a note on the second order non autonomous neutral stochastic evolution equations with infinite delay under caratheodory conditions abstract in this note we aim to study a class of second order non autonomous neutral stochastic evolution equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion with hurst parameter h 1 2 1 in which the initial value belongs to the abstract space b we establish the existence and uniqueness of mild solutions for this kind of equations under some caratheodory conditions by means of the successive approximation the obtained result extends some well known results an example is proposed to illustrate the theory

lifted polynomial size formulations for the homogeneous and heterogeneous vehicle routing problems abstract we propose compact formulations for the symmetric and asymmetric capacitated vehicle routing problems these formulations are obtained by lifting using the reformulation linearization technique a novel polynomial size ordered path based formulation we show that the strongest proposed formulation is equivalent to the strongest multi commodity flow formulation presented so far in addition we propose polynomial size valid inequalities that aim at further tightening the proposed formulations also the tightest formulation is extended to model the fleet size and mix vehicle routing problem with fixed costs we show that the new derived model is not comparable with a state of the art polynomial length formulation we present the results of computational experiments that demonstrate the tightness of the proposed formulations and the impact of the valid inequalities

polyhedral results for a vehicle routing problem abstract the vehicle routing problem is a well known and hard combinatorial problem whose polyhedral structure has deserved little attention in this paper we consider the particular case in which all the demands are equal since in the general case the associated polytope may be empty from a known formulation of the problem we obtain the dimension of the corresponding polytope and we study the facetial properties of every inequality in it

asymptotic behavior of stochastic fitzhugh nagumo systems on unbounded thin domains abstract this article is concerned with the asymptotic behavior of solutions of a class of non autonomous stochastic fitzhugh nagumo systems driven by multiplicative white noise on unbounded thin domains the existence and uniqueness of tempered pullback random attractors are proved for the systems defined on n 1 dimensional unbounded narrow domains we also establish the upper semicontinuity of these attractors when a family of n 1 dimensional unbounded thin domains collapses onto an n dimensional unbounded domain a cut off method and a decomposition technique are employed to derive the pullback asymptotic compactness of solutions in order to overcome the difficulties caused by the non compactness of sobolev embeddings on unbounded domains as well as the lack of regularity of one component of the solutions

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

functional differential equations driven by a fractional brownian motion in this paper we prove a global existence and uniqueness result for the solution of a stochastic functional differential equation driven by a fractional brownian motion with hurst parameter h 1 2 we also study the dependence of the solution on the initial condition

vector valued stochastic delay equations a weak solution and its markovian representation abstract a class of stochastic delay equations in a type 2 umd banach space e driven by the cylindrical wiener process is studied we investigate two concepts of solutions weak and generalised strong and give conditions under which they are equivalent we present an evolution equation approach in a banach space e p e l p 1 0 e proving that the solutions can be reformulated as e p valued markov processes based on the markovian representation we prove the existence and continuity of the solutions the results are applied to stochastic reaction diffusion equations with delays

existence stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations abstract in this paper we study the existence stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise we first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions we then examine the existence and stability of random complete quasi solutions and establish the relations of these solutions and the structures of tempered attractors when the stochastic equations are incorporated with periodic forcing we obtain the existence and stability of random periodic solutions for the stochastic chafee infante equation we further establish the multiplicity and stochastic bifurcation of complete and periodic solutions

existence of almost automorphic mild solutions to non autonomous neutral stochastic differential equations abstract in this paper we consider the existence and uniqueness of square mean and weighted pseudo almost automorphic mild solutions to a class of nonautonomous stochastic neutral differential equations with infinite delay in real separable hilbert spaces a new set of sufficient conditions are established for obtaining the required result to prove the main result we use banach contraction principle together with evolution family of operators some known results are generalized and improved an application to the stochastic nonlinear heat equation with infinite delay is provided to illustrate the obtained theory

moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional brownian motion in this manuscript we consider a class of fractional stochastic differential inclusions driven by fractional brownian motion in hilbert space with hurst parameter h 12 1 sufficient conditions for the existence and asymptotic stability of mild solutions are derived in mean square moment by employing fractional calculus analytic resolvent operators and bohnenblustkarlins fixed point theorem the effectiveness of the obtained theoretical results is illustrated by an example

small sample properties of the maximum likelihood estimator in the first order moving average model summary in this paper we discuss finite sample properties of the maximum likelihood estimator 0 in the first order moving average model we give a theoretical explanation for the concentration of 0 values at the invertibility boundary we derive the exact distribution of 0 for sample size n 2 which is found to be of mixed type for general n we give approximations for pr 0 1

feedback controllers for a wind tunnel model involving a delay analytical design and numerical simulation an application of a finite spectrum assignment method for time delay systems to a feedback control of mach number in a wind tunnel is presented the linearized model of mach number control is a system of three state equations with a delay in one of the state variables the proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay the spectrum of the closed loop system is finite and consists of three eigenvalues that can be placed arbitrarily four possible variants of the feedback control law are presented the calculation of feedback coefficients is very simple which makes it possible to update the controller s parameters on line with the changes of the operating point an extensive numerical simulation of the system dynamics and the feedback controllers was done and led to several conclusions in particular a very good settling time under problem constraints has been obtained and several nice features of the proposed feedback controller have been demonstrated

evolution equations driven by a fractional brownian motion abstract in this paper we study nonlinear stochastic evolution equations in a hilbert space driven by a cylindrical fractional brownian motion with hurst parameter h 1 2 and nuclear covariance operator we establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter h this result is applied to stochastic parabolic equation perturbed by a fractional white noise in this case if the coefficients are lipschitz continuous and bounded the existence and uniqueness of a solution holds if h d 4 the proofs of our results combine techniques of fractional calculus with semigroup estimates

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 cut algorithm for the two echelon capacitated vehicle routing problem with grouping constraints abstract in this paper we present a branch and cut algorithm for the two echelon capacitated vehicle routing problem with grouping constraints 2e cvrpgc which is a new problem deriving from the classical two echelon capacitated vehicle routing problem 2e cvrp by considering grouping constraints in the second echelon customers in the 2e cvrpgc are divided into several disjoint groups and the grouping constraints ensure that customers from the same group are served by vehicles from the same satellite we formulate the problem as a mixed 0 1 linear program and propose five families of valid inequalities to strengthen the model based on the model and the inequalities we implement a branch and cut algorithm to solve the problem the proposed branch and cut algorithm was evaluated on two classes of randomly generated instances the computational results show that the five families of valid inequalities can substantially improve the lower bounds yielded by the lp relaxation of the model and the branch and cut algorithm can solve more instances to optimality than cplex we also conduct additional experiments to analyze the impacts of the grouping constraints on the problem and illustrate the differences between the 2e cvrpgc and the 2e cvrp

convergence of solutions of mixed stochastic delay differential equations with applications the paper is concerned with a mixed stochastic delay differential equation involving both a wiener process and a holder continuous process with 1 2 e g a fractional brownian motion with hurst parameter greater than 1 2 it is shown that its solution depends continuously on the coefficients and the initial data two applications of this result are given the convergence of solutions to equations with vanishing delay to the solution of equation without delay and the convergence of euler approximations for mixed stochastic differential equations as a side result of independent interest the integrability of solution to mixed stochastic delay differential equations is established

stochastic calculus with respect to gaussian processes in this paper we develop a stochastic calculus with respect to a gaussian process of the form b t int t 0 k t s dw s where w is a wiener process and k t s is a square integrable kernel using the techniques of the stochastic calculus of variations we deduce change of variable formulas for the indefinite integrals and we study the approximation by riemann sums the particular case of the fractional brownian motion is discussed

dynamics of the non autonomous stochastic p laplace equation driven by multiplicative noise we investigate the asymptotic behavior of solutions of the p laplace equation driven simultaneously by non autonomous deterministic forcing and multiplicative white noise on r n we show the tails of solutions of the equation are uniformly small outside a bounded domain which is used to derive asymptotic compactness of solution operators in l 2 r n by overcoming the non compactness of sobolev embeddings on unbounded domains we then prove existence and uniqueness of random attractors and further establish upper semicontinuity of attractors as the intensity of noise approaches zero

branch and cut algorithms for the split delivery vehicle routing problem in this paper we present two exact branch and cut algorithms for the split delivery vehicle routing problem sdvrp based on two relaxed formulations that provide lower bounds to the optimum procedures to obtain feasible solutions to the sdvrp from a feasible solution to the relaxed formulations are presented computational results are presented for 4 classes of benchmark instances the new approach is able to prove the optimality of 17 new instances in particular the branch and cut algorithm based on the first relaxed formulation is able to solve most of the instances with up to 50 customers and two instances with 75 and 100 customers

maximum likelihood estimation of regression models with stochastic trend components abstract this article is concerned with the estimation of a regression model with a stochastic trend component it is shown that the probability of estimating the trend to be deterministic is very sensitive to the type of likelihood function used as the basis of inference

stability analysis based on partition trajectory approach for switched neural networks with fractional brown noise disturbance abstractin this brief the stability problem based on feedback control for two types of stochastic neural networks driven by fractional brown noise is considered one class is the switched neural networks without time delays and the other one is with time delays a novel analysis method very different to the usual approach based on the ito formula and infinitesimal operator is proposed in this paper by the idea of splitting time of trajectory and associating with holder inequality some criteria are obtained to guarantee the switched neural networks with two types to be stable in the end two numerical examples and auxiliary figures are presented to show the feasibility and effectiveness for the proposed results

the existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion abstract in this paper we investigate the existence uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional brownian motion b q h t d x t a x t f t x t d t g t d b q h t with hurst parameter h 1 2 1 we also consider the existence of weak solutions

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

existence of mild solutions to stochastic neutral partial functional differential equations with non lipschitz coefficients under a non lipschitz condition with the lipschitz condition being considered as a special case and a weakened linear growth condition the existence and uniqueness of mild solutions to stochastic neutral partial functional differential equations snpfdes is investigated some results in govindan 2003 2005 2 6 are generalized to cover a class of more general snpfdes

the pyramidal capacitated vehicle routing problem this paper introduces the pyramidal capacitated vehicle routing problem pcvrp as a restricted version of the capacitated vehicle routing problem cvrp in the pcvrp each route is required to be pyramidal in a sense generalized from the pyramidal traveling salesman problem ptsp a pyramidal route is defined as a route on which the vehicle first visits customers in increasing order of customer index and on the remaining part of the route visits customers in decreasing order of customer index moreover this paper develops an exact branch and cut and price bcp algorithm for the pcvrp a main feature of the algorithm is that exact pricing over elementary routes are done in pseudo polynomial time computational results suggest that pcvrp solutions are highly useful for obtaining near optimal solutions to the cvrp furthermore pricing of pyramidal routes may prove to be very useful in column generation for the cvrp

almost periodic solutions of neutral functional differential equations in this paper we study a non autonomous neutral functional differential equation in a banach space applying the theory of semigroups of operators to evolution equations and krasnoselskii s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration

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

regularity of random attractors for fractional stochastic reaction diffusion equations on rn abstract we investigate the regularity of random attractors for the non autonomous non local fractional stochastic reaction diffusion equations in h s r n with s 0 1 we prove the existence and uniqueness of the tempered random attractor that is compact in h s r n and attracts all tempered random subsets of l 2 r n with respect to the norm of h s r n the main difficulty is to show the pullback asymptotic compactness of solutions in h s r n due to the noncompactness of sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the wiener process we establish such compactness by the ideas of uniform tail estimates and the spectral decomposition of solutions in bounded domains

stochastic evolution equations with fractional brownian motion in this paper linear stochastic evolution equations driven by infinite dimensional fractional brownian motion are studied a necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed separate proofs are required for the cases of hurst parameter above and below 1 2 the particular case of the laplacian on the circle is discussed in detail

stochastic averaging for a class of two time scale systems of stochastic partial differential equations abstract this paper focuses on systems of stochastic partial differential equations that have a slow component driven by a fractional brownian motion and a fast component driven by a fast varying diffusion we establish an averaging principle in which the fast varying diffusion process acts as a noise and is averaged out in the limit the slow process is shown to have a limit in the l 2 sense which is characterized by the solution of a stochastic partial differential equation driven by a fractional brownian motion whose coefficients are averages of that of the original slow process with respect to the stationary measure of the fast varying diffusion this averaging principle paves a way for reduction of computational complexity the implication is that one can ignore the complex original systems and concentrate on the average systems instead

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

the demand weighted vehicle routing problem abstract in this paper we present an exact method for the demand weighted vehicle routing problem this problem arises when the objective is to minimize the distance traveled by the vehicles weighted by the number of passengers on the routes the resulting model is a non convex mixed integer quadratic program and we show how to reformulate this problem as a linear integer program with auxiliary variables the reformulation provides very tight lower bounds on the optimal solution value and little enumeration is required however the reformulated model is very large and therefore it is solved with a branch price and cut algorithm using coin or software we provide computational results with actual data from a large urban university

empirical likelihood confidence regions in time series models summary this paper develops empirical likelihood in time series models by application of whittle s estimation method one obtains an m estimator of the parameter of a stationary time series from approximately independent observations the periodogram ordinates this estimator is used to obtain an empirical likelihood ratio which is asymptotically distributed as x2 and which can be used to construct confidence regions a procedure for the bartlett correction is also proposed finally small sample properties of the empirical likelihood confidence regions are explored through a simulation

nonlinear functional differential equations of monotone type in hilbert spaces abstract in this paper we study a class of semilinear functional evolution equations with finite delay in which the nonlinearity satisfies the weak condition of demicontinuity with respect to functional variable and also a semimonotone condition we will prove the existence uniqueness and measurability of the mild solutions based on an extension of the analogous results for non delay initial value problems on banach spaces and a version of recently developed random schauder s fixed point theorem this will be done first for the generalized solutions and then we follow an approximating procedure to obtain the same results for the mild solutions

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

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

existence and uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to the class of semilinear differential equations of the form u t au t f t bu t where a is the infinitesimal generator of an analytic semigroup acting on a complex banach space x b d b x x is a densely defined closed linear operator and f r x x is a jointly continuous function under some suitable assumptions on a b and f the existence and uniqueness of a pseudoalmost periodic solution to is obtained

on almost periodic mild solutions for neutral stochastic evolution equations with infinite delay abstract in this paper a class of neutral stochastic functional evolution equations with infinite delay is investigated under some suitable assumptions the existence and uniqueness of quadratic mean almost periodic mild solutions for these equations are discussed by means of semigroups of operators and the fixed point method moreover two examples are given to illustrate our results

a decision support system for a real vehicle routing problem abstract the vehicle routing problem has been widely studied in the literature mainly because of the real world logistics and transportation problems related to it in the present paper a new two stage exact approach for solving a real problem is shown along with decision making software in the first stage all the feasible routes are generated by means of an implicit enumeration algorithm afterwards an integer programming model is designed to select in the second stage the optimum routes from the set of feasible routes the integer model uses a number of 0 1 variables ranging from 2000 to 15 000 and gives optimum solutions in an average time of 60 seconds for instances up to 60 clients an interactive decision support system was also developed the system was tested with a set of real instances and in a worst case scenario up to 60 clients the routes obtained ranged from a 7 to 12 reduction in the distance travelled and from a 9 to 11 reduction in operational costs

on the capacitated vehicle routing problem we consider the vehicle routing problem in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost this difficult combinatorial problem contains both the bin packing problem and the traveling salesman problem tsp as special cases and conceptually lies at the intersection of these two well studied problems the capacity constraints of the integer programming formulation of this routing model provide the link between the underlying routing and packing structures we describe a decomposition based separation methodology for the capacity constraints that takes advantage of our ability to solve small instances of the tsp efficiently specifically when standard procedures fail to separate a candidate point we attempt to decompose it into a convex combination of tsp tours if successful the tours present in this decomposition are examined for violated capacity constraints if not the farkas theorem provides a hyperplane separating the point from the tsp polytope we present some extensions of this basic concept and a general framework within which it can be applied to other combinatorial models computational results are given for an implementation within the parallel branch cut and price framework symphony

the capacitated m ring star problem the capacitated m ring star problem cmrsp is the problem of designing a set of rings that pass through a central depot and through some transition points and or customers and then assigning each nonvisited customer to a visited point or customer the number of customers visited and assigned to a ring is bounded by an upper limit the capacity of the ring the objective is to minimize the total routing cost plus assignment costs the problem has practical applications in the design of urban optical telecommunication networks this paper presents and discusses two integer programming formulations for the cmrsp valid inequalities are proposed to strengthen the linear programming relaxation and are used as cutting planes in a branch and cut approach the procedure is implemented and tested on a large family of instances including real world instances and the good performance of the proposed approach is demonstrated