The capacitated single-allocation p-hub location routing problem: a Lagrangian relaxation and a hyper-heuristic approach

Abstract

A variant of the hub location routing problem studied in this work, which is the problem of locating a set of hub nodes, is establishing the hub-level network and allocating the spoke nodes to the hub nodes. As a particular property of this problem, each cluster of spoke nodes allocated to a hub constitutes a directed route that starts from the hub, visits all the spokes in the same cluster, and terminates to the same hub. We propose a hybrid of hyper-heuristic and a relax-and-cut solution method, which includes cooperation among several low-level heuristics governed and controlled by a learning mechanism. This hybridization provides a mechanism in which the obtained dual information through the Lagrangian relaxation (bundle) method being utilized to guide the local searches for constructing/improving feasible solutions. Several classes of valid inequalities as well as efficient separation routings are also proposed for being used within the relax-and-cut approach. Our extensive computational experiments confirm the efficiency of this solution method in terms of quality as well as computational time.

Mathematical modeling of a bi-objective hub location-routing problem for rapid transit networks

“…In some incomplete hub models, no particular topological structure is considered for the hub-level sub-network, not even being connected [7,8], while some other models have particular structures including circle [15], tree [13], star [31] and simple paths or lines [40,41]. A spoke-level sub-network can also have these structures or other particular structures such as direct connections [3,37], multi-stops [30,57], complete sub-graphs [52] and tours [4,16,25,26,28,29,42].…”

“…Constraints (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) enforce an edge to be included in a line if it is already built in the network. Constraints (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) to (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) ensure that an edge is built in the network only if the adjacent nodes are already built. Constraints (3)(4)…”

“…In this study, all the demand centers are considered as hub and spoke candidates. In the network shown by this figure, nodes 11 and 18 are not serviced, nodes 8,14,15,16,17,19 and 20 are hub stations, and the remaining nodes are spoke ones. The network consists of two hub lines, determined by line paths along stations (17,14,15,16) and (8, 15 ,19 ,20) and four spoke lines by the line paths along stations (1,5,9,13,14), (2,6,10,15), (3,7,12,16) and (4,8).…”

“…In the network shown by this figure, nodes 11 and 18 are not serviced, nodes 8,14,15,16,17,19 and 20 are hub stations, and the remaining nodes are spoke ones. The network consists of two hub lines, determined by line paths along stations (17,14,15,16) and (8, 15 ,19 ,20) and four spoke lines by the line paths along stations (1,5,9,13,14), (2,6,10,15), (3,7,12,16) and (4,8). The RTN design model proposed based on hubs and spokes has potential applications in designing new RTNs such as subways, BRT systems and multimodal systems in large cities, as in developing countries.…”

Location‐routing problem: a classification of recent research

“…In this sense, the exact method can be deployed with a limited running time in order to generate a high-quality solution for the next heuristic approach in a collaborative combination basis, or it can also be embedded within a more complex "master"' algorithm (Puchinger and Raidl, 2005). Several recent works have already presented a successful implementation of a matheuristic algorithm to obtain high-quality solutions of LRP model (e.g., Rath and Gutjahr, 2014;Guerrero et al, 2015;Gianessi et al, 2016;Amiri et al, 2019;Danach et al, 2019;Schmidt et al, 2019). As noted by Archetti and Speranza (2014), the main advantage of this approach is that it can take advantage of the advancement of commercial solvers.…”