A genetic algorithm for the uncapacitated single allocation planar hub location problem

Given a set of n interacting points in a network, the hub location problem determines location of the hubs (transfer points) and assigns spokes (origin and destination points) to hubs so as to minimize the total transportation cost. In this study, we deal with the uncapacitated single allocation planar hub location problem (PHLP). In this problem, all flow between pairs of spokes goes through hubs, capacities of hubs are infinite, they can be located anywhere on the plane and are fully connected, and each spoke must be assigned to only one hub. We propose a mathematical formulation and a genetic algorithm (PHLGA) to solve PHLP in reasonable time. We test PHLGA on simulated and real life data sets. We compare our results with optimal solution and analyze results for special cases of PHLP for which the solution behavior can be predicted. Moreover, PHLGA results for the AP and CAB data set are compared with other heuristics.     

Formulating and solving splittable capacitated multiple allocation hub location problems

It is only recently that good formulations and properties for the basic versions of the hub location problem have become available. Now, versions closer to reality can be tackled with greater guarantees of success. This article deals with the case in which the capacity of the hubs is limited. The focus is on the following interpretation of this capacity: there is, for each hub, an upper bound on the total flow coming directly from the origins. Our problem has the so-called multiple allocation possibility, i.e., there is no hub associated to each node; on the contrary, flows with, say, the same origin but different destinations, can be sent through different routes. Moreover, it is assumed that the flow between a given origin–destination pair can be split into several routes; if this is not the case, the problem becomes quite different and cannot be approached by means of the techniques used in this paper.Tight integer linear programming formulations for the problem are presented, along with some useful properties of the optimal solutions which can be used to speed up the resolution.The computational experience shows that instances of medium size can be solved very efficiently using the new method, which outperforms other methods given in the literature.     

Capacitated single allocation hub location problem—A bi-criteria approach

A different approach to the capacitated single allocation hub location problem is presented. Instead of using capacity constraints to limit the amount of flow that can be received by the hubs, we introduce a second objective function to the model (besides the traditional cost minimizing function), that tries to minimize the time to process the flow entering the hubs. Two bi-criteria single allocation hub location problems are presented: in a first model, total time is considered as the second criteria and, in a second model, the maximum service time for the hubs is minimized. To generate non-dominated solutions an interactive decision-aid approach developed for bi-criteria integer linear programming problems is used. Both bi-criteria models are tested on a set of instances, analyzing the corresponding non-dominated solutions set and studying the reasonableness of the hubs flow charge for these non-dominated solutions. The increased information provided by the non-dominated solutions of the bi-criteria model when compared to the unique solution given by the capacitated hub location model is highlighted.     

A tabu-search based heuristic for the hub covering problem over incomplete hub networks

Hub location problems deal with finding the location of hub facilities and with the allocation of demand nodes to these located hub facilities. In this paper, we study the single allocation hub covering problem over incomplete hub networks and propose an integer programming formulation to this end. The aim of our model is to find the location of hubs, the hub links to be established between the located hubs, and the allocation of non-hub nodes to the located hub nodes such that the travel time between any origin–destination pair is within a given time bound. We present an efficient heuristic based on tabu search and test the performance of our heuristic on the CAB data set and on the Turkish network.     

New simple and efficient heuristics for the uncapacitated single allocation hub location problem

Hub-and-spoke networks are widely studied in the area of location theory. They arise in several contexts, including passenger airlines, postal and parcel delivery, and computer and telecommunication networks. Hub location problems usually involve three simultaneous decisions to be made: the optimal number of hub nodes, their locations and the allocation of the non-hub nodes to the hubs. In the uncapacitated single allocation hub location problem (USAHLP) hub nodes have no capacity constraints and non-hub nodes must be assigned to only one hub. In this paper, we propose three variants of a simple and efficient multi-start tabu search heuristic as well as a two-stage integrated tabu search heuristic to solve this problem. With multi-start heuristics, several different initial solutions are constructed and then improved by tabu search, while in the two-stage integrated heuristic tabu search is applied to improve both the locational and allocational part of the problem. Computational experiments using typical benchmark problems (Civil Aeronautics Board (CAB) and Australian Post (AP) data sets) as well as new and modified instances show that our approaches consistently return the optimal or best-known results in very short CPU times, thus allowing the possibility of efficiently solving larger instances of the USAHLP than those found in the literature. We also report the integer optimal solutions for all 80 CAB data set instances and the 12 AP instances up to 100 nodes, as well as for the corresponding new generated AP instances with reduced fixed costs.     

A branch-and-cut algorithm for the hub location and routing problem

We study the hub location and routing problem where we decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities. We devise separation routines for these inequalities and develop a branch-and-cut algorithm which is tested on CAB and AP instances from the literature. The results show that the formulation is strong and the branch-and-cut algorithm is able to solve instances with up to 50 nodes.     

A model for a reliable single allocation hub network design under massive disruption

Hub facilities may fail to operate in networks because of accidental failures such as natural disasters. In this paper, a quadratic model was presented for a reliable single allocation hub network under massive random failure of hub facilities which more than one hub may be disrupted in a route. It determines the location of the hub facilities and the primal allocation of non-hub nodes. It also determines the backup allocation in case of failure of the primal hub. First, a new lexicographic form of a bi-objective quadratic model is presented where the first objective maximizes served demands or equivalently, minimizes lost flows and the second objective minimizes total cost under a to massive disruption in the network. Then, by adding a structure-based constraint, the model is transformed to a single objective one. A linearization technique reported in the literature is applied on the quadratic model to convert it into classic linear zero–one mixed integer model while enhancing it by finding tighter bounds. The tight bounds’ technique is compared with other techniques in terms of computational time and its better performance was approved in some problem instances. Finally, due to the NP-hardness of the problem, an iterated local search algorithm was developed to solve large sized instances in a reasonable computational time and the computational results confirm the efficiency of the proposed heuristic, ILS can solve all CAB and IAD data set instances in less than 15 and 24 seconds, respectively. Moreover, the proposed model was compared with the classical hub network using a network performance measure, and the results show the increased efficiency of the model.     

A 2-phase algorithm for solving the single allocation p-hub center problem

The single allocation p-hub center problem is an NP-hard location–allocation problem which consists of locating hub facilities in a network and allocating non-hub nodes to hub nodes such that the maximum distance/cost between origin–destination pairs is minimized. In this paper we present an exact 2-phase algorithm where in the first phase we compute a set of potential optimal hub combinations using a shortest path based branch and bound. This is followed by an allocation phase using a reduced sized formulation which returns the optimal solution. In order to get a good upper bound for the branch and bound we developed a heuristic for the single allocation p-hub center problem based on an ant colony optimization approach. Numerical results on benchmark instances show that the new solution approach is superior over traditional MIP-solver like CPLEX. As a result we are able to provide new optimal solutions for larger problems than those reported previously in literature. We are able to solve problems consisting of up to 400 nodes in reasonable time. To the best of our knowledge these are the largest problems solved in the literature to date.     

A cascade evolutionary algorithm for the bodyguard allocation problem

The bodyguard allocation problem (BAP) is an optimization problem that illustrates the behavior of processes with contradictory individual goals in some distributed systems. The objective function of this problem is the maximization of a parameter called the social welfare. Although the main method proposed to solve this problem, known as CBAP, is simple and time efficient, it lacks the ability to generate a diverse set of solutions, which is one of the most important feature to improve the chances to reach the global optimum. To overcome this drawback, we address the BAP with an evolutionary algorithm, the EBAP. Later, we take advantage of the best properties of both algorithms, EBAP and CBAP, to generate a two-stage cascade evolutionary algorithm called FFC-BAP. Extensive experimental results show that the algorithm FFC-BAP outperforms both the EBAP and the CBAP, in terms of quality of solutions.     

The SR-GCWS hybrid algorithm for solving the capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) is a well known problem which has long been tackled by researchers for several decades now, not only because of its potential applications but also due to the fact that CVRP can be used to test the efficiency of new algorithms and optimization methods. The objective of our work is to present SR-GCWS, a hybrid algorithm that combines a CVRP classical heuristic with Monte Carlo simulation using state-of-the-art random number generators. The resulting algorithm is tested against some well-known benchmarks. In most cases, our approach is able to compete or even outperform much more complex algorithms, which is especially interesting if we consider that our algorithm does not require any previous parameter fine-tuning or set-up process. Moreover, our algorithm has been able to produce high-quality solutions almost in real-time for most tested instances. Another important feature of the algorithm worth mentioning is that it uses a randomized constructive heuristic, capable of generating hundreds or even thousands of alternative solutions with different properties. These alternative solutions, in turn, can be really useful for decision-makers in order to satisfy their utility functions, which are usually unknown by the modeler. The presented methodology may be a fine framework for the development of similar algorithms for other complex combinatorial problems in the routing arena as well as in some other research fields.     

A novel grouping harmony search algorithm for the multiple-type access node location problem

In this paper we present a novel grouping harmony search algorithm for the Access Node Location Problem (ANLP) with different types of concentrators. The ANLP is a NP-hard problem where a set of distributed terminals, with distinct rate demands, must be assigned to a variable number of concentrators subject to capacity constraints. We consider the possibility of choosing between different concentrator models is given in order to provide service demand at different cost. The ANLP is relevant in communication networks design, and has been considered before within the design of MPLS networks, for example. The approach we propose to tackle the ANLP problem consists of a hybrid Grouping Harmony Search (GHS) algorithm with a local search method and a technique for repairing unfeasible solutions. Moreover, the presented scheme also includes the adaptation of the GHS to a differential scheme, where each proposed harmony is obtained from the same harmony in the previous iteration. This differential scheme is perfectly adapted to the specifications of the ANLP problem, as it utilizes the grouping concept based on the proximity between nodes, instead of being only based on the grouping concept. This allows for a higher efficiency on the searching process of the algorithm. Extensive Monte Carlo simulations in synthetic instances show that this proposal provides faster convergence rate, less computational complexity and better statistical performance than alternative algorithms for the ANLP, such as grouping genetic algorithms, specially when the size of the scenario increases. We also include practical results for the application of GHS to a real wireless network deployment problem in Bizkaia, northern Spain.     

A genetic algorithm for a bi-objective capacitated arc routing problem

The capacitated arc routing problem (CARP) is a very hard vehicle routing problem for which the objective—in its classical form—is the minimization of the total cost of the routes. In addition, one can seek to minimize also the cost of the longest trip.In this paper, a multi-objective genetic algorithm is presented for this more realistic CARP. Inspired by the second version of the Non-dominated sorted genetic algorithm framework, the procedure is improved by using good constructive heuristics to seed the initial population and by including a local search procedure. The new framework and its different flavour is appraised on three sets of classical CARP instances comprising 81 files.Yet designed for a bi-objective problem, the best versions are competitive with state-of-the-art metaheuristics for the single objective CARP, both in terms of solution quality and computational efficiency: indeed, they retrieve a majority of proven optima and improve two best-known solutions.     

A simple and effective genetic algorithm for the two-stage capacitated facility location problem

This paper presents a simple and effective Genetic Algorithm (GA) for the two-stage capacitated facility location problem (TSCFLP). The TSCFLP is a typical location problem which arises in freight transportation. In this problem, a single product must be transported from a set of plants to meet customers demands, passing out by intermediate depots. The objective is to minimize the operation costs of the underlying two-stage transportation system thereby satisfying demand and capacity constraints of its agents. For this purpose, a GA is proposed and computational results are reported comparing the heuristic results with those obtained by two state-of-the-art Lagrangian heuristics proposed in the literature for the problem.     

Tight bounds from a path based formulation for the tree of hub location problem

This paper considers the tree of hub location problem. We propose a four index formulation which yields much tighter LP bounds than previously proposed formulations, although at a considerable increase of the computational burden when obtained with a commercial solver. For this reason we propose a Lagrangean relaxation, based on the four index formulation, that exploits the structure of the problem by decomposing it into independent subproblems which can be solved quite efficiently. We also obtain upper bounds by means of a simple heuristic that is applied at the inner iterations of the method that solves the Lagrangean dual. As a consequence, the proposed Lagrangean relaxation produces tight upper and lower bounds and enable us to address instances up to 100 nodes, which are notably larger than the ones previously considered in the literature, with sizes up to 20 nodes. Computational experiments have been performed with benchmark instances from the literature. The obtained results are remarkable. For most of the tested instances we obtain or improve the best known solution and for all tested instances the deviation between our upper and lower bounds, never exceeds 10%.     

On the selection of hub airports for an airline hub-and-spoke system

We consider the 1-stop multiple allocation p-hub median problem. We formulate the problem as a p-median problem and propose a branch-and-bound algorithm and a greedy-type heuristic algorithm. We report computational results for problems with airline passenger interactions between 25 US cities in 1970 evaluated by the Civil Aeronautics Board. For further investigation, we made computational experiments with some random data. The obtained results also show that the proposed algorithms work better than the well-known nested-dual algorithm, particularly for relatively small problems.     

A genetic algorithm approach to solving the anti-covering location problem

Abstract: In this paper we address the problem of locating a maximum weighted number of facilities such that no two are within a specified distance from each other. A natural process of evolution approach, more specifically a genetic algorithm, is proposed to solve this problem. It is shown that through the use of a commercially available spreadsheet-based genetic algorithm software package, the decision-maker with a fundamental knowledge of spreadsheets can easily set up and solve this optimization problem. Also, we report on our extensive computational experience using three different data sets.     

An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design

This paper presents a new multi-objective mathematical model for a multi-modal hub location problem under a possibilistic-stochastic uncertainty. The presented model aims to minimize the total transportation and traffic noise pollution costs. Furthermore, it aims to minimize the maximum transportation time between origin-destination nodes to ensure a high probability of meeting the service guarantee. In order to cope with the uncertainties and the multi-objective model, we propose a two-phase approach, including fuzzy interactive multi-objective programming approach and an efficient method based on the Me measure. Due to the NP-hardness of the presented model, two meta-heuristic algorithms, namely hybrid differential evolution and hybrid imperialist competitive algorithm, are developed. Furthermore, a number of sensitivity analyses are provided to demonstrate the effectiveness of the presented model. Finally, the foregoing meta-heuristics are compared together through different comparison metrics.     

Applying two efficient hybrid heuristics for hub location problem with fully interconnected backbone and access networks

This paper considers the design of two-layered networks with fully interconnected backbone and access networks. The problem, a specific application of hub location to network design, is known as fully interconnected network design problem (FINDP). A novel mathematical programming formulation advantageous over an earlier formulation is presented to model the problem. Two hybrid heuristics are proposed to solve the problem, namely SA_VNS and TS_VNS which incorporate a variable neighborhood search (VNS) algorithm into the framework of simulated annealing (SA) and tabu search (TS). The proposed algorithms are able to easily obtain the optimal solutions for 24 small instances existing in the literature in addition to efficiently solve new generated medium and large instances. Results indicate that the proposed algorithms generate high quality solutions in a quite short CPU time.     

最小费用充电站选址问题的分支定界算法

电动汽车的充电站选址问题是当前社会的热点问题,其实质是组合优化中经典的NP-hard问题。基于最小开设费用对充电站选址问题进行研究,首先对该问题进行了数学建模,进而研究了该问题的数学性质并给予相应的证明,利用这些性质减小问题的规模,从而降低问题的求解难度;然后设计了上下界子算法以及降阶子算法,基于这些子算法提出了一种可以快速缩小问题规模同时得到最优解的分支定界算法,降低了时间复杂度,同时可以对解空间进行大量剪枝加快求解速度;最后通过分析和求解一个示例来进一步阐述所提算法的原理和执行过程。     

A multi-objective evolutionary algorithm to exploit the similarities of resource allocation problems

The complexity of a resource allocation problem (RAP) is usually NP-complete, which makes an exact method inadequate to handle RAPs, and encourages heuristic techniques to this class of problems for obtaining approximate solutions in polynomial time. Different heuristic techniques have already been investigated for handling various RAPs. However, since the properties of an RAP can help in characterizing other RAPs, instead of individual solution techniques, the similarities of different RAPs might be exploited for developing a common solution technique for them. Two RAPs of quite different nature, namely university class timetabling and land-use management, are considered here for such a study. The similarities between the problems are first explored, and then a common multi-objective evolutionary algorithm (a kind of heuristic techniques) for them is developed by exploiting those similarities. The algorithm is problem-dependent to some extent and can easily be extended to other similar RAPs. In the present work, the algorithm is applied to two real instances of the considered problems, and its properties are derived from the obtained results.