randomized heuristics for the capacitated clustering problem in this paper we investigate the adaptation of the greedy randomized adaptive search procedure grasp and iterated greedy methodologies to the capacitated clustering problem ccp in particular we focus on the effect of the balance between randomization and greediness on the performance of these multi start heuristic search methods when solving this np hard problem the former is a memory less approach that constructs independent solutions while the latter is a memory based method that constructs linked solutions obtained by partially rebuilding previous ones both are based on the combination of greediness and randomization in the constructive process and coupled with a subsequent local search phase we propose these two multi start methods and their hybridization and compare their performance on the ccp additionally we propose a heuristic based on the mathematical programming formulation of this problem which constitutes a so called matheuristic we also implement a classical randomized method based on simulated annealing to complete the picture of randomized heuristics our extensive experimentation reveals that iterated greedy performs better than grasp in this problem and improved outcomes are obtained when both methods are hybridized and coupled with the matheuristic in fact the hybridization is able to outperform the best approaches previously published for the ccp this study shows that memory based construction is an effective mechanism within multi start heuristic search techniques

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

on local search for weighted k set packing given a collection of sets of cardinality at most k with weights for each set the maximum weighted packing problem is that of finding a collection of disjoint sets of maximum total weight we study the worst case behavior of the t local search heuristic for this problem proving a tight bound of k 1 1 t as a consequence for any given r 1 k 1 we can compute in polynomial time a solution whose weight is at least r times the optimal

a path integral time domain method for electromagnetic scattering a new full wave time domain formulation for the electromagnetic field is obtained by means of a path integral the path integral propagator is derived via a state variable approach starting with maxwell s differential equations in tensor form a numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed an absorbing boundary condition is demonstrated for the one dimensional 1 d case it is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the nyquist limit two numerical points per wavelength as a consequence the calculated fields are not subject to numerical dispersion other advantages in comparison to presently popular time domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods

a sufficient condition for exact penalty in constrained optimization in this paper we use the penalty approach to study three constrained minimization problems a penalty function is said to have the exact penalty property j b hiriart urruty and c lemarechal convex analysis and minimization algorithms 2 vols springer verlag berlin 1993 if there exists a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish a very simple sufficient condition for the exact penalty property

existence and stability of exact penalty for optimization problems with mixed constraints abstract in this paper we use the penalty approach in order to study minimization problems with mixed constraints in banach spaces a penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem in this paper we show that the generalized exact penalty property holds and is stable under perturbations of objective functions constraint functions and the right hand side of constraints

a hybrid finite difference surface green s function method for computing transmission losses in an inhomogeneous atmosphere over irregular terrain a standard parabolic equation spe is used to approximate the helmholtz equation for electromagnetic propagation in an inhomogeneous atmosphere an implicit finite difference ifd scheme to solve the spe is applied between the irregularly shaped ground and an altitude z z sub h below which all inhomogeneities of the medium are assumed localized the boundary condition at z z sub h is obtained by matching the ifd solution to a surface green s function sgf solution within the uniform region above z z sub h for ground slopes above about 1 degrees the ifd implementation of the impedance boundary condition at the ground is shown to maintain the validity of the approximation only for vertically polarized waves predictions using this hybrid finite difference fd sgf method agree well with results obtained using other computational methods

a greedy randomized adaptive search procedure for the two partition problem we present a greedy randomized adaptive search procedure grasp for the network 2 partition problem the heuristic is empirically compared with the kernighan lin k l method on a wide range of instances the grasp approach dominates k l with respect to solution value on a large percentage of the instances tested the ability of grasp to find optimal solutions is assessed by comparing its performance with a general purpose mixed integer programming package

an artificial bee colony algorithm for the maximally diverse grouping problem in this paper an artificial bee colony algorithm is proposed to solve the maximally diverse grouping problem this complex optimisation problem consists of forming maximally diverse groups with restricted sizes from a given set of elements the artificial bee colony algorithm is a new swarm intelligence technique based on the intelligent foraging behaviour of honeybees the behaviour of this algorithm is determined by two search strategies an initialisation scheme employed to construct initial solutions and a method for generating neighbouring solutions more specifically the proposed approach employs a greedy constructive method to accomplish the initialisation task and also employs different neighbourhood operators inspired by the iterated greedy algorithm in addition it incorporates an improvement procedure to enhance the intensification capability through an analysis of the experimental results the highly effective performance of the proposed algorithm is shown in comparison to the current state of the art algorithms which address the problem

existence of approximate exact penalty in constrained optimization in this paper we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish the exact penalty property for a large class of inequality constrained minimization problems

a numerically stable formulation of the green s function parabolic equation subtracting the surface wave pole the original formulation of the green s function parabolic equation gfpe can have numerical accuracy problems for large normalized surface impedances to solve the accuracy problem an improved form of the gfpe has been developed the improved gfpe formulation is similar to the original formulation but it has the surface wave pole subtracted the improved gfpe is shown to be accurate for surface impedances varying over 2 orders of magnitude with the largest having a magnitude exceeding 1000 also the improved formulation is slightly faster than the original formulation because the surface wave component does not have to be computed separately

a 3 d split step fourier algorithm based on a discrete spectral representation of the propagation equation a propagation method self consistent in the discrete domain for the simulation of large distance scenarios in a 3 d inhomogeneous atmosphere is proposed first a spectral representation of the field in a discrete 3 d domain over an infinite perfect ground is introduced in cylindrical coordinates a discrete spectral propagator is then derived as in 2 d methods the inhomogeneous atmosphere is considered in the spatial domain using phase screens an explicit numerical scheme is introduced for directive sources a sectoral propagation is proposed to reduce the computation time by limiting the computation domain the method is tested by simulation scenarios involving refractive effects in both vertical and azimuthal directions the 3 d refractive effects are shown to be properly simulated

exact penalty property in optimization with mixed constraints via variational analysis in this paper we use the penalty approach in order to study constrained minimization problems in infinite dimensional asplund spaces with nonsmooth nonconvex mixed constraints a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish sufficient conditions for the exact penalty properties using the notion of the mordukhovich basic subdifferential

an angle dependent impedance boundary condition for the split step parabolic equation method a formulation of the impedance boundary condition ibc is derived which can be used in split step parabolic wave equation solvers to accurately represent an interface with arbitrary dielectric properties the approach relies on ensuring that the plane wave decomposition of the field satisfies the appropriate ibc for each spectral component numerical experiments illustrating the robustness of the approach for low contrast interfaces and angles of incidence near the brewster angle are presented

an improved impedance boundary algorithm for fourier split step solutions of the parabolic wave equation a new implementation of the previously published mixed fourier transform mft method for including impedance boundaries in split step parabolic equation solutions is described and demonstrated the new algorithm is formulated entirely in the discrete domain which results in extended applicability and increased computation speed a brief review of the original mft solution is followed by a detailed description of the discrete formulation the performance of the new algorithm is then demonstrated with a few examples which rely heavily on the accuracy of the impedance boundary these examples include 10 mhz surface wave propagation over smooth and rough sea surfaces and 10 ghz calculations utilizing an effective rough surface impedance

existence of exact penalty for optimization problems with mixed constraints in banach spaces in this paper we use the penalty approach in order to study constrained minimization problems in a banach space with nonsmooth nonconvex mixed constraints a penalty function is said to have the exact penalty property j b hiriart urruty c lemarechal convex analysis and minimization algorithms springer berlin 1993 if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish sufficient conditions for the exact penalty property

existence of exact penalty for constrained optimization problems in hilbert spaces in this paper we use the penalty approach in order to study constrained minimization problems in a complete metric space with locally lipschitzian mixed constraints a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish sufficient conditions for the exact penalty property

a wide angle split step algorithm for the parabolic equation in this paper we describe a new wide angle parabolic equation based on an operator splitting that permits the use of a marching type fourier transform solution method the equation was first presented by feit and fleck appl opt 17 3990 3998 1978 for studying propagation within optical fibers existing computer codes which numerically solve the standard parabolic equation of ocean acoustics by the split step algorithm of tappert and hardin are easily modified to accommodate the wide angle capability of the new equation in addition since the new wide angle equation is less sensitive to the value of the reference wavenumber the effects of phase errors are greatly reduced the results of a simple error analysis indicate that improved accuracy can be achieved by the new wide angle equation for propagation conditions typical of deep ocean environments this is supported by our numerical experience a summary of which is presented in the paper for test cases where the variation of the acoustic index

an alternative direction decomposition scheme and error analysis for parabolic equation model alternate direction implicit adi method has been widely used to analyze the tunnel propagation or electromagnetic scattering problem for the finite difference method in this paper a novel alternate direction decomposition add scheme is proposed to simplify the split step fourier transform ssft algorithm in parabolic equation pe model the spatial matrix of electric field is decoupled into two subarrays by add ssft algorithm which is used to decrease the computational burden for 3 d pe problems in a large scale environment after the integration order exchanged also the phase error of this approximation is analyzed to show the algorithm performance along with several numerical results including the tunnel cases with traditional modal theory and they are provided to validate and calibrate the pe model and demonstrate the efficiency and accuracy of the proposed algorithm moreover the scattering computation is investigated and compared with multilevel fast multipole method to show that add ssft is appropriate for solving the scattering problems for the electrical large target

one half approximation algorithms for the k partition problem the k partition problem seeks to cluster the vertices of an edge weighted graph g v e into k sets of v k vertices each such that the total weight of the edges having both endpoints in the same cluster is maximized bottom up type heuristics based on matchings are presented for this problem these heuristics are shown to yield solutions that are at least one half the weight of the optimal solution for k equal to v 3 and v 4

horizontal parabolic equation solution of radiowave propagation problems on large domains the modeling of radiowave propagation in the troposphere often involves field strength calculations in very large domains for which the usual parabolic equation techniques become prohibitively expensive the horizontal parabolic equation method hpe provides a rigorous and efficient full wave solution for this type of problem taking advantage of the fact that refractive index perturbations in the troposphere are usually confined to a limited portion of the integration domain above the height where the medium becomes standard fourier and laplace transform techniques are used to compute the field on a given horizontal with convolution kernels based on exponential or airy functions the field on the initial horizontal may be obtained by any available method the environment below the initial height may be range dependent and include terrain variations substantial computing gains in both memory requirements and execution time are obtained the method has been validated by comparison to the standard vertical pe