optimal solution of vehicle routing problems using minimum k trees we consider the problem of optimally scheduling a fleet of k vehicles to make deliveries to n customers subject to vehicle capacity constraints given a graph with n 1 nodes a k tree is defined to be a set of n k edges that span the graph we show that the vehicle routing problem can be modeled as the problem of finding a minimum cost k tree with two k edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once the side constraints are dualized to obtain a lagrangian problem that provides lower bounds in a branch and bound algorithm this algorithm has produced proven optimal solutions for a number of difficult problems including a well known problem with 100 customers and several real problems with 25 71 customers

vehicle routing with time windows two optimization algorithms we describe two optimization methods for vehicle routing problems with time windows these are a k tree relaxation with time windows added as side constraints and a lagrangian decomposition in which variable splitting is used to divide the problem into two subproblems a semi assignment problem and a series of shortest path problems with time windows and capacity constraints we present optimal solutions to problems with up to 100 customers

ergodic primal convergence in dual subgradient schemes for convex programming lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large structured optimization prob lems the dual subgradient scheme does not automatically produce primal feasible solutions there is an abundance of techniques for computing such solutions via penalty functions tangential approximation schemes or the solution of auxiliary primal programs all of which require a fair amount of computational effort we consider a subgradient optimization scheme applied to a lagrangean dual formulation of a convex program and construct at minor cost an ergodic sequence of subproblem solutions which converges to the primal solution set numerical experiments performed on a traffic equilibrium assignment problem under road pricing show that the computation of the ergodic sequence results in a considerable improvement in the quality of the primal solutions obtained compared to those generated in the basic subgradient scheme

an exact algorithm for the capacitated vehicle routing problem based on a two commodity network flow formulation the capacitated vehicle routing problem cvrp is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints in this paper we describe a new integer programming formulation for the cvrp based on a two commodity network flow approach we present a lower bound derived from the linear programming lp relaxation of the new formulation which is improved by adding valid inequalities in a cutting plane fashion moreover we present a comparison between the new lower bound and lower bounds derived from the lp relaxations of different cvrp formulations proposed in the literature a new branch and cut algorithm for the optimal solution of the cvrp is described computational results are reported for a set of test problems derived from the literature and for new randomly generated problems

optimal routing under capacity and distance restrictions this paper describes an integer linear programming algorithm for vehicle routing problems involving capacity and distance constraints the method uses constraint relaxation and a new class of subtour elimination constraints two versions of the algorithm are presented depending upon the nature of the distance matrix exact solutions are obtained for problems involving up to sixty cities

system identification for passive linear quantum systems system identification is a key enabling component for the implementation of quantum technologies including quantum control in this paper we consider the class of passive linear input output systems and investigate several basic questions 1 which parameters can be identified 2 given sufficient input output data how do we reconstruct the system parameters 3 how can we optimize the estimation precision by preparing appropriate input states and performing measurements on the output we show that minimal systems can be identified up to a unitary transformation on the modes and systems satisfying a hamiltonian connectivity condition called infecting are completely identifiable we propose a frequency domain design based on a fisher information criterion for optimizing the estimation precision for coherent input state as a consequence of the unitarity of the transfer function we show that the heisenberg limit with respect to the input energy can be achieved using non classical input states

stronger k tree relaxations for the vehicle routing problem abstract a lagrangian based exact solution algorithm for the vehicle routing problem vrp defined on an undirected graph is introduced in this paper lower bounds are obtained by allowing exponentially many inequalities as candidates to lagrangian dualization three different families of strong valid inequalities each one with exponentially many elements are used within vrp formulations for each of them separation procedures are proposed for points that define incidence vectors of k trees violated inequalities identified in this way are then dualized in a relax and cut framework upper bounds are generated through a lagrangian clarke and wright heuristic a variable fixation test based on approximating linear programming reduced costs is also implemented computational results are presented for the proposed algorithm

transfer function approach to quantum control part i dynamics of quantum feedback systems this paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators a quantum optical closed loop including a plant and controller is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view in order to facilitate the use of control theory in microscopic world described by quantum theory in particular an input output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed this would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics this paper is divided into two parts the first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device cavity that can be regarded as a unit of quantum dynamics of bosonic modes the formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations the input output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems in the follow up paper the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory uncertainty principle e g and some applications are presented

large neighborhood search for multi trip vehicle routing abstract we consider the multi trip vehicle routing problem in which each vehicle can perform several routes during the same working shift to serve a set of customers the problem arises when customers are close to each other or when their demands are large a common approach consists of solving this problem by combining vehicle routing heuristics with bin packing routines in order to assign routes to vehicles we compare this approach with a heuristic that makes use of specific operators designed to tackle the routing and the assignment aspects of the problem simultaneously two large neighborhood search heuristics are proposed to perform the comparison we provide insights into the configuration of the proposed algorithms by analyzing the behavior of several of their components in particular we question the impact of the roulette wheel mechanism we also observe that guiding the search with an objective function designed for the multi trip case is crucial even when exploring the solution space of the vehicle routing problem we provide several best known solutions for benchmark instances

a unified solution framework for multi attribute vehicle routing problems vehicle routing attributes are extra characteristics and decisions that complement the academic problem formulations and aim to properly account for real life application needs hundreds of methods have been introduced in recent years for specific attributes but the development of a single general purpose algorithm which is both efficient and applicable to a wide family of variants remains a considerable challenge yet such a development is critical for understanding the proper impact of attributes on resolution approaches and to answer the needs of actual applications this paper contributes towards addressing these challenges with a component based design for heuristics targeting multi attribute vehicle routing problems and an efficient general purpose solver the proposed unified hybrid genetic search metaheuristic relies on problem independent unified local search genetic operators and advanced diversity management methods problem specifics are confined to a limited part of the method and are addressed by means of assignment sequencing and route evaluation components which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities extensive computational experiments on 29 prominent vehicle routing variants 42 benchmark instance sets and overall 1099 instances demonstrate the remarkable performance of the method which matches or outperforms the current state of the art problem tailored algorithms thus generality does not necessarily go against efficiency for these problem classes

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

on physical realizability of nonlinear quantum stochastic differential equations in this article we study physical realizability for a class of nonlinear quantum stochastic differential equations qsdes physical realizability is a property in which a qsde corresponds to the dynamics of an open quantum system we derive a sufficient and necessary condition for a nonlinear qsde to be physically realizable

a cluster based optimization approach for the multi depot heterogeneous fleet vehicle routing problem with time windows this paper presents a novel three phase heuristic algorithmic approach for the multi depot routing problem with time windows and heterogeneous vehicles it has been derived from embedding a heuristic based clustering algorithm within a vrptw optimization framework to this purpose a rigorous milp mathematical model for the vrptw problem is first introduced likewise other optimization approaches the new formulation can efficiently solve case studies involving at most 25 nodes to optimality to overcome this limitation a preprocessing stage clustering nodes together is initially performed to yield a more compact cluster based milp problem formulation in this way a hierarchical hybrid procedure involving one heuristic and two algorithmic phases was developed phase i aims to identifying a set of cost effective feasible clusters while phase ii assigns clusters to vehicles and sequences them on each tour by using the cluster based milp formulation ordering nodes within clusters and scheduling vehicle arrival times at customer locations for each tour through solving a small milp model is finally performed at phase iii numerous benchmark problems featuring different sizes clustered random customer locations and time window distributions have been solved at acceptable cpu times

guided local search and its application to the traveling salesman problem abstract the traveling salesman problem tsp is one of the most famous problems in combinatorial optimization in this paper we are going to examine how the techniques of guided local search gls and fast local search fls can be applied to the problem gls sits on top of local search heuristics and has as a main aim to guide these procedures in exploring efficiently and effectively the vast search spaces of combinatorial optimization problems gls can be combined with the neighborhood reduction scheme of fls which significantly speeds up the operations of the algorithm the combination of gls and fls with tsp local search heuristics of different eiciency and effectiveness is studied in an effort to determine the dependence of gls on the underlying local search heuristic used comparisons are made with some of the best tsp heuristic algorithms and general optimization techniques which demonstrate the advantages of gls over alternative heuristic approaches suggested for the problem

global optimality conditions for discrete and nonconvex optimizationwith applications to lagrangian heuristics and column generation the well known and established global optimality conditions based on the lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero we develop a set of global optimality conditions that are structurally similar but are consistent for any size of the duality gap this system characterizes a primaldual optimal solution by means of primal and dual feasibility primal lagrangian e optimality and in the presence of inequality constraints a relaxed complementarity condition analogously called complementarity the total size e of those two perturbations equals the size of the duality gap at an optimal solution further the characterization is equivalent to a near saddle point condition which generalizes the classic saddle point characterization of a primaldual optimal solution in convex programming the system developed can be used to explain to a large degree when and why lagrangian heuristics for discrete optimization are successful in reaching near optimal solutions further experiments on a set covering problem illustrate how the new optimality conditions can be utilized as a foundation for the construction of new lagrangian heuristics finally we outline possible uses of the optimality conditions in column generation algorithms and in the construction of core problems

aspects of conservation in finite element flow computations in this paper we consider different aspects of conservation in the finite element method in particular we address the problem of conservation using numerical integration related to mass lumping simplified projections quasilinear formulations and non conservative variables numerical results concerning simplified projection algorithms are given

coherent h infty control for a class of annihilation operator linear quantum systems this paper considers a coherent h control problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only for this class of quantum systems a solution to the h control problem can be obtained in terms of a pair of complex algebraic riccati equations in addition the question of physical realizability of the resulting quantum controllers is related to a bounded real property

a new approach to quadrature for finite elements incorporating hourglass control as a special case the purpose of this paper is to suggest a simple alternative approach to gaussian quadrature in the finite element method we show that this quadrature rule may be used to derive hourglass control stabilization matrices we also show that the proposed quadrature scheme does not destroy the order of the bilinear finite element method

exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations we consider the problem of routing vehicles stationed at a central facility depot to supply customers with known demands in such a way as to minimize the total distance travelled the problem is referred to as the vehicle routing problem vrp and is a generalization of the multiple travelling salesman problem that has many practical applications we present tree search algorithms for the exact solution of the vrp incorporating lower bounds computed from i shortest spanning k degree centre tree k dct and ii q routes the final algorithms also include problem reduction and dominance tests computational results are presented for a number of problems derived from the literature the results show that the bounds derived from the q routes are superior to those from k dct and that vrps of up to about 25 customers can be solved exactly

nonconforming rotated q1 tetrahedral element with explicit time stepping for elastodynamics in this paper we apply a rotated bilinear tetrahedral element recently introduced by hansbo to elastodynamics in r3 this element performs superior to the constant strain element in bending and un

separating capacity constraints in the cvrp using tabu search abstract branch and cut methods have shown to be very successful in the resolution of some hard combinatorial optimization problems the success has been remarkable for the symmetric traveling salesman problem tsp the crucial part in the method is the cutting plane algorithm the algorithm that looks for valid inequalities that cut off the current nonfeasible linear program lp solution in turn this part relies on a good knowledge of the corresponding polyhedron and our ability to design algorithms that can identify violated valid inequalities this paper deals with the separation of the capacity constraints for the capacitated vehicle routing problem cvrp three algorithms are presented a constructive algorithm a randomized greedy algorithm and a very simple tabu search procedure as far as we know this is the first time a metaheuristic is used in a separation procedure the aim of this paper is to present this application no advanced tabu technique is used we report computational results with these heuristics on difficult instances taken from the literature as well as on some randomly generated instances these algorithms were used in a branch and cut procedure that successfully solved to optimality large cvrp instances

a branch and bound algorithm for the capacitated vehicle routing problem on directed graphs we consider the asymmetric capacitated vehicle routing problem cvrp a particular case of the standard asymmetric vehicle routing problem in which only the vehicle capacity constraints are imposed cvrp is known to be np hard and finds practical applications in distribution and scheduling we describe two new bounding procedures for cvrp based on the so called additive approach each procedure computes a sequence of nondecreasing lower bounds obtained by solving different relaxations of cvrp effective implementations of the procedures are also outlined which considerably reduce the computational effort the two procedures are combined into an overall bounding algorithm a branch and bound exact algorithm is then proposed whose performance is enhanced by means of reduction procedures dominance criteria and feasibility checks extensive computational results on both real world and random test problems are presented showing that the proposed approach favorably compares with previous algorithms from the literature

the series product and its application to quantum feedforward and feedback networks the purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks these methods build on and generalize existing methods for series or cascade connections by allowing for more general interfaces and by introducing an efficient algebraic tool the series product we also introduce another product which we call the concatenation product that is useful for assembling and representing systems without necessarily having connections we show how the concatenation and series products can be used to describe feedforward and feedback networks a selection of examples from the quantum control literature are analyzed to illustrate the utility of our network modeling methodology

coherent quantum lqg control based on a recently developed notion of physical realizability for quantum linear stochastic systems we formulate a quantum lqg optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum such a control scheme is often referred to in the quantum control literature as coherent feedback control it distinguishes the present work from previous works on the quantum lqg problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom the difference in our formulation is the presence of additional non linear and linear constraints on the coefficients of the sought after controller rendering the problem as a type of constrained controller design problem due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard lqg problem we propose a numerical procedure for solving this problem based on an alternating projections algorithm and as an initial demonstration of the feasibility of this approach we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained for comparison we also consider the case of classical linear controllers that use direct or indirect measurements and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones

stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications this papers summarizes two linear tetrahedral fe formulations that have been recently proposed to overcome volumetric locking in nearly incompressible explicit dynamic applications in particular the average nodal pressure anp technique described by bonet and burton communications in numerical methods in engineering 1998 14 437 449 is briefly reviewed in addition the split based formulation proposed by zienkiewicz et al international journal for numerical methods in engineering 1998 43 565 583 is described here in terms of a time integration of the nodal jacobian this will make it simple to compare both techniques and will enable a new combined method to be presented the paper will then discuss the stability constraints that each technique places on the timestep size a von neuman stability analysis on simple 1 d uniform meshes will show that the anp element permits the use of much larger timesteps than the split based formulations finally numerical examples corroborating in 3 d this analytical conclusions will be presented copyright 2001 john wiley sons ltd

a polynomial algorithm for the degree constrained minimum k tree problem given a graph with n 1 nodes a k tree is defined to be a set of n k edges that span the graph this paper presents an algorithm for finding a minimum cost k tree with a specified degree at a designated node the algorithm runs in o n3 time and is useful in the optimal solution of certain lagrangian relaxations arising in vehicle routing

a result on projection for the vehicle routing ptoblem abstract in this paper we present a result on projection for the vehicle routing problem vrp the vrp is closely related to delivery type problems and appears in a large number of practical situations concerning the distribution of commodities the present work focuses on a commodity flow formulation presented by gavish and graves this formulation includes two sets of variables and hence it also must include coupling constraints between the two sets of variables these coupling constraints can be defined in several ways the main result of this work establishes that when the strongest form of the coupling constraints is used in the flow formulation the equivalent formulation using only the x ij variables satisfies the so called multistar constraints which for certain parameters induce facets of the non directed vrp polytope using an idea taken from gouveia we show how to derive a more compact representation in the number of constraints of the multistar constraints some consequences of our projection result are also discussed

on realization theory of quantum linear systems the purpose of this paper is to study the realization theory of quantum linear systems it is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple matrix rank condition based on controllability and observability a specific realization is proposed for general quantum linear systems in which an uncontrollable and unobservable subspace is identified when restricted to the passive case it is found that a realization is minimal if and only if it is hurwitz stable computational methods are proposed to find the cardinality of minimal realizations of a quantum linear passive system it is found that the transfer function g s of a quantum linear passive system can be written as a fractional form in terms of a matrix function s moreover g s is lossless bounded real if and only if s is lossless positive real a type of realization for multi input multi output quantum linear passive systems is derived which is related to its controllability and observability decomposition two realizations namely the independent oscillator realization and the chain mode realization are proposed for single input single output quantum linear passive systems and it is shown that under the assumption of minimal realization the independent oscillator realization is unique and these two realizations are related to the lossless positive real matrix function s

applying the attribute based hill climber heuristic to the vehicle routing problem abstract the attribute based hill climber abhc is a variant of the general tabu search principle which has shown to be competitive with respect to quality as well as efficiency to other local search heuristics for the two corner stone problems in combinatorial optimization the travelling salesman problem and the quadratic assignment problem abhc is completely parameter free and its generic logic depends on the concept of partitioning the solution space based on solution attributes which is the problem specific choice in this paper we analyze the effectiveness of this concept and the efficiency of the abhc heuristic for the general vehicle routing problem

a subpath ejection method for the vehicle routing problem generically ejection chains are methods conceived to allow solution transformations to be efficiently carried out by modifying a variable number of their components at each step of a local search algorithm we consider a subpath ejection chain method for the vehicle routing problem vrp under capacity and route length restrictions the method undertakes the identification of a substructure named the flower reference structure which besides coordinating moves during an ejection chain construction allows the creation of neighborhood structures with interesting combinatorial characteristics specifically we base the method on a fundamental property of creating alternating paths and cycles during an ejection chain construction a new algorithm based on a tabu search framework is proposed and computational results on a set of academic and real world problems indicate that the algorithm may be a good alternative to the best heuristic algorithms for the vrp

a heuristic algorithm for the asymmetric capacitated vehicle routing problem abstract we consider the asymmetric capacitated vehicle routing problem acvrp a particular case of the standard asymmetric vehicle routing problem arising when only the vehicle capacity constraints are imposed acvrp is known to be np hard and finds practical applications e g in distribution and scheduling in this paper we describe the extension to acvrp of the two well known clarke wright and fisher jaikumar heuristic algorithms we also propose a new heuristic algorithm for acvrp that starting with an initial infeasible solution determines the final set of vehicle routes through an insertion procedure as well as intea route and inter route arc exchanges the initial infeasible solution is obtained by using the additive bounding procedures for acvrp described by fischetti toth and vigo in 1992 extensive computational results on several classes of randomly generated test problems involving up to 300 customers and on some real instances of distribution problems in urban areas are presented the results obtained show that the proposed approach favourably compares with previous algorithms from the literature

a 2n constraint formulation for the capacitated minimal spanning tree problem in this paper we present a new formulation for the capacitated minimal spanning tree cmst problem one advantage of the new formulation is that it is more compact in the number of constraints than a well known formulation additionally we show that the linear programming relaxation of both formulations produces optimal solutions with the same cost we present a brief discussion concerning valid inequalities for the cmst which are directly derived from the new formulation we show that some of the new inequalities are not dominated by some sets of facet inducing inequalities for the cmst we derive some lagrangian relaxation based methods from the new formulation and present computational evidence showing that reasonable improvements on the original linear programming bounds can be obtained if these methods are strengthened by the use of cutting planes the reported computational results indicate that one of the methods presented in this paper dominates in most of the cases the previous best methods reported in the literature the most significant improvements are obtained in the instances with the root in the corner

physical realizability and preservation of commutation and anticommutation relations for n level quantum systems the purpose of this paper is to address the problem of physical realizability for n level quantum systems we provide necessary and sufficient conditions for quantum stochastic differential equat

polyhedral study of the capacitated vehicle routing problem the capacitated vehicle routing problem cvrp considered in this paper occurs when goods must be delivered from a central depot to clients with known demands usingk vehicles of fixed capacity each client must be assigned to exactly one of the vehicles the set of clients assigned to each vehicle must satisfy the capacity constraint the goal is to minimize the total distance traveled when the capacity of the vehicles is large enough this problem reduces to the famous traveling salesman problem tsp a variant of the problem in which each client is visited by at least one vehicle called the graphical vehicle routing problem gvrp is also considered in this paper and used as a relaxation of cvrp our approach for cvrp and gvrp is to extend the polyhedral results known for tsp for example the subtour elimination constraints can be generalized to facets of both cvrp and gvrp interesting classes of facets arise as a generalization of the comb inequalities depending on whether the depot is in a handle a tooth both or neither we report on the optimal solution of two problem instances by a cutting plane algorithm that only uses inequalities from the above classes

augmented lagrangean based algorithms for centralized network design capacitated spanning tree problems appear frequently as fundamental problems in many communication network design problems an integer programming formulation and a new set of valid inequalities are presented for the linear characterization of the problem a combination of a subgradient optimization procedure and an augmented lagrangean based procedure is used to generate tight lower bounds the procedure begins with an explicit representation of a subset of the constraints and the corresponding lagrangean problem is solved the solution is examined in order to identify implicit constraints that are violated those are added to the lagrangean problem forming an expanded problem and an efficient dual ascent procedure is then applied when no further improvement is possible through this procedure a subgradient optimization procedure is invoked in order to further tighten the lower bound value an exchange heuristic is applied to the nonfeasible lagrangean solution in an attempt to generate good feasible solutions to the problem the procedure has been tested and has generated bounds that are significantly better than ones obtained through previously published procedures

a heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls we consider an extension of the capacitated vehicle routing problem vrp known as the vehicle routing problem with backhauls vrpb in which the set of customers is partitioned into two subsets linehaul and backhaul customers each linehaul customer requires the delivery of a given quantity of product from the depot whereas a given quantity of product must be picked up from each backhaul customer and transported to the depot vrpb is known to be np hard in the strong sense and many heuristic algorithms were proposed for the approximate solution of the problem with symmetric or euclidean cost matrices we present a cluster first route second heuristic which uses a new clustering method and may also be used to solve problems with asymmetric cost matrix the approach exploits the information of the normally infeasible vrpb solutions associated with a lower bound the bound used is a lagrangian relaxation previously proposed by the authors the final set of feasible routes is built through a modified traveling salesman problem tsp heuristic and inter route and intra route arc exchanges extensive computational tests on symmetric and asymmetric instances from the literature show the effectiveness of the proposed approach

decomposition and dynamic cut generation in integer linear programming decomposition algorithms such as lagrangian relaxation and dantzig wolfe decomposition are well known methods that can be used to generate bounds for mixed integer linear programming problems traditionally these methods have been viewed as distinct from polyhedral methods in which bounds are obtained by dynamically generating valid inequalities to strengthen an initial linear programming relaxation recently a number of authors have proposed methods for integrating dynamic cut generation with various decomposition methods to yield further improvement in computed bounds in this paper we describe a framework within which most of these methods can be viewed from a common theoretical perspective we then discuss how the framework can be extended to obtain a decomposition based separation technique we call decompose and cut as a by product we describe how these methods can take advantage of the fact that solutions with known structure such as those to a given relaxation can frequently be separated much more easily than arbitrary real vectors

h infty control of linear quantum stochastic systems the purpose of this paper is to formulate and solve a h infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology the paper includes results on the class of such systems for which the quantum commutation relations are preserved such a requirement must be satisfied in a physical quantum system a quantum version of standard classical dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived this enables a quantum version of the two riccati solution to the h infin control problem to be presented this result leads to controllers which may be realized using purely quantum purely classical or a mixture of quantum and classical elements this issue of physical realizability of the controller is examined in detail and necessary and sufficient conditions are given our results are constructive in the sense that we provide explicit formulas for the hamiltonian function and coupling operator corresponding to the controller

a new branch and cut algorithm for the capacitated vehicle routing problem we present a new branch and cut algorithm for the capacitated vehicle routing problem cvrp the algorithm uses a variety of cutting planes including capacity framed capacity generalized capacity strengthened comb multistar partial multistar extended hypotour inequalities and classical gomory mixed integer cuts for each of these classes of inequalities we describe our separation algorithms in detail also we describe the other important ingredients of our branch and cut algorithm such as the branching rules the node selection strategy and the cut pool management computational results for a large number of instances show that the new algorithm is competitive in particular we solve three instances b n50 k8 b n66 k9 and b n78 k10 of augerat to optimality for the first time

transfer function approach to quantum control part ii control concepts and applications based on the stochastic differential equation of quantum mechanical feedback obtained in the first part of this paper detailed control concepts and applications are discussed for quantum systems interacting with a noncommutative noise source a feedback system in our framework is purely nonclassical in the sense that feedback control is performed via local operation and quantum communication through a quantum channel the role of the controller is to alter the quantum dynamic characteristics of the plant through entanglement shared between the plant and controller by sending quantum states that is modulated by the hamiltonian on the controller the input output relation of quantum systems provides a natural extension of control theory to the quantum domain this enables one to present a control theoretical interpretation of some fundamental quantum mechanical notions such as the uncertainty principle but also to find applications of ideas and tools of control theory one of the most important applications is the production of squeezed states which has been an important issue of quantum theory in relation to quantum computation and quantum communication the method proposed here reduces the application to a conventional noise reduction problem with feedback the h sub spl infin control then leads to complete squeezing

multistars partial multistars and the capacitated vehicle routing problem in an unpublished paper araque hall and magnanti considered polyhedra associated with the capacitated vehicle routing problem cvrp in the special case of unit demands among the valid and facet inducing inequalities presented in that paper were the so called multistar and partial multistar inequalities each of which came in several versions some related inequalities for the case of general demands have appeared subsequently and the result is a rather bewildering array of apparently different classes of inequalities the main goal of the present paper is to present two relatively simple procedures that can be used to show the validity of all known and some new multistar and partial multistar inequalities in both the unit and general demand cases the procedures provide a unifying explanation of the inequalities and perhaps more importantly ideas that can be exploited in a cutting plane algorithm for the cvrp computational results show that the new inequalities can be useful as cutting planes for certain cvrp instances

brief paper cascade cavity realization for a class of complex transfer functions arising in coherent quantum feedback control this paper presents a realization algorithm for a class of complex transfer function matrices corresponding to physically realizable linear quantum systems the aim of the realization algorithm is to enable a coherent quantum feedback controller which has been synthesized using methods such as quantum h control or quantum lqg control to be constructed using optical components such as cavities and phase shifters the class of linear quantum systems under consideration are passive linear quantum systems which can be described purely in terms of annihilation operators the proposed algorithm enables a complex transfer function matrix to be realized as a pure cascade connection involving only cavities and phase shifters

a nonconforming rotated q1 approximation on tetrahedra in this paper we construct an approximation that uses midpoints of edges on tetrahedra in three dimensions the construction is based on the three dimensional version of the rotated q 1 approximation proposed by rannacher and turek 1992 16 we prove a priori error estimates for finite element solutions of the elasticity equations using the new element since it contains rotated bilinear terms it performs substantially better than the standard constant strain element in bending it also allows for under integration in the form of one point gauss integration of volumetric terms in near incompressible situations numerical examples are included c 2010 elsevier b v all rights reserved

robust branch and cut and price for the capacitated vehicle routing problem the best exact algorithms for the capacitated vehicle routing problem cvrp have been based on either branch and cut or lagrangean relaxation column generation this paper presents an algorithm that combines both approaches it works over the intersection of two polytopes one associated with a traditional lagrangean relaxation over q routes the other defined by bound degree and capacity constraints this is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods the resulting branch and cut and price algorithm can solve to optimality all instances from the literature with up to 135 vertices this more than doubles the size of the instances that can be consistently solved

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

the k dissimilar vehicle routing problem abstract in this paper we define a new problem the aim of which is to find a set of k dissimilar solutions for a vehicle routing problem vrp on a single instance this problem has several practical applications in the cash in transit sector and in the transportation of hazardous materials a min max mathematical formulation is proposed which requires a maximum similarity threshold between vrp solutions and the number k of dissimilar vrp solutions that need to be generated an index to measure similarities between vrp solutions is defined based on the edges shared between pairs of alternative solutions an iterative metaheuristic to generate k dissimilar alternative solutions is also presented the solution approach is tested using large and medium size benchmark instances for the capacitated vehicle routing problem