traditional Dual Ascent procedure on the dual side with an improvement method on the primal side, together with adaptive memory structures. The overall performance of the proposed algorithm was tested on standard Australian Post (AP) and Civil Aeronautics Boarding (CAB) instances, comprising 192 test instances. The effectiveness of our approach has been proven by comparing with other state-of-the-art algorithms. © Springer Nature Switzerland AG 2019.

Abstract
This paper presents a Dual-RAMP algorithm for the solution of the multiple allocation hub location problem (UMAHLP). This approach combines information of a lagrangean relaxation procedure with subgradient optimization on the dual side with primal-feasible solutions on primal side, that are obtained by a simple improvement method. The overall performance of the proposed algorithm was tested on standard Australian Post (AP) and Civil Aeronautics Boarding (CAB) instances, comprising 192 test instances. The effectiveness of our approach has been proven by comparing our results with other state-of-the-art algorithms. © 2020, Springer Nature Switzerland AG.

Abstract
In this paper, we address the Capacitated Single Allocation ?-Hub Location Problem (CSA?HLP) in which the capacities of the hubs limit the flows in the network and every non-hub node must be allocated to only one hub. The objective is to choose a fixed number of ? nodes to be established as hubs that minimizes the costs of allocating all the non-hub nodes to the chosen hubs. We propose a simple Relaxation Adaptive Memory Programming (RAMP) approach that uses Lagrangean Relaxation with subgradient optimization to explore the dual side, a projection method to project dual solutions into the primal solutions space and an improvement method to guide the search in the primal side. The computational results obtained on a classical set of benchmark problems showed that our algorithm achieved the best results in the literature, demonstrating the advantages of exploring primal-dual relationships.

Abstract
We consider the Capacitated Single Allocation Hub Location Problem (CSAHLP) in which the objective is to choose the set of hubs from all nodes in a given network in such way that the allocation of all the nodes to the chosen hubs is optimal. We propose a Relaxation Adaptive Memory Programming (RAMP) approach for the CSAHLP. Our method combines Lagrangean Subgradient search with an improvement method to explore primal-dual relationships and create advanced memory structures that integrate information from both primal and dual solutions spaces. The algorithm was tested on the standard dataset and produced extremely competitive results that include new best-known solutions. Comparisons with the current best performing algorithms for the CSAHLP show that our RAMP algorithm exhibits excellent results.