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The capacitated single assignment hub location problem with modular link capacities is a variant of the classical hub location problem in which the cost of using edges is not linear but stepwise, and the hubs are restricted in terms of transit capacity rather than in the incoming traffic. We propose a metaheuristic algorithm based on strategic osci...
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... The study proposed efficient heuristic methods that outperform previous approaches, utilize memory structures to enhance search algorithms, and are compared with previous heuristics using benchmark instances and incorporating frequency information in the constructive method. Corberán et al. (2016) addressed the capacitated single-assignment HLP with modular link capacities. They developed a metaheuristic algorithm based on strategic oscillation, originally used in tabu search. ...
Hub networks play a crucial role in optimizing transportation costs in air and road systems. Their main objective is to strategically locate hubs and allocate non-hub nodes within the network. The modular hub location problem is a specific area of hub network design that focuses on accurately calculating transportation costs, considering factors like trip numbers and capacity constraints in network routes. This study proposes a mixed-integer programming model to address the modular hub location problem with multiple allocations. It considers dependent and independent costs associated with vehicles per trip between hub network routes, considering specific vehicle capacities. Two datasets are utilized for validation: the CAB dataset representing 25 nodes of US airports and the TR dataset representing the Turkish transportation system with 81 nodes. To tackle the NP-hard nature of hub location models and the computational complexity of the proposed model, two solutions are developed. Firstly, a novel LP relaxation-based method using GAMS software provides near-optimal solutions for medium-sized instances. Additionally, a Genetic Algorithm (GA) implemented in MATLAB handles larger instances. The GA's efficiency is enhanced by tuning its parameters using the Taguchi method. Results analysis shows that both proposed algorithms yield high-quality solutions within significantly reduced timeframes compared to the CPLEX solver in GAMS software. The LP relaxation-based method performs well for medium-sized instances, while the GA approach is efficient for larger instances after parameter tuning with the Taguchi method.
... Martin-Santamaria et al. (2022) applied the SO method to solve the balanced minimum sum-of-squares clustering problem, in which the cluster size constraints are allowed to be relaxed by increasing each cluster size by a percentage during the search. The SO method has also been applied to solve other optimization problems, such as the α-neighbor p-center problem and the capacitated hub location problems with modular links (Corberán et al., 2016). Different oscillation strategies have been proposed to maintain a balanced search between the feasible and infeasible search regions for the algorithm to explore the search space more effectively. ...
... The algorithm adopts the strategic oscillation search framework with an original responsive mechanism to guide the search to oscillate around the boundary of feasible and infeasible regions. Previous investigations have disclosed the general idea of strategic oscillation (SOS, [12]) to be quite effective for a number of constrained optimization problems, such as the quadratic multiple knapsack problem [11], the capacitated hub location problem [9], the maximally diverse grouping problem [10], the quadratic minimum spanning tree problem [31], the α-neighbor p-center problem [40], and the bipartite boolean quadratic programming problem [45,49]. In this work, we show the benefits of strategic oscillation for solving the DCKP. ...
... S ← S /* S replaces S when the threshold T is satisfied */ 11: break; 12: As shown in Algorithm 2, the FLS procedure first performs some initialization tasks (lines [3][4][5]. Then the search enters the 'while' loop (lines [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to improve the input solution S iteratively by sequentially exploring three neighborhoods N F 1 to N F 3 (see [46] for more details). Each iteration of the 'while' loop performs three operations. ...
... As shown in Algorithm 3, after some initialization tasks (lines 3-7), the SOS procedure performs the 'while' loop to examine candidate solutions (lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Each iteration of the loop calculates, according to Equation (8), the critical value CV (S ) of each non-prohibited neighboring solution S within the neighborhood N + (line 10), where N + is the union of three relaxed neighborhoods (see Section 2.5.2 for these relaxed neighborhoods.) ...
Given a directed graph G = ( V, E ), a feedback vertex set is a vertex subset C whose removal makes the graph G acyclic. The feedback vertex set problem is to find the subset C * whose cardinality is the minimum. As a general model, this problem has a variety of applications. However, the problem is known to be NP-hard, and thus computationally challenging. To solve this difficult problem, this article develops an iterated dynamic thresholding search algorithm, which features a combination of local optimization, dynamic thresholding search, and perturbation. Computational experiments on 101 benchmark graphs from various sources demonstrate the advantage of the algorithm compared with the state-of-the-art algorithms, by reporting record-breaking best solutions for 24 graphs, equally best results for 75 graphs, and worse best results for only two graphs. We also study how the key components of the algorithm affect its performance of the algorithm.
... The algorithm adopts the strategic oscillation search framework with an original responsive mechanism to guide the search to oscillate around the boundary of feasible and infeasible regions. Previous investigations have disclosed the general idea of strategic oscillation (SOS, [12]) to be quite effective for a number of constrained optimization problems, such as the quadratic multiple knapsack problem [11], the capacitated hub location problem [9], the maximally diverse grouping problem [10], the quadratic minimum spanning tree problem [31], the α-neighbor p-center problem [40], and the bipartite boolean quadratic programming problem [45,49]. In this work, we show the benefits of strategic oscillation for solving the DCKP. ...
... S ← S /* S replaces S when the threshold T is satisfied */ 11: break; 12: As shown in Algorithm 2, the FLS procedure first performs some initialization tasks (lines [3][4][5]. Then the search enters the 'while' loop (lines [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to improve the input solution S iteratively by sequentially exploring three neighborhoods N F 1 to N F 3 (see [46] for more details). Each iteration of the 'while' loop performs three operations. ...
... As shown in Algorithm 3, after some initialization tasks (lines 3-7), the SOS procedure performs the 'while' loop to examine candidate solutions (lines [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Each iteration of the loop calculates, according to Equation (8), the critical value CV (S ) of each non-prohibited neighboring solution S within the neighborhood N + (line 10), where N + is the union of three relaxed neighborhoods (see Section 2.5.2 for these relaxed neighborhoods.) ...
... After obtaining a solution = ( , ), we combine a hub and its assigned nodes to form a subset expressed as ℎ (ℎ ∈ ), where ℎ = ∈ : = ℎ indicates that the subset contains all spokes assigned to hub ℎ. To evaluation of a solution = ( , ) , there are three types of cargo flow according to the method mentioned in Corberán et al. [37]. Mikić et al. [38] proposed three types of flows to evaluate feasible solutions = ( , ). ...
The hub-and-spoke network (HSN) design generally assumes direct transportation between a spoke node and its assigned hub, while the spoke’s demand may be far less than a truckload. Therefore, the total number of trucks on the network increases unnecessarily. We form a drone-based traveling salesman problem (TSP-D) for the cluster of spokes assigned to a hub. A truck starts from the hub, visiting each spoke node of the hub in turn and finally returning to the hub. We propose a three-stage decomposition model to solve the HSN with TSPD (HSNTSP-D). The corresponding three-stage decomposition algorithm is developed, including cooperation among variable neighborhood search (VNA) heuristics and nearest neighbor algorithm (NNA), and then the spoke-to-hub assignment algorithm through the reassignment strategy (RA) method. The performance of the three-stage decomposition algorithm is tested and compared on standard datasets (CAB, AP, and TR). The numerical analysis of the scenarios shows that whether it is trunk hub-level transportation or drone spoke-level transportation, it integrates resources to form a scale effect, which can reduce transport devices significantly, as well as decreasing the investment and operating costs.
... Most of other heuristics were designed for particular type of hub location problems. For instance, Corberán et al. (2016) proposed a greedy-strategic oscillation method to solve the capacitated single allocation hub location problem with modular links. In this problem, the cost for using links is step-wise, and the capacities of hubs are use to restrict the transit flows rather than the incoming flows. ...
Our study provides an experimental benchmark for state-of-the-art solution algorithms with hub location problems. Such problems are fundamental optimization problems in location science with widespread application areas, such as transportation, telecommunications, economics, and geography. Given they combine aspects of facility location and quadratic assignment problems, the majority of hub location problems are NP-hard and, accordingly, several solution techniques have been proposed for solving these problems. In this study, we report on the results of a large benchmark and reproduction effort to investigate 12 fundamental hub location problems that combine single or multiple allocation, a p-hub median objective or fixed hub set-up costs, capacitated or uncapacitated hubs, and complete or incomplete networks. We implemented four standard exact algorithms on these 12 problems as proposed in the literature. Algorithms are evaluated on subsets of three standard data sets in the field (CAB, TR, and AP); we computed more than 5,000 optimal solutions for these data sets. We report comparisons of solution techniques regarding wall clock time, convergence speed, memory use, and the impact of data features. In addition, we identify patterns in optimal solutions across these 12 problems, extracting insights regarding solution similarity, hub set candidates, and economies of scale. All results and programs are being made available to the public for free academic use.
... Link based dimensioning of vehicles: Be it an incomplete or a complete hub network design, the common underlying inherent assumption of classical hub location is that one or more vehicles will be reserved to each link that will carry out round-trips between the two hub endpoints with some frequency. Even in the rare cases (such as Yaman and Carello (2005), Yaman (2005), Corberán et al. (2016) and Serper and Alumur (2016)) where vehicles that will carry the flow are also dimensioned, this dimensioning might be unnecessarily conservative since this association is done without considering the operations on the transportation end. The same vehicle can carry the flow on two consecutive hub links, provided the time limit allows. ...
We propose a novel hub location model that jointly eliminates some of the traditional assumptions on the structure of the network and on the discount as a result of economies of scale in an effort to better reflect real-world logistics and transportation systems. Our model extends the hub literature in various facets: instead of connecting nonhub nodes directly to hub nodes, we consider routes with stopovers; instead of connecting pairs of hubs directly, we design routes that can visit several hub nodes; rather than dimensioning pairwise connections, we dimension routes of vehicles; and rather than working with a homogeneous fleet, we use intermodal transportation. Decisions pertinent to strategic and tactical hub location and transportation network design are concurrently made through the proposed optimization scheme. An effective branch-and-cut algorithm is developed to solve realistically sized problem instances and to provide managerial insights.
... In his proposed model, every demand node has a backup hub in the case of disruption. Corberán et al. (2016) also considered a single allocation hub location problem with link capacities. They proposed a meta-heuristic algorithm in accordance with the strategic oscillation and demonstrated that their proposed algorithm has a better performance compared to the tabu search. ...
This paper presents a new bi-objective multi-modal hub location problem with
multiple assignment and capacity considerations for the design of an urban public
transportation network under uncertainty. Because of high construction costs of hub
links in an urban public transportation network, it is not economic to create a complete
hub network, so the presented hub network is supposed to be incomplete. Moreover, the
demand is assumed to be dependent on the utility proposed by each hub. Thus, the
elasticity of the demand is considered in this paper. The presented model also has the
ability to compute the number of each type of transportation vehicles between every
two hubs. The objectives of this model are to maximize the benefits of transportation by
establishing the hub facilities and minimize the total network transportation time. As
exact values of some parameters are not specified in advance, a fuzzy multi-objective
programming based approach is proposed to optimally solve small-sized problems. For
medium and large-sized problems, a meta-heuristic algorithm, namely multi-objective
particle swarm optimization (MOPSO) is applied and its performance is compared with
results from the non-dominated sorting genetic algorithm (NSGA-II). It is demonstrated
that the developed model is applicable and a number of sensitivity analyses are carried
out on a real-case study inspired by a monorail project of Qom city.
... They develop an exact and a heuristic method for modular link hub location problem. For the same problem,[26] propose a metaheuristic and compare the computational performance of the algorithm with the results given in[79]. ...
... When the hubs are fully interconnected, the above setting leads to a so-called uncapacitated r -allocation p -hub median problem with non-stop services and network design decisions. It corresponds, in fact, to the deterministic version of the family of problems investigated by Peiró et al. (2016) ; it also includes the uncapacitated r -allocation p -hub median problem (U r A p HMP) introduced by Yaman (2011) as a particular case. ...
... Peiró et al. (2014) , Todosijevic et al. (2015) , and Martí et al. (2015) propose a GRASP heuristic, a VNS, and a scatter search procedure for the U r A p HMP, respectively. For an extension of the above problem that includes setup costs for the allocation of terminals to hubs as well as stochasticity in the costs and demands, Peiró et al. (2016) devise a new type of heuristic yielding sharp upper bounds. Corberán et al. (2016) develop a strategic oscillation algorithm for a capacitated single allocation hub location problem with modular links. ...
... For an extension of the above problem that includes setup costs for the allocation of terminals to hubs as well as stochasticity in the costs and demands, Peiró et al. (2016) devise a new type of heuristic yielding sharp upper bounds. Corberán et al. (2016) develop a strategic oscillation algorithm for a capacitated single allocation hub location problem with modular links. ...
This work focuses on a broad class of uncapacitated p-hub median problems that includes non-stop services and setup costs for the network structures. In order to capture both the single and the multiple allocation patterns as well as any intermediate case of interest, we consider the so-called r-allocation pattern with r denoting the maximum number of hubs a terminal can be allocated to. We start by revisiting an optimization model recently proposed for the problem. For that model, we introduce several families of valid inequalities as well as optimality cuts. Moreover, we consider a relaxation of the model that contains several sets of set packing constraints. This motivates a polyhedral study that we perform and that leads to the identification of many families of facets and other valid inequalities to the relaxed problem that, in turn, provide valid inequalities for the original model. Some of these families are too large for being handled directly. For those cases, separation algorithms are also presented. Finally, we gather all the above elements in a branch-and-cut procedure that we devise and implement for tackling the problem. The methodological developments proposed are tested computationally using data generated from the well-known AP data set.
