numerical solution of differential algebraic equations with index 2 abstract in this paper numerical solution of differential algebraic equations daes with index 2 has been presented using pade approximation method an index reduction for differential algebraic equation with index 2 is suggested first index 2 system is reduced to index 1 system then we have applied the method for solving differential algebraic equations with index 2 numerically

the approximate regularization of index 2 differential algebraic problems the approximate regularization method is introduced for the solution of index 2 hessenberg systems of differential algebraic equations this approach is based on using a taylor series type method which results in a singular perturbation ordinary differential systems for linear problems it is shown that this approach is stable to compare with a partial regularization the approximate regularization appears to be promising

discriminant analysis by gaussian mixtures fisher rao linear discriminant analysis lda is a valuable tool for multigroup classification lda is equivalent to maximum likelihood classification assuming gaussian distributions for each class in this paper we fit gaussian mixtures to each class to facilitate effective classification in non normal settings especially when the classes are clustered low dimensional views are an important by product of lda our new techniques inherit this feature we can control the within class spread of the subclass centres relative to the between class spread our technique for fitting these models permits a natural blend with nonparametric versions of lda

specialized runge kutta methods for index 2 differential algebraic equations we consider the numerical solution of systems of semi explicit index 2 differential algebraic equations daes by methods based on runge kutta rk coefficients for nonstiffly accurate rk coefficients such as gauss and radau ia coefficients the standard application of implicit rk methods is generally not superconvergent to reestablish superconvergence projected rk methods and partitioned rk methods have been proposed in this paper we propose a simple alternative which does not require any extra projection step and does not use any additional internal stage moreover symmetry of gauss methods is preserved the main idea is to replace the satisfaction of the constraints at the internal stages in the standard definition by enforcing specific linear combinations of the constraints at the numerical solution and at the internal stages to vanish we call these methods specialized runge kutta methods for index 2 daes srk dae2

regularization of higher index differential algebraic equations with rank deficient constraints in this paper we present several regularizations for higher index differential algebraic equations with rank deficient or singular constraints these types of problems arise for example in the solution of constrained mechanical systems when a mechanism s trajectory passes through or near a kinematic singularity we derive a class of regularizations for these problems which is based on minimization of the norm of the constraints the new regularizations are analogous to trust region methods of numerical optimization we give convergence results for the regularizations and present some numerical experiments which illustrate their effectiveness

on asymptotics in case of linear index 2 differential algebraic equations asymptotic properties of solutions of general linear differential algebraic equations daes and those of their numerical counterparts are discussed new results on the asymptotic stability in the sense of lyapunov as well as on contractive index 2 daes are given the behavior of the backward differentiation formula bdf implicit runge kutta irk and projected implicit runge kutta pirk methods applied to such systems is investigated in particular we clarify the significance of certain subspaces closely related to the geometry of the dae asymptotic properties like a stability and l stability are shown to be preserved if these subspaces are constant moreover algebraically stable irk dae are b stable under this condition the general results are specialized to the case of index 2 hessenberg systems

energy conserving runge kutta methods for the incompressible navier stokes equations energy conserving methods have recently gained popularity for the spatial discretization of the incompressible navier stokes equations in this paper implicit runge kutta methods are investigated which keep this property when integrating in time firstly a number of energy conserving runge kutta methods based on gauss radau and lobatto quadrature are constructed these methods are suitable for convection dominated problems such as turbulent flows because they do not introduce artificial diffusion and are stable for any time step secondly to obtain robust time integration methods that work also for stiff problems the energy conserving methods are extended to a new class of additive runge kutta methods which combine energy conservation with l stability in this class the radau iia b method has the best properties results for a number of test cases on two stage methods indicate that for pure convection problems the additive radau iia b method is competitive with the gauss methods however for stiff problems such as convection dominated flows with thin boundary layers both the higher order gauss and radau iia b method suffer from order reduction overall the gauss methods are the preferred method for energy conserving time integration of the incompressible navier stokes equations

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

bare bones differential evolution the barebones differential evolution bbde is a new almost parameter free optimization algorithm that is a hybrid of the barebones particle swarm optimizer and differential evolution differential evolution is used to mutate for each particle the attractor associated with that particle defined as a weighted average of its personal and neighborhood best positions the performance of the proposed approach is investigated and compared with differential evolution a von neumann particle swarm optimizer and a barebones particle swarm optimizer the experiments conducted show that the bbde provides excellent results with the added advantage of little almost no parameter tuning moreover the performance of the barebones differential evolution using the ring and von neumann neighborhood topologies is investigated finally the application of the bbde to the real world problem of unsupervised image classification is investigated experimental results show that the proposed approach performs very well compared to other state of the art clustering algorithms in all measured criteria

locating multiple optima using particle swarm optimization many scientific and engineering applications require optimization methods to find more than one solution to multimodal optimization problems this paper presents a new particle swarm optimization pso technique to locate and refine multiple solutions to such problems the technique nichepso extends the inherent unimodal nature of the standard pso approach by growing multiple swarms from an initial particle population each subswarm represents a different solution or niche optimized individually the outcome of the nichepso algorithm is a set of particle swarms each representing a unique solution experimental results are provided to show that nichepso can successfully locate all optima on a small set of test functions these results are compared with another pso niching algorithm lbest pso and two genetic algorithm niching approaches the influence of control parameters is investigated including the relationship between the swarm size

a piecewise linear chaotic map and sequential quadratic programming based robust hybrid particle swarm optimization this paper presents a novel robust hybrid particle swarm optimization rhpso based on piecewise linear chaotic map pwlcm and sequential quadratic programming sqp the aim of the present research is to develop a new single objective optimization approach which requires no adjustment of its parameters for both unconstrained and constrained optimization problems this novel algorithm makes the best of ergodicity of pwlcm to help pso with the global search while employing the sqp to accelerate the local search five unconstrained benchmarks eighteen constrained benchmarks and three engineering optimization problems from the literature are solved by using the proposed hybrid approach the simulation results compared with other state of art methods demonstrate the effectiveness and robustness of the proposed rhpso for both unconstrained and constrained problems of different dimensions

symplectic partitioned runge kutta methods for constrained hamiltonian systems this article deals with the numerical treatment of hamiltonian systems with holonomic constraints a class of partitioned runge kutta methods consisting of the couples of s stage lobatto iiia and lobatto iiib methods has been discovered to solve these problems efficiently these methods are symplectic preserve all un derlying constraints and are superconvergent with order 2s 2 for separable hamiltonians of the form h q p frac 1 2 p t m 1 p u q the rattle algorithm based on the verlet method was up to now the only known symplectic method preserving the constraints in fact this method turns out to be equivalent to the 2 stage lobatto iiia iiib method of order 2 numerical examples have been performed which illustrate the theoretical results

new answers to an old question in the theory of differential algebraic equations in the context of linear differential algebraic equations daes one finds different associated explicit ordinary differential equations odes among them essential underlying and inherent explicit regular ones abbreviated euodes and ierodes euodes have been introduced in 1991 for index 2 daes in hessenberg form by means of special transformations ierodes result within the framework of the projector based decoupling each such explicit ode is occasionally considered to rule the flow of the dae the question to which extend euodes and ierodes are related to each other has been asked promptly after 1991 for index 2 hessenberg form daes answers have been given in 2005 saying that euodes represent somehow condensed ierodes recently euodes have been indicated for general arbitrary index daes and it has been proved that they are condensed ierodes the understanding of the relation between the ierode and the euodes enables to uncover the stability behavior of the dae flow in the present paper we show that both the ierodes and euodes of a dae with arbitrary high index do not at all depend on derivatives of the right hand side we consider adjoint pairs of daes and provide generalizations of the classical lagrange identity furthermore we address lyapunov spectra and lyapunov regularity

structural bias in population based algorithms challenging optimisation problems are abundant in all areas of science and industry since the 1950s scientists have responded to this by developing ever diversifying families of black box optimisation algorithms the latter are designed to be able to address any optimisation problem requiring only that the quality of any candidate solution can be calculated via a fitness function specific to the problem for such algorithms to be successful at least three properties are required i an effective informed sampling strategy that guides the generation of new candidates on the basis of the fitnesses and locations of previously visited candidates ii mechanisms to ensure efficiency so that for example the same candidates are not repeatedly visited and iii the absence of structural bias which if present would predispose the algorithm towards limiting its search to specific regions of the solution space the first two of these properties have been extensively investigated however the third is little understood and rarely explored in this article we provide theoretical and empirical analyses that contribute to the understanding of structural bias in particular we state and prove a theorem concerning the dynamics of population variance in the case of real valued search spaces and a flat fitness landscape this reveals how structural bias can arise and manifest as non uniform clustering of the population over time critically theory predicts that structural bias is exacerbated with independently increasing population size and increasing problem difficulty these predictions supported by our empirical analyses reveal two previously unrecognised aspects of structural bias that would seem vital for algorithm designers and practitioners respectively i increasing the population size though ostensibly promoting diversity will magnify any inherent structural bias and ii the effects of structural bias are more apparent when faced with many classes of difficult problems our theoretical result also contributes to the exploitation exploration conundrum in optimisation algorithm design by suggesting that two commonly used approaches to enhancing exploration increasing the population size and increasing the disruptiveness of search operators have quite distinct implications in terms of structural bias

projected collocation for higher order higher index differential algebraic equations abstract higher order higher index hessenberg systems of initial and boundary value differential algebraic equations daes are considered these types of systems arise in a variety of applications including multibody systems we extend a class of recently introduced projected implicit runge kutta methods and define a new class of projected piecewise polynomial collocation methods for the solution of these problems stabilizing reformulations are considered as well and a new projected invariant method is proposed the higher order ode part of the dae is collocated directly by a piecewise polynomial a projection modification helps restore all the properties of stability and superconvergence which a corresponding collocation method for an ode possesses higher order collocation at radau points is recommended for initial value problems the projection methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations like collocation at gauss points previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for higher index problems we consider reformulation methods of stabilizing index reduction we propose new methods of projected invariants to handle particularly tough higher index problems the advantages offered by these methods are demonstrated numerically

a modified particle swarm optimization via particle visual modeling analysis a particle is treated as a whole individual in all researches on particle swarm optimization pso currently these are not concerned with the information of every particle s dimensional vector a visual modeling method describing particle s dimensional vector behavior is presented in this paper based on the analysis of visual modeling the reason for premature convergence and diversity loss in pso is explained and a new modified algorithm is proposed to ensure the rational flight of every particle s dimensional component meanwhile two parameters of particle distribution degree and particle dimension distance are introduced into the proposed algorithm in order to avoid premature convergence simulation results of the new pso algorithm show that it has a better ability of finding the global optimum and still keeps a rapid convergence as with the standard pso

mechanical systems subject to holonomic constraints differential algebraic formulations and conservative integration abstract the numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered schemes are introduced for the direct treatment of a differential algebraic form of the equations that preserve the constraints the total energy and other integrals such as linear and angular momentum arising from affine symmetries moreover the schemes can be shown to preserve the property of time reversibility in an appropriate sense an example is given to illustrate various aspects of the proposed methods

solving algebraically explicit daes with the manpak manifold algorithms abstract recently the author introduced a package of algorithms called manpak for effective computations on implicitly defined submanifolds of r n here algebraically explicit differential algebraic equations daes are considered that is daes in which either the algebraic equations and or the algebraic variables are explicitly specified existence proofs for several types of such daes of index one two and three are given which directly suggest computational approaches this is used in the development of solution algorithms for these daes all of them intrinsically based on the manpak routines some numerical examples for the methods are included

enhancing particle swarm optimization using generalized opposition based learning particle swarm optimization pso has been shown to yield good performance for solving various optimization problems however it tends to suffer from premature convergence when solving complex problems this paper presents an enhanced pso algorithm called gopso which employs generalized opposition based learning gobl and cauchy mutation to overcome this problem gobl can provide a faster convergence and the cauchy mutation with a long tail helps trapped particles escape from local optima the proposed approach uses a similar scheme as opposition based differential evolution ode with opposition based population initialization and generation jumping using gobl experiments are conducted on a comprehensive set of benchmark functions including rotated multimodal problems and shifted large scale problems the results show that gopso obtains promising performance on a majority of the test problems

ls svm approximate solution to linear time varying descriptor systems this paper discusses a numerical method based on least squares support vector machines ls svms for solving linear time varying initial and boundary value problems in differential algebraic equations daes the method generates a closed form model based approximate solution the results of numerical experiments on different systems with index from 0 to 3 are presented and compared with analytic solutions to confirm the validity and applicability of the proposed method

a particle swarm optimizer for grouping problems many combinatorial optimization problems comprise a grouping phase the grouping problem in which the task is to partition a set of items into disjoint sets introduced in 1994 grouping genetic algorithm gga is the only evolutionary algorithm heavily modified to suit the structure of grouping problems in this paper we adapt the structure of the well known particle swarm optimization algorithm pso for grouping problems to propose the grouping version of the pso algorithm which is called gpso algorithm we develop new particle position and velocity updating equations which preserve the major characteristics of the original equations and are respondent to the structure of grouping problems the new updating equations work with groups of items rather than items isolatedly one of the main characteristics of the new equations is that they work in continuous space but their outcome is used in discrete space through a two phase procedure applications of gpso algorithm are made to the single batch machine scheduling problem and bin packing problem and results are compared with the results reported by gga computational results testify that our algorithm is efficient and can be regarded as a new solver for the wide class of grouping problems

numerical solution of differential algebraic equations in mechanical systems simulation abstract the numerical solution of the differential algebraic equations of motion of mechanical systems offers many computational challenges in this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real time simulation of mechanical systems

regularized gaussian discriminant analysis through eigenvalue decomposition abstract friedman proposed a regularization technique rda of discriminant analysis in the gaussian framework rda uses two regularization parameters to design an intermediate classifier between the linear the quadratic the nearest means classifiers in this article we propose an alternative approach called edda that is based on the reparameterization of the covariance matrix k of a group gk in terms of its eigenvalue decomposition k k d k a k d k where k specifies the volume of density contours of gk the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation variations on constraints concerning volumes shapes orientations k a k and d k lead to 14 discrimination models of interest for each model we derived the normal theory maximum likelihood parameter estimates our approach consists of selecting a model by minimizing the sample based estimate of future misclassification risk by cross validation numerical experiments on simulated and rea

stability of newton tvd runge kutta scheme for one dimensional euler equations with adaptive mesh abstract in this paper we propose a moving mesh method with a newton total variation diminishing tvd runge kutta scheme for the euler equations our scheme improves time discretization in the moving mesh algorithms by analyzing the semi discrete euler equations with the discrete moving mesh equations as constraints the stability of the newton tvd runge kutta scheme is proved thus we can conclude that the proposed algorithm can generate a weak solution to the euler equations finally numerical examples are presented to verify the theoretical results and demonstrate the accuracy of the proposed scheme

the numerical solution of higher index differential algebraic equations by implicit methods this paper studies the order stability and convergence properties of implicit runge kutta irk methods applied to differential algebraic systems with index greater than one these methods do not in general attain the same order of accuracy for higher index differential algebraic systems as they do for index 1 systems or for purely differential systems necessary and sufficient conditions on the method coefficients are derived to ensure that the local and global errors of the method attain a given order of accuracy for higher index linear constant coefficient systems irk methods applied to nonlinear semi explicit index 2 systems are studied and a sufficient set of conditions is derived which ensures that a method is accurate to a given order for these systems finally some numerical experiments are presented that illustrate the theoretical results and demonstrate the effects of roundoff errors on the solution

collocation methods for solving linear differential algebraic boundary value problems we consider boundary value problems for linear differential algebraic equations with variable coefficients with no restriction on the index a well known regularisation procedure yields an equivalent index one problem with d differential and a n d algebraic equations collocation methods based on the regularised bvp approximate the solution x by a continuous piecewise polynomial of degree k and deliver in particular consistent approximations at mesh points by using the radau schemes under weak assumptions the collocation problems are uniquely and stably solvable and if the unique solution x is sufficiently smooth convergence of order min k 1 2k 1 and superconvergence at mesh points of order 2k 1 is shown finally some numerical experiments illustrating these results are presented

stabilization of daes and invariant manifolds many methods have been proposed for the stabilization of higher index differential algebraic equations daes such methods often involve constraint differentiation and problem stabilization thus obtaining a stabilized index reduction a popular method is baumgarte stabilization but the choice of parameters to make it robust is unclear in practice here we explain why the baumgarte method may run into trouble we then show how to improve it we further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature our approach is to i consider stabilization of odes with invariants ii discretize the stabilizing term in a simple way generally different from the ode discretization and iii use orthogonal projections whenever possible the best methods thus obtained are related to methods of coordinate projection we discuss them and make concrete algorithmic suggestions

multi objective particle swarm optimization with time variant inertia and acceleration coefficients in this article we describe a novel particle swarm optimization pso approach to multi objective optimization moo called time variant multi objective particle swarm optimization tv mopso tv mopso is made adaptive in nature by allowing its vital parameters viz inertia weight and acceleration coefficients to change with iterations this adaptiveness helps the algorithm to explore the search space more efficiently a new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front tv mopso has been compared with some recently developed multi objective pso techniques and evolutionary algorithms for 11 function optimization problems using different performance measures

inter particle communication and search dynamics of lbest particle swarm optimizers an analysis particle swarm optimization pso is arguably one of the most popular nature inspired algorithms for real parameter optimization at present the existing theoretical research on pso focuses on the issues like stability convergence and explosion of the swarm however all of them are based on the gbest global best communication topology which usually is susceptible to false or premature convergence over multi modal fitness landscapes the present standard pso spso 2007 uses an lbest local best topology where a particle is stochastically attracted not towards the best position found in the entire swarm but towards the best position found by any particle in its topological neighborhood this article presents a first step towards a probabilistic analysis of the particle interaction and information exchange in an lbest pso with variable random neighborhood topology as found in spso 2007 it addresses issues like the distribution of particles over neighborhoods the probability distributions of the social and cognitive terms in lbest model and the explorative power of the lbest pso it also presents a state space model of the lbest pso and draws important conclusions regarding the stability and convergence of the particle dynamics in the light of control theory

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

regularization of index 1 differential algebraic equations with rank deficient constraints abstract in this paper we present a regularization for semiexplicit index 1 differential algebraic equations with rank deficient or singular constraints we consider those problems for which the solution is well defined through the singularity we give convergence results for the regularization applied to linear daes and present some numerical experiments which illustrate its effectiveness

improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem 1 evolutionary algorithms eas have been applied successfully to many water resource problems such as system design management decision formulation and model calibration the performance of an ea with respect to a particular problem type is dependent on how effectively its internal operators balance the exploitation exploration trade off to iteratively find solutions of an increasing quality for a given problem different algorithms are observed to produce a variety of different final performances but there have been surprisingly few investigations into characterizing how the different internal mechanisms alter the algorithm s searching behavior in both the objective and decision space to arrive at this final performance this paper presents metrics for analyzing the searching behavior of ant colony optimization algorithms a particular type of ea for the optimal water distribution system design problem which is a classical np hard problem in civil engineering using the proposed metrics behavior is characterized in terms of three different attributes 1 the effectiveness of the search in improving its solution quality and entering into optimal or near optimal regions of the search space 2 the extent to which the algorithm explores as it converges to solutions and 3 the searching behavior with respect to the feasible and infeasible regions a range of case studies is considered where a number of ant colony optimization variants are applied to a selection of water distribution system optimization problems the results demonstrate the utility of the proposed metrics to give greater insight into how the internal operators affect each algorithm s searching behavior

convergence proof of an enhanced particle swarm optimisation method integrated with evolutionary game theory this paper proposes an enhanced particle swarm optimisation pso algorithm and examines its performance in the proposed pso approach pso is combined with evolutionary game theory to improve convergence one of the main challenges of such stochastic optimisation algorithms is the difficulty in the theoretical analysis of the convergence and performance therefore this paper analytically investigates the convergence and performance of the proposed pso algorithm the analysis results show that convergence speed of the proposed pso is superior to that of the standard pso approach this paper also develops another algorithm combining the proposed pso with the standard pso algorithm to mitigate the potential premature convergence issue in the proposed pso algorithm the combined approach consists of two types of particles one follows standard pso and the other follows the proposed pso this enables exploitation of both diversification of the particles exploration and adaptation of the search direction

reducing index and pseudospectral methods for differential algebraic equations in this paper numerical solution of linear differential algebraic equations is considered by pseudospectral method also an index reduction technique for them is suggested for hessenberg index 2 system the index reduction technique is defined and its use is demonstrated we give a condition under which the general linear form problem can be easily transformed to the index reduced form by a simple formulation furthermore with providing some examples the aforementioned cases are dealt with numerically

a predicted sequential regularization method for index 2 hessenberg daes the sequential regularization method srm is a dynamic iterative method for the numerical solution of higher index differential algebraic equations daes the srm has the advantage of being based on a regularized problem that is less stiff than those produced by standard regularization methods consequently nonstiff integrators may be used making the srm a competitive alternative to popular integrators in past work the number of srm iterations was taken to be roughly equal to the order of the numerical method used in each dynamic iteration in this paper we propose a predicted srm psrm that reduces the number of iterations in each dynamic iteration to one we give a new error analysis for explicit runge kutta methods applied to linear index 2 hessenberg daes with or without singularities we also give numerical examples to confirm the predicted convergence rates for the psrm extrapolation formulas and methods based on the differential part of the daes serve as a predictor and the srm iteration serves as a corrector implementation of higher order schemes for the psrm makes use of continuous extensions of runge kutta methods in particular we give a prediction scheme for the algebraic variable at intermediate stage points that suppresses order reduction in the differential variable near a singularity moreover the srm psrm provides new insight into operator splitting and fast convergence rates for waveform relaxation

handling boundary constraints for particle swarm optimization in high dimensional search space despite the fact that the popular particle swarm optimizer pso is currently being extensively applied to many real world problems that often have high dimensional and complex fitness landscapes the effects of boundary constraints on pso have not attracted adequate attention in the literature however in accordance with the theoretical analysis in 11 our numerical experiments show that particles tend to fly outside of the boundary in the first few iterations at a very high probability in high dimensional search spaces consequently the method used to handle boundary violations is critical to the performance of pso in this study we reveal that the widely used random and absorbing bound handling schemes may paralyze pso for high dimensional and complex problems we also explore in detail the distinct mechanisms responsible for the failures of these two bound handling schemes finally we suggest that using high dimensional and complex benchmark functions such as the composition functions in 19 is a prerequisite to identifying the potential problems in applying pso to many real world applications because certain properties of standard benchmark functions make problems inexplicit

boundary value methods for the solution of differential algebraic equations boundary value techniques for the solution of initial value problems of odes despite their apparent higher cost present some important advantages over initial value methods among them there is the possibility to have greater accuracy to control the global error and to have an efficient parallel implementation in this paper the same techniques are applied to the solution of linear initial value problems of daes we have considered three term numerical methods midpoint simpson and an adams type method in order to obtain a block tridiagonal linear system as a discrete problem convergence results are stated in the case of constant coefficients and numerical examples are given on linear time varying problems

median based classifiers for high dimensional data conventional distance based classifiers use standard euclidean distance and so can suffer from excessive volatility if vector components have heavy tailed distributions this difficulty can be alleviated by replacing the l2 distance by its l1 counterpart for example the l1 version of the popular centroid classifier would allocate a new data value to the population to whose centroid it was closest in l1 terms however this approach can lead to inconsistency because the centroid is defined using l2 rather than l1 distance in particular by mixing l1 and l2 approaches we produce a classifier that can seriously misidentify data in cases where the means and medians of marginal distributions take different values these difficulties motivate replacing centroids by medians however in the very high dimensional settings commonly encountered today this can be problematic if we attempt to work with a conventional spatial median therefore we suggest using componentwise medians to construct a robust class

analytical approximate solutions of systems of fractional algebraic differential equations by homotopy analysis method abstract in this paper we develop a framework to obtain approximate solutions to systems of algebraic differential equations of fractional order by employing the homotopy analysis method ham the study highlights the efficiency of the method and its dependence on the auxiliary parameter numerical examples are examined to highlight the significant features of the ham method the method shows improvements over existing analytical techniques

reprint of on convergence analysis of particle swarm optimization algorithm abstract particle swarm optimization pso a population based stochastic optimization algorithm has been successfully used to solve many complicated optimization problems however analysis on algorithm convergence is still inadequate till now in this paper the martingale theory is applied to analyze the convergence of the standard pso spso firstly the swarm state sequence is defined and its markov properties are examined according to the theory of spso two closed sets the optimal particle state set and optimal swarm state set are then obtained afterwards a supermartingale is derived as the evolutionary sequence of particle swarm with the best fitness value finally the spso convergence analysis is carried out in terms of the supermartingale convergence theorem our results show that spso reaches the global optimum in probability moreover the analysis on spso proves that the quantum behaved particle swarm optimization qpso is also a global convergence algorithm the proof of the spso convergence in this work is new simple and more effective without specific implementation

the differential ant stigmergy algorithm ant colony optimization aco is a popular swarm intelligence scheme known for its efficiency in solving combinatorial optimization problems however despite some extensions of this approach to continuous optimization high dimensional problems remain a challenge for aco this paper presents an aco based algorithm for numerical optimization capable of solving high dimensional real parameter optimization problems the algorithm called the differential ant stigmergy algorithm dasa transforms a real parameter optimization problem into a graph search problem the parameters differences assigned to the graph vertices are used to navigate through the search space we compare the algorithm results with the results of previous studies on recent benchmark functions and show that the dasa is a competitive continuous optimization algorithm that solves high dimensional problems effectively and efficiently

an algorithm for solving daes with mechanization in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm of pade approximation method for solving differential algebraic equation systems was established and a new maple procedures mainproc was established too ten examples are presented to illustrate the implementation of the program

geometric properties of runge kutta discretizations for index 2 differential algebraic equations we analyze runge kutta discretizations applied to index 2 differential algebraic equations daes the asymptotic features of the numerical and the exact solutions are compared it is shown that runge kutta methods satisfying the first order constraint condition of the dae correctly reproduce the geometric properties of the continuous system the proof combines embedding techniques of index 2 daes and ordinary differential equations odes with some invariant manifolds results of nipp and stoffer attractive invariant manifolds for maps sam research report 92 11 eth zurich switzerland 1992 the results support the favorable behavior of these runge kutta methods applied to index 2 daes for t ge 0

multi operator based biogeography based optimization with mutation for global numerical optimization biogeography based optimization bbo is a new evolutionary optimization based on the science of biogeography for global optimization we propose two extensions to bbo first we propose a new migration operation based multi parent crossover called multi parent migration model which is a generalization of the standard bbo migration operator the new migration model can satisfy a balance of exploration and exploitation second the gaussian mutation operator is integrated into multi operator biogeography based optimization mobbo to enhance its exploration ability and to improve the diversity of population experiments have been conducted on 23 benchmark problems of a wide range of dimensions and diverse complexities simulation results and comparisons demonstrate the proposed mobbo algorithm based multi parent crossover model is better or at least comparable to the bbo pbbo and evolutionary algorithms from literature when considering the quality of the solutions obtained

high dimensional classification using features annealed independence rules classification using high dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high throughput data the impact of dimensionality on classifications is largely poorly understood in a seminal paper bickel and levina 2004 show that the fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem we first demonstrate that even for the independence classification rule classification using all the features can be as bad as the random guessing due to noise accumulation in estimating population centroids in high dimensional feature space in fact we demonstrate further that almost all linear discriminants can perform as bad as the random guessing thus it is paramountly important to select a subset of important features for high dimensional classification resulting in features annealed independence rules fair the conditions under which all the important features can be selected by the two sample t statistic are established the choice of the optimal number of features or equivalently the threshold value of the test statistics are proposed based on an upper bound of the classification error simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure

shrinking hypersphere based trajectory of particles in pso this paper proposes a new shrinking hypersphere pso shpso for continuous function optimization the global best and personal best fly in the search space in the form of a hypersphere instead of particles the hyperspheres keep on shrinking as the iterations proceed and the velocity and position update equations are applied at each iteration the theoretical convergence of the shpso is proved then the performance of the proposed shpso is compared with five well known pso variants namely basic pso trelea i pso trelea ii pso clerc pso and spso 2011 the basis of comparison is 24 benchmark problems selected from collection of cec benchmark problem set the analysis is performed with t test performance index empirical cumulative distribution and time complexity it is concluded that the proposed shpso is a promising new variant of pso which will open new doors of research in this area

the numerical solution of delay differential algebraic equations of retarded and neutral type in this paper we consider the numerical solution of initial value delay differential algebraic equations ddaes of retarded and neutral types with a structure corresponding to that of hessenberg daes we give conditions under which the ddae is well conditioned and show how the ddae is related to an underlying retarded or neutral delay ordinary differential equation dode we present convergence results for linear multistep and runge kutta methods applied to ddaes of index 1 and 2 and show how higher index hessenberg ddaes can be formulated in as stable a way as index 2 hessenberg ddaes we also comment on some practical aspects of the numerical solution of these problems

attracting sets in index 2 differential algebraic equations and in their runge kutta discretizations we analyse runge kutta discretizations applied to autonomous index 2 differential algebraic equations in the vicinity of attracting sets we compare the geometric properties of the numerical and the exact solutions and show that projected and half explicit runge kutta methods reproduce the qualitative features of the continuous system correctly the proof combines invariant manifold results of schropp siam j numer anal to appear and classical results for discretized ordinary differential equations of kloeden and lorenz siam j numer anal 23 1986 986

starting algorithms for a class of rk methods for index 2 daes when semiexplicit differential algebraic equations are solved with implicit runge kutta methods rk the computational effort is dominated by the cost of solving the nonlinear systems and therefore it is important to have good starting values to begin the iterations for semiexplicit index 2 daes starting algorithms without additional cost for rk methods with regular matrix coefficient were studied in a previous paper however the regularity condition on the matrix coefficient excludes some interesting methods like lobatto iiia and esdirk methods in this paper we study starting algorithms without additional computational cost for a class of runge kutta methods in the case of index 2 daes

quantile based classifiers classification with small samples of high dimensional data is important in many application areas quantile classifiers are distance based classifiers that require a single parameter regardless of the dimension and classify observations according to a sum of weighted componentwise distances of the components of an observation to the within class quantiles an optimal percentage for the quantiles can be chosen by minimizing the misclassification error in the training sample it is shown that this choice is consistent for the classification rule with the asymptotically optimal quantile and that under some assumptions as the number of variables goes to infinity the probability of correct classification converges to unity the effect of skewness of the distributions of the predictor variables is discussed the optimal quantile classifier gives low misclassification rates in a comprehensive simulation study and in a real data application

topology selection for particle swarm optimization particle swarm optimization pso uses a social topology for particles to share information among neighbors during optimization a large number of existing literatures have shown that the topology affects the performance of pso and an optimal topology is problem dependent but currently there is a lack of study on this issue in this paper we first analyze a class of deterministic regular topologies with regard to what affect the optimality of algorithmic parameters e g the number of particles and the topological degree so as to provide a guide to topology selections for pso both theoretical analysis and numerical experiments are performed and reported in detail the theoretical analysis reveals that the optimality of algorithmic parameters is dependent on the computational budget available in particular the optimal number of particles increases unstrictly as the computational budget increases while for any fixed number of particles the optimal degree decreases unstrictly as computational budget increases the only condition is that the computational budget cannot exceed a constant measuring the hardness of the benchmark function set with a total of 198 regular topologies and 9 different numbers of particles tested on 90 benchmark functions using a recently reported data profiling technique numerical experiments verify the theoretical derivations based on these results two formulas are developed to help choose optimal topology parameters for increased ease and applicability of pso to real world problems

numerical solution of differential algebraic equations and computation of consistent initial boundary conditions boundary value methods for the solution of differential algebraic equations are described we consider both initial and boundary value problems and derive an algorithm that does not require additional information from the user but only the initial or boundary conditions needed in theory to obtain a unique solution

on fast and accurate block based motion estimation algorithms using particle swarm optimization both fast and accurate block matching algorithms are critical to efficient compression of video frames using motion estimation and compensation while the particle swarm optimization approach holds the promise of alleviating the local optima problem suffered typically by existing very fast block matching methods motion estimation algorithms based on particle swarm optimization in the literature appear to be either much slower than some leading fast block matching methods for a given accuracy of motion estimation or less accurate for a given computational complexity in this paper we show that the conventional particle swarm optimization approach which was originally designed to solve general optimization problems where fast convergence of the algorithm might not be a primary concern could be modified appropriately so that it could provide accurate motion estimation with very low computational cost in the specific context of video motion estimation to this end we proposed a new block matching algorithm based on a set of strategies adapted from the standard particle swarm optimization approach extensive simulations showed that the proposed method could achieve significant improvements over leading fast block matching methods including the diamond search and the cross diamond search methods in terms of both estimation accuracy and computational cost in particular the proposed method based on particle swarm optimization is not only much faster but also remarkably more accurate about 2db higher in terms of the peak signal to noise ratio than the competing methods on video sequences with large motion

a study of particle swarm optimization particle trajectories particle swarm optimization pso has shown to be an efficient robust and simple optimization algorithm most of the pso studies are empirical with only a few theoretical analyses that concentrate on understanding particle trajectories these theoretical studies concentrate mainly on simplified pso systems this paper overviews current theoretical studies and extend these studies to investigate particle trajectories for general swarms to include the influence of the inertia term the paper also provides a formal proof that each particle converges to a stable point an empirical analysis of multi dimensional stochastic particles is also presented experimental results are provided to support the conclusions drawn from the theoretical findings

semi lagrangian multistep exponential integrators for index 2 differential algebraic systems implicit explicit imex multistep methods are very useful for the time discretization of convection diffusion pde problems such as the burgers equations and the incompressible navier stokes equations in the latter as well as in pde models of plasma physics and of electromechanical systems semi discretization in space gives rise to differential algebraic dae system of equations often of index higher than 1 in this paper we propose a new class of exponential integrators for index 2 daes arising from the semi discretization of pdes with a dominating and typically nonlinear convection term this class of problems includes the incompressible navier stokes equations the integration methods are based on the backward differentiation formulae bdf and they can be applied without modifications in the semi lagrangian integration of convection diffusion problems the approach gives improved performance at low viscosity regimes

sequential regularization methods for higher index daes with constraint singularities the linear index 2 case standard stabilization techniques for higher index differential algebraic equations daes often involve elimination of the algebraic solution components this may not work well if there are singularity points where the constraint jacobian matrix becomes rank deficient this paper proposes instead a sequential regularization method srm a functional iteration procedure for solving problems with isolated singularities which have smooth differential solution components for linear index 2 daes we consider both initial value problems ivps and boundary value problems bvps the convergence of the srm is described and proved in detail we believe that this is the first convergence proof for any method for daes with this type of constraint singularities moreover the regularization parameter in our method is not necessarily very small so the srm is an important improvement over usual regularization methods various aspects of the subsequent numerical discretization of the regularized problems are discussed as well and some numerical verifications are carried out

differential transform method applied to high index differential algebraic equations abstract in ayaz 2004 f ayaz applications of differential transform method to differential algebraic equations appl math comput 152 2004 649 657 numerical solution of linear differential algebraic equations daes is considered by differential transform method two index 1 daes have been solved by using the method and the numerical solutions coincide with the exact solution very well in this paper high index daes are considered index 2 daes can be done in a similar way a counter example is proposed to explain that the method is not suitable for all index 3 daes

on the numerical solution of differential algebraic equations with index 2 in this paper numerical solution of differential algebraic equations daes with index 2 is considered an index reduction for dae with index 2 is suggested first index 2 system is reduced to index 1 system then we have applied the method for solving daes with index 2 numerically

numerical solutions of linear time varying descriptor systems via hybrid functions state analysis of linear time varying descriptor systems via hybrid functions are proposed in this paper based upon some useful properties of hybrid functions a special product matrix and a related coefficient matrix are applied to solve the descriptor systems the unknown coefficient matrix will be in generalized lyapunov equation form which is solved via the kronecker product method the advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems we propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions the high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples

solving more general index 2 differential algebraic equations abstract the paper deals with a class of quasilinear index 2 differential algebraic equations which covers both linear variable coefficient systems as well as hessenberg form equations supposing low smoothness only the solvability of initial value problems is stated via classical analytical techniques for that class of differential algebraic equations backward differentiation formulas and runge kutta methods as well as projected versions are discussed with respect to feasibility in stability convergence and asymptotical behaviour

analyzing the stability behaviour of solutions and their approximations in case of index 2 differential algebraic systems when integrating regular ordinary differential equations numerically one tries to match carefully the dynamics of the numerical algorithm with the dynamical behaviour of the true solution the present paper deals with linear index 2 differential algebraic systems it is shown how knowledge pertaining to numerical regular ordinary differential equations applies provided a certain subspace which is closely related to the tangent space of the constraint manifold remains invariant

reservoir characterization and inversion uncertainty via a family of particle swarm optimizers history matching provides to reservoir engineers an improved spatial distribution of physical properties to be used in forecasting the reservoir response for field management the ill posed character of the history matching problem yields nonuniqueness and numerical instabilities that increase with the reservoir complexity these features might cause local optimization methods to provide unpredictable results not being able to discriminate among the multiple models that fit the observed data production history also the high dimensionality of the inverse problem impedes estimation of uncertainties using classical markov chain monte carlo methods we attenuated the ill conditioned character of this history matching inverse problem by reducing the model complexity using a spatial principal component basis and by combining as observables flow production measurements and time lapse seismic crosswell tomographic images additionally the inverse problem was solved in a stochastic framework for this purpose

an improved particle swarm optimizer for parametric optimization of flexible satellite controller abstract parametric optimization of flexible satellite controller is an essential for almost all modern satellites particle swarm algorithm is a global optimization algorithm but it suffers from two major shortcomings that of premature convergence and low searching accuracy to solve these problems this paper proposes an improved particle swarm optimization ipso which substitute poorly fitted particles with a cross operation based on decision possibility the cross operation can interchange local optima between three particles thereafter the swarm is split in two halves and random number s get generated by crossing the dimension of particle from both halves this produces a new swarm now the new swarm and old swarm are mixed and based on relative fitness a half of the particles are selected for the next generation as a result of the cross operation ipso can easily jump out of local optima has improved searching accuracy and accelerates the convergence speed some test functions with different dimensions are used to analyze the performance of ipso algorithm simulation results show that the ipso has more advantages than standard pso and genetic algorithm pso gapso in that it has a more stable performance and lower level of complexity thus the ipso is applied for parametric optimization of flexible satellite control for a satellite having solar wings and antennae simulation results shows that the ipso can effectively get the best controller parameters vis a vis the other optimization methods

implementation of linear multistep methods for solving constrained equations of motion a class of multistep methods for numerical integration of the equations of motion of constrained mechanical systems is considered they are based on different local parametrizations of the differentiable manifold defined by the kinematic constraints during integration the kinematic constraints are preserved at all levels position velocity and acceleration the numerical implementations described in the paper require only one symmetric matrix factorization at each integration step

on the numerical solution of differential algebraic equations with index 3 in this study numerical solution of differential algebraic equations daes with index 3 has been presented by pade approximation an index reduction for differential algebraic equation with index 3 is suggested first index 3 system is reduced to index 1 system then we have applied the method for solving differential algebraic equations with index 3 numerically

least squares collocation for linear higher index differentialalgebraic equations differentialalgebraic equations with higher index give rise to essentially ill posed problems therefore their numerical approximation requires special care in the present paper we state the notion of ill posedness for linear differentialalgebraic equations more precisely based on this property we construct a regularization procedure using a least squares collocation approach by discretizing the pre image space numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index 1 differentialalgebraic equations convergence is shown for a limited class of linear higher index differentialalgebraic equations

complex system fault diagnosis based on a fuzzy robust wavelet support vector classifier and an adaptive gaussian particle swarm optimization this paper proposes a robust loss function that penalizes hybrid noise i e gaussian noise singularity points and larger magnitude noise in a complex fuzzy fault diagnosis system a mapping relationship between fuzzy numbers and crisp real numbers that allows a fuzzy sample set to be transformed into a crisp real sample set is also presented furthermore the paper proposes a novel fuzzy robust wavelet support vector classifier frwsvc based on a wavelet base function and develops an adaptive gaussian particle swarm optimization agpso algorithm to seek the optimal unknown parameter of the frwsvc the results of experiments that apply the hybrid diagnosis model based on the frwsvc and the agpso algorithm to fault diagnosis demonstrate that it is both feasible and effective tests comparing the method proposed in this paper against other fuzzy support vector classifier fsvc machines show that it outperforms them

on numerical differential algebraic problems with application to semiconductor device simulation this paper considers questions regarding conditioning of and numerical methods for certain differential algebraic equations subject to initial and boundary conditions the approach taken is that of separating differential and algebraic solution components at least theoretically this yields conditioning results for differential algebraic boundary value problems in terms of pure differential problems for which existing theory is well developed the process is carried out for problems with global index 1 or 2 for semi explicit boundary value problems of index 1 where solution components are separated a convergence theorem is given for a special class of collocation methods for general index 1 problems advantages and disadvantages of certain symmetric difference schemes are discussed for initial value problems with index 2 the use of bdf schemes is examined with a summary of conditions for their successful and stable utilization finally the present considerations and analysis are applied to

a new heuristic approach for non convex optimization problems in this work a new optimization method called the heuristic kalman algorithm hka is presented this new algorithm is proposed as an alternative approach for solving continuous non convex optimization problems the principle of hka is to explicitly consider the optimization problem as a measurement process designed to give an estimate of the optimum a specific procedure based on the kalman estimator was developed to improve the quality of the estimate obtained through the measurement process the main advantage of hka compared to other metaheuristics lies in the small number of parameters that need to be set by the user further it is shown that hka converges almost surely to a near optimal solution the efficiency of hka was evaluated in detail using several non convex test problems both in the unconstrained and constrained cases the results were then compared to those obtained via other metaheuristics the numerical experiments show that hka is a promising approach for solving non convex optimization problems particularly in terms of computation time and success ratio