Hub Median Problem Research Articles

A simheuristic algorithm for video streaming flows optimisation with QoS threshold modelled as a stochastic single-allocation p-hub median problem

ABSTRACT Modern telecommunication networks are comprised of a countless number of nodes exchanging data among them. In particular, multimedia traffic – composed of audio, video, and images – represents a challenging scenario requiring link optimisation techniques. The hub-and-spoke topology is frequently used to design more effective telecommunication networks. This work considers a hub-and-spoke network in which a large number of nodes are exchanging real-time multimedia data, and where the quantity of data sent from one node to another is a random variable. Given a fixed number of hubs, , the goal is to select the best location for these hubs in order to minimise the total expected cost of transmission. This scenario is modelled as an uncapacitated single-allocation -hub median problem under uncertainty conditions. Additionally, with the purpose of considering the effect of transmission delays on the video signal, service quality thresholds are assigned to every potential hub in the network. Since real-life networks tend to be large in size, we propose a simheuristic algorithm to cope with this stochastic and large-scale optimisation problem. A series of computational experiments illustrate these concepts and allow for testing the performance of our simheuristic approach. Finally, a statistical analysis of the obtained results is provided.

Hybrid evolutionary algorithms and Lagrangian relaxation for multi-period star hub median problem considering financial and service quality issues

Hub facilities are centralized locations that consolidate and distribute the commodities in transportation networks. In many real world applications, transport service providers may prefer to lease hub facilities for a time horizon rather than being owned or constructed. In this paper, a modeling framework is proposed for the multi-period hub location problem that arises in the design of the star–star network with two types of hubs and links. It includes a designated static central hub, some movable hub facilities and a set of nodes with pairwise demands. A periodic growth in the amount of budget is considered at each period to expand the transportation network and an interest rate is also applied to the unused budget available during each period. Since the overall quality of services in the hub and spoke systems rely on the length of the paths, upper bound constraints are considered for the paths between nodes. Numerical experiments are carried out to show the applicability of the proposed model. Due to the computational complexity of the model, an improved genetic algorithm (GA) and a hybrid particle swarm optimization (HPSO) are utilized to find near optimal solutions. Both algorithms employ caching strategy to improve the computation times. Moreover, the HPSO benefits from genetic operators and local search methods to update the particles. In order to assess the effectiveness of the proposed methods, the results are compared with a pure GA and a proper lower bound achieved by a Lagrangian relaxation method.

A mathematical model for P-hub median location problem to multiple assignments between non-hub to hub nodes under fuzzy environment

One group of the optimization problems is Hub location problem. Hub facilities are used in transportation network which are provided transfer of products, information, passengers and postal package through of intermediate node instead of direct transfer. One main group of these problems is discrete hub median location that seeks to minimize total transportation cost. In this paper, we present hub median location problem with multiple allocation of non-hub nodes to hub nodes, moreover it is possible to connect non-hub nodes directly with considering a penalty coefficient. The numerical example for CAB25data set -which is related to flow and distance between 25 cities in America- with establishment cost under fuzzy circumstance solved and presented.

A new distributionally robust p-hub median problem with uncertain carbon emissions and its tractable approximation method

• A new DRO model is given for p -hub median problem with uncertain carbon emissions. • The tractable approximations for the ambiguous chance constraint are derived. • A Southeast Asia hub network design problem is investigated. • The proposed DRO model is applied in CAB data set. • The quality of numerical results and comparison findings support our arguments. The p -hub median problem is to determine the optimal location for p hubs and assign the remaining nodes to hubs so as to minimize the total transportation costs. Under the carbon cap-and-trade policy, we study this problem by addressing the uncertain carbon emissions from the transportation, where the probability distributions of the uncertain carbon emissions are only partially available. A novel distributionally robust optimization model with the ambiguous chance constraint is developed for the uncapacitated single allocation p -hub median problem. The proposed distributionally robust optimization problem is a semi-infinite chance-constrained optimization model, which is computationally intractable for general ambiguity sets. To solve this hard optimization model, we discuss the safe approximation to the ambiguous chance constraint in the following two types of ambiguity sets. The first ambiguity set includes the probability distributions with the bounded perturbations with zero means. In this case, we can turn the ambiguous chance constraint into its computable form based on tractable approximation method. The second ambiguity set is the family of Gaussian perturbations with partial knowledge of expectations and variances. Under this situation, we obtain the deterministic equivalent form of the ambiguous chance constraint. Finally, we validate the proposed optimization model via a case study from Southeast Asia and CAB data set. The numerical experiments indicate that the optimal solutions depend heavily on the distribution information of carbon emissions. In addition, the comparison with the classical robust optimization method shows that the proposed distributionally robust optimization method can avoid over-conservative solutions by incorporating partial probability distribution information. Compared with the stochastic optimization method, the proposed method pays a small price to depict the uncertainty of probability distribution. Compared with the deterministic model , the proposed method generates the new robust optimal solution under uncertain carbon emissions.

The 2-allocation p-hub median problem and a modified Benders decomposition method for solving hub location problems

We study the uncapacitated 2-allocation p-hub median problem (U2ApHMP), which is a special case of the well-studied hub median problem. The hub median problem designs a hub network in which the location of p hubs needs to be decided (the hubs are fully interconnected). The other nodes (known as access nodes) in the hub median problem are then allocated to one or many hubs. In the U2ApHMP, each access node is allocated to exactly two hubs. We discuss how this problem provides an alternative network design option for well-known p-hub median problems. We show its relevance and usefulness in the context of survivable network design and show that it addresses network survivability, a feature that has often been largely overlooked in hub network design research to date. We show that U2ApHMP is NP-hard even for a fixed/known set of hubs. We propose a mathematical formulation and develop a modified Benders decomposition method for this problem. In this, we convert the corresponding subproblems to minimum cost network flow problems. This allows us to solve large instances efficiently. We believe that, while our resulting method solves the U2ApHMP efficiently, it is also generalisable and can potentially be employed for solving other classes and types of hub location problems too.

A 2‐stage biased‐randomized iterated local search for the uncapacitated single allocation p‐hub median problem

AbstractThe hub location problem has gained attention over the last decades. In telecommunications network, a hub is a place of concurrence in where the work of the network is centralized with the purpose of delivering out the data that arrives from one or more directions to other destinations. There are different versions of the hub location problem depending upon (1) the existence or not of restrictions on the capacity related to the volume of flow a hub is allowed to support, (2) the existence or not of a set‐up cost associated with selecting any node as a hub, etc. In these types of configurations, the hubs serve as connection point between 2 installations, allowing, in this way, to replace a large amount of direct connections between all pair of the nodes, therefore, minimizing the total transportation cost of the network. Thus, this work proposes a 2‐stage metaheuristic based on the combination of biased‐randomized technique with an iterated local search framework for solving the uncapacitated single allocation p‐hub median problem, with computational results that validate the methodology for large‐size instances from the literature.

Models and solution methods for the uncapacitated r‐allocation p‐hub equitable center problem

AbstractHub networks are commonly used in telecommunications and logistics to connect origins to destinations in situations where a direct connection between each origin–destination (o‐d) pair is impractical or too costly. Hubs serve as switching points to consolidate and route traffic in order to realize economies of scale. The main decisions associated with hub‐network problems include (1) determining the number of hubs (p), (2) selecting the p‐nodes in the network that will serve as hubs, (3) allocating non‐hub nodes (terminals) to up to r‐hubs, and (4) routing the pairwise o‐d traffic. Typically, hub location problems include all four decisions while hub allocation problems assume that the value of p is given. In the hub median problem, the objective is to minimize total cost, while in the hub center problem the objective is to minimize the maximum cost between origin–destination pairs. We study the uncapacitated (i.e., links with unlimited capacity) r‐allocation p‐hub equitable center problem (with) and explore alternative models and solution procedures.

A general variable neighborhood search for solving the uncapacitated $$r$$ r -allocation $$p$$ p -hub median problem

The \(p\)-hub median problem consists of choosing \(p\) hub locations from a set of nodes with pairwise traffic demands in order to route the traffic between the origin-destination pairs at minimum cost. We accept general assumption that transportation between non-hub nodes is possible only via \(r\)-hub nodes, to which non-hub nodes are assigned. In this paper we propose a general variable neighborhood search heuristic to solve the problem in an efficient and effective way. Moreover, for the first time full nested variable neighborhood descent is applied as a local search within Variable neighborhood search. Computational results outperform the current state-of-the-art results obtained by GRASP based heuristic.

Solving the continuous multiple allocation p-hub median problem by the hyperbolic smoothing approach

Hub-and-spoke (HS) networks constitute an important approach for designing transportation and telecommunications systems. The continuous multiple allocation -hub median problem consists in finding the least expensive HS network, locating a given number of hubs in planar space and assigning traffic to them, given the demands between each origin-destination pair and the respective transportation costs, where each demand centre can receive and send flow through more than one hub. The specification of the problem corresponds to a strongly non-differentiable min-sum-min formulation. The proposed method overcomes this difficulty with the hyperbolic smoothing strategy, which has been proven able to solve large instances of clustering problems quite efficiently. The solution is ultimately obtained by solving a sequence of differentiable unconstrained low-dimension optimization subproblems. The consistency of the method is shown through a set of computational experiments with large hub-and-spoke problems in continuous space with up to 1000 cities.

Using a fuzzy approach for a new bi-objective model for a multi-modal tree p-hub median location problem

One main group of transportation networks is a hub location problem that deals with finding the location of hub nodes and allocation of non-hub nodes to located hubs. This paper presents a capacitated multi-modal p -hub median location problem with a single assignment, in which different transportation modes can be established between hub nodes. This problem makes a decision on how the hub networks with different possible transportation modes should be designed. Moreover, high setup costs for links lead to use incomplete hub network; so we allow the connected hubs by means of a tree and consider a fixed cost for establishing hub links. The objectives of this model are to minimise the total cost and minimise the total transportation time (including the transportation time between nodes and the operation time at hub nodes). As the real values of parameters are not precisely known in advance, a fuzzy approach is proposed to cope with the uncertain parameters. The multi-objective model is also converted into a single objective one by the TH method. Furthermore, some numerical examples are provided to illustrate the correctness of the proposed model. Finally, the conclusion is provided.

The single-allocation hierarchical hub median location problem with fuzzy demands

Although, many papers have appeared in the literature of hub location problem, most of them deal with the problem in a crisp environment. In this paper, the single-allocation hierarchical hub median problem (SA-H-MP) with fuzzy demands is addressed. The structure of the model is derived from Yaman (2009) and consists of a three-level network of demand nodes, non-central hubs, and central hubs. It has been assumed that the demands are not known precisely and are estimated using fuzzy variables. In order to solve the problem, a simulation-embedded variable neighborhood search (VNS) is applied. The results of running the proposed approach on the well-known CAB dataset verify that it is able to solve test problems with less than one percent of error.

The hierarchical hub median problem with single assignment

We study the problem of designing a three level hub network where the top level consists of a complete network connecting the so-called central hubs and the second and third levels are unions of star networks connecting the remaining hubs to central hubs and the demand centers to hubs and central hubs, respectively. The problem is to decide on the locations of a predetermined number of hubs and central hubs and the connections in order to minimize the total routing cost in the resulting network. This problem includes the classical p-hub median problem as a special case. We also consider a version of this problem where service quality considerations are incorporated through delivery time restrictions. We propose mixed integer programming models for these two problems and report the outcomes of a computational study using the CAB data and the Turkey data.

Uncapacitated single and multiple allocation p-hub center problems

The hub median problem is to locate hub facilities in a network and to allocate non-hub nodes to hub nodes such that the total transportation cost is minimized. In the hub center problem, the main objective is one of minimizing the maximum distance/cost between origin destination pairs. In this paper, we study uncapacitated hub center problems with either single or multiple allocation. Both problems are proved to be NP-hard. We even show that the problem of finding an optimal single allocation with respect to a given set of hubs is already NP-hard. We present integer programming formulations for both problems and propose a branch-and-bound approach for solving the multiple allocation case. Numerical results are reported which show that the new formulations are superior to previous ones.

Integer programming formulations of discrete hub location problems

Abstract Hubs are facilities that serve as transshipment and switching points for transportation and telecommunication systems with many origins and destinations. This paper present integer programming formulations for four types of discrete hub location problems: the p -hub median problem, the uncapacitated hub location problem, p -hub center problems and hub covering problems. Hub median and uncapacitated hub location problems have received limited attention from researchers. This paper introduces discrete hub center and hub covering problems. Basic formulations and formulations with flow thresholds for spokes are presented.

Neural versus traditional approaches to the location of interacting hub facilities

In this paper we consider the optimal location of interacting hub facilities. Using the well-known quadratic integer programming formulation of the uncapacitated, single allocation, p -hub median problem (USApHMP), we demonstrate a mapping onto a Hopfield neural network which guarantees feasibility of the final solution. We also propose a novel modification to the Hopfield network which enables escape from local minima, thus improving final solution quality. A practical application of the USApHMP—a postal delivery network—is used to demonstrate that the quality of these Hopfield network solutions compares favorably to those obtained using both exact methods and simulated annealing. Well-known data sets from the literature are also tested using the Hopfield network approaches, and provide further evidence that optimal or near-optimal solutions can consistently be obtained. The speed advantages which can be attained when implementing neural networks in hardware make the Hopfield neural network a very attractive potential alternative to the existing solution techniques.