a note on the selection of benders cuts a new cut selection criterion for benders cuts is proposed and computationally analyzed the results show that the new criterion is more robust and often considerably faster than the standard ones

the tree of hubs location problem this paper presents the tree of hubs location problem it is a network hub location problem with single assignment where a fixed number of hubs have to be located with the particularity that it is required that the hubs are connected by means of a tree the problem combines several aspects of location network design and routing problems potential applications appear in telecommunications and transportation systems when set up costs for links between hubs are so high that full interconnection between hub nodes is prohibitive we propose an integer programming formulation for the problem furthermore we present some families of valid inequalities that reinforce the formulation and we give an exact separation procedure for them finally we present computational results using the well known ap and cab data sets

bandwidth scaling for fading multipath channels we show that very large bandwidths on fading multipath channels cannot be effectively utilized by spread spectrum systems that in a particular sense spread the available power uniformly over both time and frequency the approach is to express the input process as an expansion in an orthonormal set of functions each localized in time and frequency the fourth moment of each coefficient in this expansion is then uniformly constrained we show that such a constraint forces the mutual information to 0 inversely with increasing bandwidth simply constraining the second moment of these coefficients does not achieve this effect the results suggest strongly that conventional direct sequence code division multiple access cdma systems do not scale well to extremely large bandwidths to illustrate how the interplay between channel estimation and symbol detection affects capacity we present results for a specific channel and cdma signaling scheme

analysis of locking and stress oscillations in a general curved beam element the exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force the functional re constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations the orthogonally correct field consistent interpolations are determined for the optimal form of the element and it is shown that the popular two point gaussian integrated13 version of the element is non orthogonal and has a cubic13 oscillation in the shear force that curiously vanishes at the barlow points

locating tree shaped facilities using the ordered median objective in this paper we consider the location of a tree shaped facility s on a tree network using the ordered median function of the weighted distances to represent the total transportation cost objective this function unifies and generalizes the most common criteria used in location modeling e g median and center if there are n demand points at the nodes of the tree t v e this function is characterized by a sequence of reals 1 n satisfying 1 2 n 0 for a given subtree s let x s x1 xn be the set of weighted distances of the n demand points from s the value of the ordered median objective at s is obtained as follows sort the n elements in x s in nonincreasing order and then compute the scalar product of the sorted list with the sequence two models are discussed in the tactical model there is an explicit bound l on the length of the subtree and the goal is to select a subtree of size l which minimizes the above transportation cost function in the strategic model the length of the subtree is variable and the objective is to minimize the sum of the transportation cost and the length of the subtree we consider both discrete and continuous versions of the tactical and the strategic models we note that the discrete tactical problem is np hard and we solve the continuous tactical problem in polynomial time using a linear programming lp approach we also prove submodularity properties for the strategic problem these properties allow us to solve the discrete strategic version in strongly polynomial time moreover the continuous version is also solved via lp for the special case of the k centrum objective we obtain improved algorithmic results using a dynamic programming dp algorithm and discretization and nestedness results

capacity and reliability function for small peak signal constraints the capacity and the reliability function as the peak constraint tends to zero are considered for a discrete time memoryless channel with peak constrained inputs prelov and van der meulen 1993 showed that under mild conditions the ratio of the capacity to the squared peak constraint converges to one half the maximum eigenvalue of the fisher information matrix and if the fisher information matrix is nonzero the asymptotically optimal input distribution is symmetric antipodal signaling under similar conditions it is shown in the first part of the paper that the reliability function has the same asymptotic shape as the reliability function for the power constrained infinite bandwidth white gaussian noise channel the second part of the paper deals with rayleigh fading channels for such channels the fisher information matrix is zero indicating the difficulty of transmission over such channels with small peak constrained signals asymptotics for the rayleigh channel are derived and applied to obtain the asymptotics of the capacity of the marzetta and hochwald 1999 fading channel model for small peak constraints and to obtain a result of the type of medard and gallager for wide band fading channels

the benders decomposition algorithm a literature review the benders decomposition algorithm has been successfully applied to a wide range of difficult optimization problems this paper presents a state of the art survey of this algorithm emphasizing its use in combinatorial optimization we discuss the classical algorithm the impact of the problem formulation on its convergence and the relationship to other decomposition methods we introduce a taxonomy of algorithmic enhancements and acceleration strategies based on the main components of the algorithm the taxonomy provides the framework to synthesize the literature and to identify shortcomings trends and potential research directions we also discuss the use of the benders decomposition to develop efficient meta heuristics describe the limitations of the classical algorithm and present extensions enabling its application to a broader range of problems

a branch and cut algorithm for hub location problems with single assignment the hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network there may also be capacity restrictions on the amount of traffic that can transit by hubs the aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results

channel coherence in the low snr regime channel capacity in the limit of vanishing signal to noise ratio snr per degree of freedom is known to be linear in snr for fading and nonfading channels regardless of channel state information at the receiver csir it has recently been shown that the significant engineering difference between the coherent and the noncoherent fading channels including the requirement of peaky signaling and the resulting spectral efficiency is determined by how the capacity limit is approached as snr tends to zero or in other words the sublinear term in the capacity expression in this paper we show that this sublinear term is determined by the channel coherence level which we define to quantify the relation between the snr and the channel coherence time this allows us to trace a continuum between the case with perfect csir and the case with no csir at all using this approach we also evaluate the performance of suboptimal training schemes

solving large single allocation p hub problems with two or three hubs abstract in this paper we present an efficient approach for solving single allocation p hub problems with two or three hubs two different variants of the problem are considered the uncapacitated single allocation p hub median problem and the p hub allocation problem we solve these problems using new mixed integer linear programming formulations that require fewer variables than those formerly used in the literature the problems that we solve here are the largest single allocation problems ever solved the numerical results presented here will demonstrate the superior performance of our mixed integer linear programs over traditional approaches for large problems finally we present the first mixed integer linear program for solving single allocation hub location problems that requires only o n 2 variables and o n 2 constraints that is valid for any number of hubs

tight linear programming relaxations of uncapacitated p hub median problems abstract the problem of locating hub facilities and allocating non hub nodes to those hubs arises frequently in the design of communication networks airline passenger flow and parcel delivery networks in this paper we consider uncapacitated multiple and single allocation p hub median problems we develop new mixed 0 1 linear formulations with tight linear programming relaxations the approach is tested on a well known and heavily used benchmark data set of real world problems with resulting lp relaxations ranging from 10010 to 391 250 variables and from 2 101 to 31 901 constraints which proved to be difficult linear programs yet this approach proved to be very effective in almost all instances the linear programming solution was integer in cases with fractional solutions the integrality was achieved by adding a small partial set of integrality constraints therefore we extended the range of optimally solvable instances of these np hard hub location problems which have defied researchers for the last ten years as an additional result for the single allocation case we were able to establish optimality of all heuristic solutions obtained via tabu search algorithm from a previous study for the more difficult single allocation p hub median problem we also used the best known heuristic solution as a guidance in adding integrality constraints this novel linkage between optimal and heuristic solutions has a potential impact in a number of other problem settings where efficient heuristic solutions exist and are probably but not provably optimal

a quadratic integer program for the location of interacting hub facilities abstract this paper reports a new formulation of a general hub location model as a quadratic integer program non convexity of the objective function makes the problem difficult a variety of alternative solution strategies are discussed computational results from two simple heuristics are presented for the task of siting 2 3 or 4 hubs to serve interactions between sets of 10 15 20 and 25 u s cities the effects of different computational shortcuts are examined

improving benders decomposition using a genetic algorithm we develop and investigate the performance of a hybrid solution framework for solving mixed integer linear programming problems benders decomposition and a genetic algorithm are combined to develop a framework to compute feasible solutions we decompose the problem into a master problem and a subproblem a genetic algorithm along with a heuristic are used to obtain feasible solutions to the master problem whereas the subproblem is solved to optimality using a linear programming solver over successive iterations the master problem is refined by adding cutting planes that are implied by the subproblem we compare the performance of the approach against a standard benders decomposition approach as well as against a stand alone solver cplex on miplib test problems

lagrangian relaxation based approaches to capacitated hub and spoke network design problem abstract the main purpose of this paper is to introduce the capacitated hub and spoke network design problem in which hubs have limited capacity for channelling flows between the nodes served by the system the problem is formulated under a networking policy allowing both direct nonstop and hub connected one hub stop and two hub stop services between the nodes a branch and bound algorithm and a heuristic procedure partitioning the set of solutions on the basis of hub locations are presented in both algorithms after identifying a set of hub locations the problem is reduced into a smaller routing problem subgradient optimization is then applied to a lagrangian relaxation of the reduced problem the model and the proposed algorithms were applied to the air transportation system using data on passenger flows between the top forty us cities in 1989 accounting for 73 32 of the surveyed passenger flow computational results from 141 problems suggest that both algorithms are effective at finding good solutions to this problem

asymptotic behavior of error exponents in the wideband regime in this paper we investigate the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent specifically we consider both additive white gaussian noise awgn and rayleigh fading channels where the input symbols are assumed to have a peak constraint for the awgn channel model the optimal values of rz 0 and rz 0 are calculated where rz 1 b is the maximum rate at which information can be transmitted over a channel with bandwidth b when the error exponent is constrained to be greater than or equal to z the computation of rz 0 follows gallager s infinite bandwidth reliability function computation while the computation of rz 0 is new and parallels verdu s second order calculation for channel capacity based on these calculations we say that a sequence of input distributions is near optimal if both rz 0 and rz 0 are achieved we show that quaternary phase shift keying qpsk a widely used signaling scheme is near optimal within a large class of input distributions for the awgn channel similar results are also established for a fading channel where full channel side information csi is available at the receiver

mimo channels in the low snr regime communication rate error exponent and signal peakiness we consider multiple input multiple output mimo fading channels and characterize the reliability function in the low signal to noise snr regime as a function of the number of transmit and receive antennas for the case when the fading matrix h has independent entries we show that the number of transmit antennas plays a key role in reducing the peakiness in the input signal required to achieve the optimal error exponent for a given communication rate further by considering a correlated channel model we show that the maximum performance gain in terms of the error exponent and communication rate is achieved when the entries of the channel fading matrix are fully correlated the results we presented in this work in the low snr regime can also be applied to the infinite bandwidth regime

large scale mixed integer programming benders type heuristics abstract the limited success of exact methods for solving integer programming problems has prompted the development of heuristic procedures which have performed surprisingly well in their search for near optimal solutions the present paper constitutes an attempt to generalize these procedures to the mixed integer case the approach is based on the utilization of the benders partitioning method bpm which separates the integer from the continuous variables a number of alternatives are presented for integrating ip heuristics in the bpm thus alleviating its main limitation the necessity of solving a sequence of integer master problems the rationale and its usefulness are illustrated on large scale applications from the fields of power systems and network flows

an improved benders decomposition algorithm for the tree of hubs location problem abstract the tree of hubs location problem is a particularly hard variant of the so called hub location problems when solving this problem by a benders decomposition approach it is necessary to deal with both optimality and feasibility cuts while modern implementations of the benders decomposition method rely on pareto optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems the proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature

disaggregated benders decomposition and branch and cut for solving the budget constrained dynamic uncapacitated facility location and network design problem abstract we present an approach for solving to optimality the budget constrained dynamic uncapacitated facility location and network design problem duflndp this is a problem where a network must be constructed or expanded and facilities placed in the network subject to a budget in order to satisfy a number of demands with the demands satisfied the objective is to minimise the running cost of the network and the cost of moving demands to facilities the problem can be disaggregated over two different sets simultaneously leading to many smaller models that can be solved more easily using disaggregated benders decomposition embedded in a branch and cut framework we solve many instances to optimality that have not previously been solved we use an analytic procedure to generate benders optimality cuts that are provably pareto optimal

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

combinatorial benders cuts for mixed integer linear programming mixed integer programs mips involving logical implications modeled through big m coefficients are notoriously among the hardest to solve in this paper we propose and analyze computationally an automatic problem reformulation of quite general applicability aimed at removing the model dependency on the big m coefficients our solution scheme defines a master integer linear problem ilp with no continuous variables which contains combinatorial information on the feasible integer variable combinations that can be distilled from the original mip model the master solutions are sent to a slave linear program lp which validates them and possibly returns combinatorial inequalities to be added to the current master ilp the inequalities are associated to minimal or irreducible infeasible subsystems of a certain linear system and can be separated efficiently in case the master solution is integer the overall solution mechanism closely resembles the benders one but the cuts we produce are purely co

field consistency and violent stress oscillations in the finite element method the fact that finite element models can give rise to13 violent stress oscillations has been known for some time it is also well known that in many problems there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations however it is less well known that these oscillations arise in a specific class of problems where there are multiple strain fields arising from one or more field variables and where one or more of these strain fields must be constrained in particular physical13 limits in this paper we show that unless the interpolations for these constrained strain fields are x2018 field consistentx2019 violent oscillations would set in these oscillations represent spurious self equilibrating stress fields generating spurious energy terms that lead to x2018 lockingx2019

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

benders decomposition for large scale uncapacitated hub location this paper describes an exact algorithm capable of solving large scale instances of the well known uncapacitated hub location problem with multiple assignments the algorithm applies benders decomposition to a strong path based formulation of the problem the standard decomposition algorithm is enhanced through the inclusion of several features such as the use of a multicut reformulation the generation of strong optimality cuts the integration of reduction tests and the execution of a heuristic procedure extensive computational experiments were performed to evaluate the efficiency and robustness of the algorithm computational results obtained on classical benchmark instances with up to 200 nodes and on a new and more difficult set of instances with up to 500 nodes confirm the efficiency of the algorithm

out of plane dynamic response of curved beams an analytical model abstract an analytical model for the vibration response of a curved beam is developed and presented the model is based on the solution closed solution of the dynamic differential equations of equilibrium for an infinitesimal element vibrating out of its initial plane of curvature and allows for inclusion of the effects of rotary inertia and or shear deformation final solutions are presented under the form of elements of the tip dynamic stiffness matrix for a free free beam the validity of the model is assessed by comparison of theoretical and experimental results for several examples of curved beams

consistency aspects of out of plane bending torsion and shear in a quadratic curved beam element curved beams in civil engineering applications call for out of plane bending and torsion under the action of out of plane transverse shear loads the design of a quadratic displacement type curved beam element capable of representing shear deformation as in the timoshenko beam theory will call for special attention to be paid to the manner in which the shear strain is to be represented field inconsistent representations of the out of plane transverse shear strain will result in a loss gf efficiency and introduce spuriou oscillations in the bending moment torsional moment and shear force the optimal field consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations

a multicut algorithm for two stage stochastic linear programs outer linearization methods such as van slyke and wets s l shaped method for stochastic linear programs generally apply a single cut on the nonlinear objective at each major iteration the structure of stochastic programs allows for several cuts to be placed at once this paper describes a multicut algorithm to carry out this procedure it presents experimental and theoretical justification for reductions in major iterations

fixing variables and generating classical cutting planes when using an interior point branch and cut method to solve integer programming problems abstract branch and cut methods for integer programming problems solve a sequence of linear programming problems traditionally these linear programming relaxations have been solved using the simplex method the reduced costs available at the optimal solution to a relaxation may make it possible to fix variables at zero or one if the solution to a relaxation is fractional additional constraints can be generated which cut off the solution to the relaxation but donot cut off any feasible integer points gomory cutting planes and other classes of cutting planes are generated from the final tableau in this paper we consider using an interior point method to solve the linear programming relaxations we show that it is still possible to generate gomory cuts and other cuts without having to recreate a tableau and we also show how variables can be fixed without using the optimal reduced costs the procedures we develop do not require that the current relaxation be solved to optimality this is useful for an interior point method because early termination of the current relaxation results in an improved starting point for the next relaxation

reduced minimization theory in beam elements by using the field consistency and least squares fit concepts reduced minimization theory is proposed to show the effect of numerical integration on the behaviour of c0 continuous beam elements when the jacobian is constant within an element the theory provides a unified viewpoint on the relationship between spurious constraint the location of optimal sampling points and integration order the conventional uniformly reduced integration uri and selective reduced integration sri are redefined by using reduced minimization theory we also present numerical reduced minimization theory which explains the effects of more than two order lower reduced integration when gaussian quadrature is employed

new formulations for the uncapacitated multiple allocation hub location problem in this paper we review the integer linear formulations of the uncapacitated multiple allocation hub location problem we study the scope of validity of these formulations and give new ones that generalize the older formulations our formulations allow one or two visits to hubs and include a more general cost structure that needs not satisfy the triangle inequality we prove that the constraints defined by cliques of a related intersection graph are tighter constraints than the classical ones we also discuss a pre processing of the problem which is very useful for reducing its size finally we check the strength of the new formulations and compare them with others in the literature by solving instances of two commonly used data sets the cab civil aeronautics board and ap australian post and also randomly generated instances our computational results clearly show that our formulations outperform all others previously used for small and medium problems

accelerating benders decomposition algorithmic enhancement and model selection criteria this paper proposes methodology for improving the performance of benders decomposition when applied to mixed integer programs it introduces a new technique for accelerating the convergence of the algorithm and theory for distinguishing good model formulations of a problem that has distinct but equivalent mixed integer programming representations the acceleration technique is based upon selecting judiciously from the alternate optima of the benders subproblem to generate strong or pareto optimal cuts this methodology also applies to a much broader class of optimization algorithms that includes dantzig wolfe decomposition for linear and nonlinear programs and related cutting plane type algorithms that arise in resource directive and price decomposition when specialized to network location problems this cut generation technique leads to very efficient algorithms that exploit the underlying structure of these models in discussing the proper formulation of mixed integer programs we suggest criteri

exact and heuristic algorithms for the uncapacitated multiple allocation p hub median problem in this paper new milp formulations for the multiple allocation p hub median problem are presented these require fewer variables and constraints than those traditionally used in the literature an efficient heuristic algorithm based on shortest paths is described lp based solution methods as well as an explicit enumeration algorithm are developed to obtain exact solutions computational results are presented for well known problems from the literature which show that exact solutions can be found in a reasonable amount of computational time our algorithms are also benchmarked on a different data set this data set which includes problems that are larger than those used in the literature is based on a postal delivery network and has been treated by the authors in an earlier paper

stochastic uncapacitated hub location we study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs we show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem evp in which random variables are replaced by their expectations in the case of uncertain independent transportation costs the corresponding stochastic problem is not equivalent to its evp and specific solution methods need to be developed we describe a monte carlo simulation based algorithm that integrates a sample average approximation scheme with a benders decomposition algorithm to solve problems having stochastic independent transportation costs numerical results on a set of instances with up to 50 nodes are reported

a multi modal approach to the location of a rapid transit line abstract the location of a rapid transit line rtl represents a very complex decision problem because of the large number of decision makers unquantifiable criteria and uncertain data in this context operational research can help in the design process by providing tools to generate and assess alternative solutions for this purpose two bicriterion mathematical programming models the maximum coverage shortest path model and the median shortest path model have been developed in the past in this paper a new bicriterion model which can evaluate in a more realistic way the attractivity of an rtl is introduced to calculate an estimation of the non inferior solution set of the problem a procedure based on a k shortest path algorithm was developed this approach was applied to a well known sample problem and the results are discussed and compared with those obtained using a median shortest path model