particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

brief paper global stabilization of semilinear systems using switching controls this paper considers feedback stabilization of distributed semilinear systems using switching controls the semilinear processes together with the switched controllers constitute a type of switched nonlinear system three kinds of stabilizabilities namely weak strong and exponential stabilizabilities are investigated one by one sets of sufficient conditions are obtained for each case a necessary condition for strong stabilizability is given the stabilizing control is characterized using a minimization problem applications to parabolic and hyperbolic like equations are considered

the fast multipole method fmm for electromagnetic scattering problems the fast multipole method fmm developed by v rokhlin 1990 to efficiently solve acoustic scattering problems is modified and adapted to the second kind integral equation formulation of electromagnetic scattering problems in two dimensions the present implementation treats the exterior dirichlet problem for two dimensional closed conducting objects of arbitrary geometry the fmm reduces the operation count for solving the second kind integral equation from o n sup 3 for gaussian elimination to o n sup 4 3 per conjugate gradient iteration where n is the number of sample points on the boundary of the scatterer a sample technique for accelerating convergence of the iterative method termed complexifying k the wavenumber is also presented this has the effect of bounding the condition number of the discrete system consequently the operation count of the entire fmm all iterations becomes o n sup 4 3 computational results for moderate values of ka where a is the characteristic size of the scatterer are given

accuracy analysis and optimization of the method of auxiliary sources mas for scattering by a circular cylinder this paper presents a rigorous accuracy analysis of the method of auxiliary sources mas when applied to scattering problems a benchmark canonical geometry consisting of a perfectly conducting infinite circular cylinder is chosen for clarity and simplicity for this particular structure it is shown that the mas square matrix can be inverted analytically yielding exact mathematical expressions for the discretization error and the condition number of the pertinent linear system it is also demonstrated that the error increases very abruptly for source locations associated with the characteristic eigenvalues of the scattering geometry precisely as predicted in theory various plots depict comparisons between analytical and computational data for the boundary condition error and all occurring discrepancies are fully explained among several important results of the analysis the fundamental mas question concerning the optimal location of the auxiliary sources is thoroughly investigated and resolved on the grounds of error minimization

exact semi internal control of an euler bernoulli equation this paper proves exact semi internal controllability of an euler bernoulli equation with variable coefficients the basic principle of the proof is the hilbert uniqueness method for this a multiplier technique and a unique continuation property have been used the proof of the unique continuation property is the main feature of this work

control of wave processes with distributed controls supported on a subregion it is proved that solutions of one dimensional wave equations satisfying general boundary conditions at the ends of a bounded interval i can be exactly controlled to any finite energy state by means of distributed controls which vanish outside of any fixed nonempty subinterval of i an example is given which shows that no such general analogous result can hold in higher dimensions in this case for a spherical region those states are characterized which can be exactly controlled to zero by means of controls supported in an annulus within the region it is found that very strong controllability obtains when the controls are distributed near the boundary but that only rather weak controllability is possible with controls supported in an interior annulus applications of these results to boundary control problems in annular regions are also discussed

controllability and observability for non autonomous evolution equations the averaged hautus test abstract we consider the observability problem for non autonomous evolution systems i e the operators governing the system depend on time we introduce an averaged hautus condition and prove that for skew adjoint operators it characterizes exact observability next we extend this to more general class of operators under a growth condition on the associated evolution family we give an application to the schrodinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient

controllability cost of conservative systems resolvent condition and transmutation abstract this article concerns the exact controllability of unitary groups on hilbert spaces with unbounded control operator it provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality by the transmutation of controls in some time l for the corresponding second order conservative system it is proved that the cost of controls in time t for the unitary group grows at most like exp l 2 t as t tends to 0 in the application to the cost of fast controls for the schrodinger equation l is the length of the longest ray of geometric optics which does not intersect the control region this article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system

traveling salesman problem heuristics leading methods implementations and latest advances heuristics for the traveling salesman problem tsp have made remarkable advances in recent years we survey the leading methods and the special components responsible for their successful implementa tions together with an experimental analysis of computational tests on a challenging and diverse set of symmetric and asymmetric tsp benchmark problems the foremost algorithms are represented by two families deriving from the lin kernighan lk method and the stem and cycle s c method we show how these families can be conveniently viewed within a common ejection chain framework which sheds light on their similarities and differences and gives clues about the nature of potential enhance ments to today s best methods that may provide additional gains in solving large and difficult tsps

feedback stabilization for a bilinear control system under weak observability inequalities abstract in this paper we discuss the feedback stabilization of bilinear systems under weak observation properties in this case the uniform stability is not guaranteed thus we provide an explicit weak decay rate for all regular initial data applications to schrodinger and wave equations are provided

exponential stability of nondissipative linear system in banach space and application to unbounded bilinear systems abstract we consider linear control systems of the form d z t d t a z t b z t where is a real parameter a is the infinitesimal generator of a linear c 0 semigroup of contractions s 0 t on a banach space x and the linear perturbation b is a relatively bounded operator with respect to a we provide necessary and sufficient conditions for exponential stability of the above system our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators applications to hyperbolic like equations are considered

new trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems abstract we present an approach based on comparison principles for energy and interpolation properties to derive lower energy estimates for nonlinearly either locally damped or boundary damped vibrating systems we show how the dissipation relation provides strong information on the asymptotic behavior of the energy of solutions the geometrical situations are either one dimensional or radial two dimensional or three dimensional for annulus domains we also consider the case of general domains but in this case for solutions with bounded velocities in time and space in all these cases the nonlinear damping function is assumed to have arbitrary strictly sublinear growth at the origin we give results for strong solutions and stronger lower estimates for smoother solutions the results are presented in two forms either on the side of energy comparison principles or through time pointwise lower estimates under additional geometric assumptions we give the resulting lower and upper estimates for four representative examples of damping functions we further give a weak lower estimate in the sense of a certain lim sup t and an upper estimate of the velocity for smoother solutions in case of general damping functions and for radial as well as multi dimensional domains we also discuss these estimates in the framework of optimality which is not proved here and indicate open problems raised by these results

unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets abstract we consider a restricted dirichlet to neumann map s r t associated with the operator t 2 g a q where g is the laplace beltrami operator of a riemannian manifold m g and a and q are a vector field and a function on m the restriction s r t corresponds to the case where the dirichlet traces are supported on 0 t s and the neumann traces are restricted on 0 t r here s and r are open sets which may be disjoint on the boundary of m we show that s r t determines uniquely up the natural gauge invariance the lower order terms a and q in a neighborhood of the set r assuming that r is strictly convex and that the wave equation is exactly controllable from s in time t 2 we give also a global result under a convex foliation condition the main novelty is the recovery of a and q when the sets r and s are disjoint we allow a and q to be non self adjoint and in particular the corresponding physical system may have dissipation of energy

reconstructing initial data using observers error analysis of the semi discrete and fully discrete approximations a new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in ramdani et al automatica 46 10 1616 1625 2010 based on the concept of observers also called luenberger observers this algorithm covers a large class of abstract evolution pde s in this paper we are concerned with the convergence analysis of this algorithm more precisely we provide a complete numerical analysis for semi discrete in space and fully discrete approximations derived using finite elements in space and an implicit euler method in time the analysis is carried out for abstract schrodinger and wave conservative systems with bounded observation locally distributed

theory and applications of infinitesimal dipole models for computational electromagnetics the recently introduced quantum particle swarm optimization qpso algorithm is employed to find infinitesimal dipole models idm for antennas with known near fields measured or computed the idm can predict accurately both the near fields and the far fields of the antenna a theory is developed to explain the mechanism behind the idm using the multipole expansion method the idm obtained from single frequency solutions is extrapolated over a frequency range around the design frequency the method is demonstrated by analyzing conducting and dielectric type antennas a calibration procedure is proposed to systematically implement infinitesimal dipoles within existing method of moment mom codes the interaction of the idm with passive and active objects is studied through several examples the idm proved to predict the interaction efficiently a closed form expression for the mutual admittance between similar or dissimilar antennas with arbitrary orientations and or locations is derived using the reaction theorem

weak and strong stabilisation of bilinear systems in a banach space abstractin this paper we study the feedback stabilisation of homogeneous bilinear systems on a banach state space sufficient conditions for weak and strong stabilisation are given a decay rate o

on the global finite time stabilization of bilinear systems by homogeneous feedback laws applications to some pde s abstract in this paper the problem of global finite time stabilization of bilinear control systems by means of homogeneous feedback law is investigated we prove under some reasonable assumptions on the operators a and b that continuous bounded and discontinuous unbounded feedbacks stabilize globally in finite time the closed loop system for illustrative the examples of heat schrodinger and transport equations are considered where homogeneous stabilizing feedback is built for these systems

traveling salesman problems with pagerank distance on complex networks reveal community structure abstract in this paper we propose a new algorithm for community detection problems cdps based on traveling salesman problems tsps labeled as tsp cda since tsps need to find a tour with minimum cost cities close to each other are usually clustered in the tour this inspired us to model cdps as tsps by taking each vertex as a city then in the final tour the vertices in the same community tend to cluster together and the community structure can be obtained by cutting the tour into a couple of paths there are two challenges the first is to define a suitable distance between each pair of vertices which can reflect the probability that they belong to the same community the second is to design a suitable strategy to cut the final tour into paths which can form communities in tsp cda we deal with these two challenges by defining a pagerank distance and an automatic threshold based cutting strategy the pagerank distance is designed with the intrinsic properties of cdps in mind and can be calculated efficiently in the experiments benchmark networks with 1000 10 000 nodes and varying structures are used to test the performance of tsp cda a comparison is also made between tsp cda and two well established community detection algorithms the results show that tsp cda can find accurate community structure efficiently and outperforms the two existing algorithms

stabilisation and polynomial decay estimate for distributed semilinear systems in this article we propose a family of feedback controls that guarantee weak and strong stabilisability for distributed semilinear systems in the case of strong stabilisation an optimal decay of the state is estimated applications to wave equations are provided

feedback stabilisation and polynomial decay estimate for time delay bilinear systems in this paper we are concerned with the question of weak and strong stabilisation for distributed bilinear systems with time delay using continuous feedback controls in the case of strong stabili

spectral conditions for admissibility and observability of wave systems applications to finite element schemes in this article we derive uniform admissibility and observability properties for the finite element space semi discretizations of ddot u a 0 u 0 where a 0 is an unbounded self adjoint positive definite operator with compact resolvent to address this problem we present a new spectral approach based on several spectral criteria for admissibility and observability of such systems our approach provides very general admissibility and observability results for finite element approximation schemes of ddot u a 0 u 0 which stand in any dimension and for any regular mesh in the sense of finite elements our results can be combined with previous works to derive admissibility and observability properties for full discretizations of ddot u a 0 u 0 we also present applications of our results to controllability and stabilization problems

frictional versus viscoelastic damping in a semilinear wave equation in this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping the equation that models this problem is given by begin eqnarray u tt kappa 0 delta u int 0 t mbox div a x g t s nabla u s ds f u b x h u t 0 mbox in omega times bbb r quad end eqnarray where a b are nonnegative functions a in c 1 overline omega b in l infty omega satisfying the assumption begin eqnarray a x b x geq delta 0 quad forall x in omega end eqnarray and f and h are power like functions we observe that the assumption 0 2 gives us a wide assortment of possibilities from which to choose the functions a x and b x and the most interesting case occurs when one has simultaneous and complementary damping mechanisms taking this point of view into account a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily strategically localized dissipations as considered in the prior literature

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

controllability of the linear one dimensional wave equation with inner moving forces we address the null inner controllability of the one dimensional wave equation with supports of the controls that may vary with respect to the time variable we consider theoretical and numerical aspects assuming a geometric optic condition on the support of the controls we first prove a generalized observability inequality for the homogeneous wave equation implying the controllability we then introduce and prove the well posedness of a mixed formulation that characterizes the controls of minimal square integrable norm a numerical approximation of this formulation based on a conformal space time finite element method is then presented several numerical experiments are finally reported

distributed source identification for wave equations an offline observer based approach in this paper we consider the 1 d wave equation where the spatial domain is a bounded interval assuming the initial conditions to be known we are here interested in identifying an unknown source term while we take the neumann derivative of the solution on one of the boundaries as the measurement output applying a back and forth iterative scheme and constructing well chosen observers that will be applied in an offline manner we retrieve the source term from the measurement output in the minimal observation time

feedback stabilisation and polynomial decay estimate for distributed bilinear parabolic systems with time delay in this paper we examine the feedback stabilisation for distributed bilinear parabolic systems described by partial differential equation with time delay the stabilisation of a such system reduce

comparable upper and lower bounds for boundary values of neumann eigenfunctions and tight inclusion of eigenvalues for smooth bounded domains in rn we prove upper and lower l2 bounds on the boundary data of neumann eigenfunctions and we prove quasiorthogonality of this boundary data in a spectral window the bounds are tight in the sense that both are independent of the eigenvalues this is achieved by working with an appropriate norm for boundary functions which includes a spectral weight that is a function of the boundary laplacian this spectral weight is chosen to cancel concentration at the boundary that can happen for whispering gallery type eigenfunctions these bounds are closely related to wave equation estimates due to tataru using this we bound the distance from an arbitrary helmholtz parameter e 0 to the nearest neumann eigenvalue in terms of boundary normal derivative data of a trial function u solving the helmholtz equation e u 0 this inclusion bound improves over previously known bounds by a factor of e5 6 analogously to a recently improved inclusion bound in the dirichlet case due to the first two authors finally we apply our theory to present an improved numerical implementation of the method of particular solutions for computation of neumann eigenpairs on smooth planar domains we show that the new inclusion bound improves the relative accuracy in a computed neumann eigenvalue around the 42000th from nine to fourteen digits with negligible extra numerical effort

exact controllability of the one dimensional wave equation with locally distributed control the one dimensional wave equation with variable wave speed and locally distributed control is considered it is shown that the adjoint system is observable using a multiplier method with a multiplier being the solution of an ordinary differential equation it is also shown that a sufficient condition for exact controllability is that a related minimization problem always has an optimal solution since the objective function for this minimization problem would be coercive if the adjoint system is observable this establishes the exact controllability of the original system

stabilization and decay estimate for distributed bilinear systems abstract in this paper we consider the problem of feedback stabilization for the distributed bilinear system y t ay t u t by t here a is the infinitesimal generator of a linear c0 semigroup of contractions on a hilbert space h and b h h is a linear bounded operator a sufficient condition for feedback stabilization is given and explicit decay estimate is established applications to vibrating systems are presented

exact and approximation algorithms for the min max k traveling salesmen problem on a tree abstract given k identical salesmen where k 2 is a constant independent of the input size the min max k traveling salesmen problem on a tree is to determine a set of k tours for the salesmen to serve all customers that are located on a tree shaped network so that each tour starts from and returns to the root of the tree with the maximum total edge weight of the tours minimized the problem is known to be np hard even when k 2 in this paper we have developed a pseudo polynomial time exact algorithm for this problem with any constant k 2 closing a question that has remained open for a decade along with this we have further developed a 1 approximation algorithm for any 0

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

partial stabilisation of non homogeneous bilinear systems abstractin this work we study in a hilbert state space the partial stabilisation of non homogeneous bilinear systems using a bounded control necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions applications to parabolic and hyperbolic equations are presented

strong stabilization with decay estimate of semilinear systems this paper considers feedback stabilization for distributed semilinear systems a sufficient condition for an appropriate feedback control to ensure strong stabilization with explicit decay rate is given application to petrowsky equation is presented

a fast domain decomposition method for the solution of electromagnetic scattering by large objects a nonoverlapping domain decomposition method is proposed for the finite element solution of the scattering problem by electrically large inhomogeneous infinite cylinders of arbitrary cross section to minimize the size of the total computational domain a second order absorbing boundary condition abc is applied upon an outer boundary of arbitrary shape which may be conformal to the surface of the scatterer this domain is then partitioned into concentric subdomains circumscribing the object a second order transmission condition derived from the abc is prescribed upon the interfaces between two adjacent subdomains this particular configuration is responsible for the fast convergence of the domain decomposition iterative algorithm which is parallelizable numerical results obtained with a nonparallelized computer code are presented which emphasize the superiority of this technique in terms of memory storage requirements and computing times over the standard finite element approach as well as over the rigorous hybrid finite element integral equation formulation

wave field interaction with complex structures using equivalence principle algorithm a domain decomposition scheme based on the equivalence principle similar to huygens principle for integral equation solvers and the method of moments is introduced the equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalence currents residing on the surface that bounds the volume it also allows the dissociation of the solution of one region from that of another region in this manner problems of high complexity can be encapsulated by surfaces of simpler shapes using less unknowns it can aid in parallel algorithms reusability of solutions as well as improving the condition number of a matrix system when disparate mesh or adaptive mesh are needed the challenge arises when an equivalence surface intercepts a current carrying conductor because the breakup of the current into separate pieces gives rise to charge singularity a junction basis can be used to mitigate this singularity however a better solution is to introduce a tap basis to model the current that intercepts with the equivalence surfaces using this scheme the current continuity is conserved and the singularity of the charges is avoided the solution is shown to be accurate

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

stabilization and control for the nonlinear schrodinger equation on a compact surface in this paper we study the stabilization property and the exact controllability for the nonlinear schrodinger equation on a two dimensional compact riemannian manifold without boundary we use a pseudo differential dissipation the proofs are based on a result of propagation of singularities and on recent dispersion estimates strichartz type inequalities due to n burq p gerard and n tzvetkov

identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements we consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial on part of the boundary dynamic boundary measurements through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations this asymptotic formula is generalized to the full time dependent maxwell s equations our formulae may be expected to lead to very effective computational identification algorithms aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements

strong stabilisation and decay estimate for unbounded bilinear systems in this article we deal with distributed bilinear systems where the operator of control is supposed to be unbounded in the sense that it is bounded from the state space into some extension then we give sufficient conditions for strong stabilisation also the rate of convergence of the state is estimated an illustrating example is given

nested equivalent source approximation for the modeling of multiscale structures we introduce a method to compress the impedance matrix of the method of moments mom for the modeling of high fidelity multiscale structures at low to moderate frequencies we start from a method recently proposed to compress static scalar problems proved to have o n computational complexity we represent far coupling between groups through equivalent source distributions on properly defined automatically generated equivalence surfaces the equivalent sources are obtained via an inverse source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy and are intrinsically multiscale this results in an o n complexity scaling of matrix vector products but reduces multiplicative constants i e reduces time and memory requirements for all structures it affords an improved representation of couplings in multiscale structures resulting in a fast convergence of iterative solvers our approach is green s function independent and easy to be implemented in existing mom codes the present version is based on the electric field integral equation efie numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures

wigner measures and observability for the schrodinger equation on the disk we analyse the structure of semiclassical and microlocal wigner measures for solutions to the linear schrodinger equation on the disk with dirichlet boundary conditions our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk we prove a structure theorem expressing the restriction of the wigner measures on each invariant torus in terms of second microlocal measures they are obtained by performing a finer localization in phase space around each of these tori at the limit of the uncertainty principle and are shown to propagate according to heisenberg equations on the circle our construction yields as corollaries a that the disintegration of the wigner measures is absolutely continuous in the angular variable which is an expression of the dispersive properties of the equation b an observability inequality saying that the l 2 norm of a solution on any open subset intersecting the boundary resp the l 2 norm of the neumann trace on any nonempty open set of the boundary controls its full l 2 norm resp h 1 norm these results show in particular that the energy of solutions cannot concentrate on periodic trajectories of the billiard flow other than the boundary

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

a data structure useful for finding hamiltonian cycles abstract we present a data structure called the reversable avl trees for maintaining a sequence of special operations called reversals this data structure is based on balanced trees and it yields an algorithm with complexity o m log n where m is the number of reversals

partial stabilisation of semilinear systems using bounded controls this paper studies a partial stabilisation problem for distributed semilinear systems this consists of steering only a part of the system s state to its equilibrium constrained controls are proposed to force the desired part of the state to approach the equilibrium necessary and sufficient conditions for weak and strong partial stabilisation are given applications are presented

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

a note on stabilization of locally damped wave equations with time delay abstract in this paper we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain r n when the local damping acts on a neighborhood of a suitable part of the boundary of we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small

a general variable neighborhood search for the one commodity pickup and delivery travelling salesman problem abstract we present a variable neighborhood search approach for solving the one commodity pickup and delivery travelling salesman problem it is characterized by a set of customers such that each of the customers either supplies pickup customers or demands delivery customers a given amount of a single product and by a vehicle whose given capacity must not be exceeded that starts at the depot and must visit each customer only once the objective is to minimize the total length of the tour thus the considered problem includes checking the existence of a feasible travelling salesman s tour and designing the optimal travelling salesman s tour which are both np hard problems we adapt a collection of neighborhood structures k opt double bridge and insertion operators mainly used for solving the classical travelling salesman problem a binary indexed tree data structure is used which enables efficient feasibility checking and updating of solutions in these neighborhoods our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best known algorithms in terms of both the solution quality and computational efforts moreover we improve the best known solutions of all benchmark instances from the literature with 200 to 500 customers we are also able to solve instances with up to 1000 customers

data structures and ejection chains for solving large scale traveling salesman problems data structures play a crucial role in the efficient implementation of local search algorithms for problems that require circuit optimization in graphs the traveling salesman problem tsp is the benchmark problem used in this study where two implementations of the stem and cycle s c ejection chain algorithm are compared the first implementation uses an array data structure organized as a doubly linked list to represent tsp tours as well as the s c reference structure the second implementation considers a two level tree structure the motivation for this study comes from the fact that the s c neighborhood structure usually requires subpaths to be reversed in order to preserve a feasible orientation for the resulting tour the traditional array structure proves to be inefficient for large scale problems since to accomplish a path reversal it is necessary to update the predecessor and the successor of each node on the path to be reversed computational results performed on a set of benchmark problems up to 316 228 nodes clearly demonstrate the relative efficiency of the two level tree data structure 2004 elsevier b v all rights reserved

relaxed tours and path ejections for the traveling salesman problem abstract we describe an edge based ejection chain method to generate compound neighborhood structures for the traveling salesman problem tsp these neighborhood structures enclose a special substructure which is not necessarily a hamiltonian tour instead the neighborhood components are linked together to compose successive levels of an ejection chain and coordinated by a suitable reference structure to generate compound moves with outstanding proprieties more precisely such a substructure can be viewed as a relaxed tour which allows solution transformations to be obtained without preserving the hamiltonian property at each step furthermore in the ejection chain process the generation of substructures produces a variety of alternating paths for the selection of subsequent ejection moves as well as for the choice of the corresponding trial moves finally we propose two algorithmic variants a preliminary and a full subpath ejection chain method p sec and f sec based on this type of compound neighborhood design both variants are guided by a simple tabu search mechanism computational results on 67 tsplib problems show that both the preliminary and the full methods find optimal and near optimal solutions very quickly frequently outperforming the best heuristic procedures for the tsp in addition the full method generally dominates the best alternative tsp procedures

uncertain multiobjective traveling salesman problem abstract traveling salesman problem is a fundamental combinatorial optimization model studied in the operations research community for nearly half a century yet there is surprisingly little literature that addresses uncertainty and multiple objectives in it a novel tsp variation called uncertain multiobjective tsp umtsp with uncertain variables on the arc is proposed in this paper on the basis of uncertainty theory and a new solution approach named uncertain approach is applied to obtain pareto efficient route in umtsp considering the uncertain and combinatorial nature of umtsp a new abc algorithm inserted with reverse operator crossover operator and mutation operator is designed to this problem which outperforms other algorithms through the performance comparison on three benchmark tsps finally a new benchmark umtsp case study is presented to illustrate the construction and solution of umtsp which shows that the optimal route in deterministic tsp can be a poor route in umtsp

exponential stabilization of distributed semilinear systems by optimal control this paper studies exponential stabilization of distributed semilinear systems the paper i gives a constrained feedback control that ensure the exponential stabilizability and ii shows that this control is the unique solution of an appropriate minimization problem examples of hyperbolic partial equations are provided

an effective implementation of the lin kernighan traveling salesman heuristic abstract this paper describes an implementation of the lin kernighan heuristic one of the most successful methods for generating optimal or near optimal solutions for the symmetric traveling salesman problem tsp computational tests show that the implementation is highly effective it has found optimal solutions for all solved problem instances we have been able to obtain including a 13 509 city problem the largest non trivial problem instance solved to optimality today

finding the largest triangle in a graph in expected quadratic time abstract finding the largest triangle in an n nodes edge weighted graph belongs to a set of problems all equivalent under subcubic reductions namely a truly subcubic algorithm for any one of them would imply that they are all subcubic a recent strong conjecture states that none of them can be solved in less than n3 time but this negative result does not rule out the possibility of algorithms with average rather than worst case subcubic running time indeed in this work we describe the first truly subcubic average complexity procedure for this problem for graphs whose edge lengths are uniformly distributed in 0 1 our procedure finds the largest triangle in average quadratic time which is the best possible complexity of any algorithm for this problem we also give empirical evidence that the quadratic average complexity holds for many other random distributions of the edge lengths a notable exception is when the lengths are distances between random points in euclidean space for which the algorithm takes average cubic time

observability and control of schrodinger equations we propose an exact controllability result for schrodinger equations in bounded domains under the bardos lebeau rauch geometric control condition with an estimate of the control which is explicit with respect to the time of controllability also we prove an explicit in time logarithmic observability estimate for the schrodinger equation where no geometrical conditions are supposed on the domain

remarks on the asymptotic behavior of the solution to damped wave equations abstract we study the diffusion phenomena for damped wave equations we prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent as an application of our approach we also study the asymptotic behavior of the damped wave equation in euclidean space under the geometric control condition

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

efficient electromagnetic scattering computation using the random auxiliary sources method for multiple composite 3 d arbitrary objects the electromagnetic em scattering problem from three dimensional 3 d arbitrary composite objects is proposed using the random auxiliary sources ras method based on direct application of the boundary conditions with the uniqueness theorem and the use of random equivalent problems concept more degrees of freedom to the sources positions are added resulting in significantly efficient solutions with lower memory requirements the technique does not require any singularity treatment due to placing the equivalent sources away from the boundaries while boundary conditions are not enforced exactly an iterative framework is introduced that can achieve an acceptable level of error in their satisfaction for an arbitrary randomly generated set of equivalent sources the presented technique promises a significant reduction in the execution time and memory requirements compared to the surface equivalent based method of moments mom the solution stability repeatability and numerical noise susceptibility are investigated thoroughly through this work also a novel edge correction scheme has been implemented to extend the capabilities of this procedure to structures with sharp edges the results of the presented technique are compared to series solutions for conducting spheres and a commercially available mom code for arbitrarily shaped objects and combinations of different materials

approximate optimal periodic scheduling of multiple sensors with constraints a constrained periodic multiple sensor scheduling problem is considered in this paper for each sensor constraints on dwell time and activation times are imposed at each time instant only one sensor can update its measurement with the estimator and the objective is to minimize the average state estimation error an approximation framework is proposed to calculate the objective function which transforms the original scheduling problem into an approximate optimal scheduling problem aosp an upper bound on the approximation error is presented to evaluate the performance of the framework to solve the aosp a necessary condition is first proposed on the optimal schedules when no constraints on activation times exist a dynamic programming based algorithm is devised to identify the optimal schedule with polynomial computational complexity when activation time constraints exist we show that the aosps can be solved by solving traveling salesman problems examples are provided to illustrate the proposed results

convergence of the wave equation damped on the interior to the one damped on the boundary abstract in this paper we study the convergence of the wave equation with variable internal damping term n x u t to the wave equation with boundary damping x x u t when n x converges to x x in the sense of distributions when the domain in which these equations are defined is an interval in r we show that under natural hypotheses the compact global attractor of the wave equation damped on the interior converges in x h 1 l 2 to the one of the wave equation damped on the boundary and that the dynamics on these attractors are equivalent we also prove in the higher dimensional case that the attractors are lower semicontinuous in x and upper semicontinuous in h 1 e h e

null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

explicit observability inequalities for the wave equation with lower order terms by means of carleman inequalities in this paper by means of carleman estimates and the usual energy estimate we obtain directly two observability inequalities for the linear wave equation with time variant nonsmooth lower order terms we do not need any unique continuation property of the linear equation a priori since this is actually one of the by products of our analysis furthermore the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation also we apply our observability estimates to exact controllability for wave equations

fast and strongly localized observation for the schrodinger equation we study the exact observability of systems governed by the schrodinger equation in a rectangle with homogeneous dirichlet respectively neumann boundary conditions and with neumann respectively dirichlet boundary observation generalizing previous results of ramdani takahashi tenenbaum and tucsnak we prove that these systems are exactly observable in arbitrarily small time moreover we show that the above results hold even if the observation regions have arbitrarily small measures more precisely we prove that in the case of homogeneous neumann boundary conditions with dirichlet boundary observation the exact observability property holds for every observation region whith non empty interior in the case of homogeneous dirichlet boundary conditions with neumann boundary observation we show that the exact observability property holds if and only if the observation region has an open intersection with an edge of each direction moreover we give explicit estimates for the blow up rate of the observability constants as the time and or the size of the observation region tend to zero the main ingredients of the proofs are an effective version of a theorem of beurling and kahane on non harmonic fourier series and an estimate for the number of lattice points in the neighbourhood of an ellipse

sharp observability estimates for heat equations the goal of this article is to derive new estimates for the cost of observability of heat equations we have developed a new method allowing one to show that when the corresponding wave equation is observable the heat equation is also observable this method allows one to describe the explicit dependence of the observability constant on the geometry of the problem the domain in which the heat process evolves and the observation subdomain we show that our estimate is sharp in some cases particularly in one space dimension and in the multi dimensional radially symmetric case our result extends those in fattorini and russell arch rational mech anal 43 272 292 1971 to the multi dimensional setting and improves those available in the literature namely those by miller j differ equ 204 1 202 226 2004 siam j control optim 45 2 762 772 2006 atti accad naz lincei cl sci fis mat natur rend lincei 9 mat appl 17 4 351 366 2006 and tenenbaum and tucsnak j differ equ 243 1 70 100 2007 our approach is based on an explicit representation formula of some solutions of the wave equation in terms of those of the heat equation in contrast to the standard application of transmutation methods which uses a reverse representation of the heat solution in terms of the wave one we shall also explain how our approach applies and yields some new estimates on the cost of observability in the particular case of the unit square observed from one side we will also comment on the applications of our techniques to controllability properties of heat type equations