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

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

convergence and stochastic stability analysis of particle swarm optimization variants with generic parameter distributions in this paper we present the convergence and stochastic stability analysis of a set of pso variants those that differ with the classical pso in the statistical distribution of the three pso tuning parameters inertia weight local and global acceleration we provide an analytical expression for the upper limit of the second order stability regions the so called usl curves of the particle trajectories that can be applied to most of these pso algorithms thus this work generalizes to this set the result found in the literature for the classical pso we apply this analysis to some of these variants finally numerical experiments have been performed that confirm the known fact that the best algorithm performance is provided tuning the pso parameters close to the usl curve

linearization techniques for singular initial value problems of ordinary differential equations linearization methods for singular initial value problems in second order ordinary differential equations are presented these methods result in linear constant coefficients ordinary differential equations which can be integrated analytically thus yielding piecewise analytical solutions and globally smooth solutions the accuracy of these methods is assessed by comparisons with exact and asymptotic solutions of homogeneous and non homogeneous linear and nonlinear lane emden equations it is shown that linearization methods provide accurate solutions even near the singularity or the zeros of the solution in fact it is shown that linearization methods provide more accurate solutions than methods based on perturbation methods it is also shown that the accuracy of these techniques depends on the nonlinearity of the ordinary differential equations and may not be a monotonic function of the step size

defect correction finite element method for the stationary incompressible magnetohydrodynamics equation in this study we give the defect correction finite element method for the stationary incompressible mhd equation firstly the nonlinear mhd equation is solved with an artificial viscosity term then the numerical solution is improved on the same grid by a linearized defect correction technique then we give the numerical analysis including stability analysis and error analysis the numerical analysis proves that our method is stable and has an optimal convergence rate then we give some numerical results from the numerical results we can see that our method is efficient for solving the mhd equations

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

threshold phenomena for a reaction diffusion system abstract we consider the pure initial value problem for the system of equations t xx w w t e w e 0 the initial data being x 0 w x 0 x 0 here v v h v a where h is the heaviside step function and a 0 1 2 this system is of the fitzhugh nagumo type and has several applications including nerve conduction and distributed chemical biochemical systems it is demonstrated that this system exhibits a threshold phenomenon this is done by considering the curve s t defined by s t sup x v x t a the initial datum x is said to be superthreshold if limt s t it is proven that the initial datum is superthreshold if x a on a sufficiently long interval x is sufficiently smooth and x decays sufficiently fast to zero as x

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

the fitness evaluation strategy in particle swarm optimization abstract the particle swarm optimization pso computational method has recently become popular however it has limitations it may trap into local optima and cause the premature convergence phenomenon especially for multimodal and high dimensional problems in this paper we focus on investigating the fitness evaluation in terms of a particle s position particularly we find that the fitness evaluation strategy in the standard pso has two drawbacks i e two steps forward and one step back and two steps back and one step forward in addition we propose a general fitness evaluation strategy gfes by which a particle is evaluated in multiple subspaces and different contexts in order to take diverse paces towards the destination position as demonstrations of gfes a series of psos with gfes are presented experiments are conducted on several benchmark optimization problems the results show that gfes is effective at handling multimodal and high dimensional problems

optimal adaptive solution of piecewise regular systems of ivps with unknown switching hypersurface we study the solution of piecewise regular systems of ivps with a switching hypersurface defined by an unknown event function our aim is to design an algorithm that is not based on heuristic steps it does not use information on the event function and preserves the order known for regular systems the algorithm is based on the adaptive mesh which differs from the equidistant mesh only by a single point we provide a rigorous that is independent of heuristic arguments analysis of its error and cost

stability of an axially accelerating string subjected to frictional guiding forces abstract the dynamic response of an axially translating continuum subjected to the combined effects of a pair of spring supported frictional guides and axial acceleration is investigated such systems are both non conservative and gyroscopic the continuum is modeled as a tensioned string translating between two rigid supports with a time dependent velocity profile the equations of motion are derived with the extended hamilton s principle and discretized in the space domain with the finite element method the stability of the system is analyzed with the floquet theory for cases where the transport velocity is a periodic function of time direct time integration using an adaptive step runge kutta algorithm is used to verify the results of the floquet theory this approach can also be employed in the general case of arbitrary time varying velocity results are given in the form of time history diagrams and instability point grids for different sets of parameters such as the location of the stationary load the stiffness of the elastic support and the values of initial tension this work showed that presence of friction adversely affects stability but using non zero spring stiffness on the guiding force has a stabilizing effect this work also showed that the use of the finite element method and floquet theory is an effective combination to analyze stability in gyroscopic systems with stationary friction loads

the convergence of shooting methods for singular boundary value problems we investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems particular attention is paid to the well posedness of the process it is shown that boundary value problems can be solved efficiently when a high order integrator for the associated singular initial value problems is available moreover convergence results for a perturbed newton iteration are discussed

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

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

a note on the sturmian theorem for singular boundary value problems in this paper we study properties of the eigenfunctions of singular boundary value problems the main results show that for a class of singular boundary value problems the sturmian oscillation theorem holds it is a generalization of the standard case to the singular case

force imitated particle swarm optimization using the near neighbor effect for locating multiple optima multimodal optimization problems pose a great challenge of locating multiple optima simultaneously in the search space to the particle swarm optimization pso community in this paper the motion principle of particles in pso is extended by using the near neighbor effect in mechanical theory which is a universal phenomenon in nature and society in the proposed near neighbor effect based force imitated pso nn fpso algorithm each particle explores the promising regions where it resides under the composite forces produced by the near neighbor attractor and near neighbor repeller which are selected from the set of memorized personal best positions and the current swarm based on the principles of superior and nearer and inferior and nearer respectively these two forces pull and push a particle to search for the nearby optimum hence particles can simultaneously locate multiple optima quickly and precisely experiments are carried out to investigate the performance of nn fpso in comparison with a number of state of the art pso algorithms for locating multiple optima over a series of multimodal benchmark test functions the experimental results indicate that the proposed nn fpso algorithm can efficiently locate multiple optima in multimodal fitness landscapes

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

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

optifel a convergent heterogeneous particle swarm optimization algorithm for takagi sugeno fuzzy modeling data driven design of accurate and reliable takagi sugeno t s fuzzy systems has attracted a lot of attention where the model structures and parameters are important and often solved in an optimization framework the particle swarm optimization pso algorithm is widely applied in the field however the classical pso suffers from premature convergence and it is trapped easily into local optima which will significantly affect the model accuracy to overcome these drawbacks we have developed a new t s fuzzy system parameters searching strategy called optifel with a heterogeneous multiswarm pso mspso to enhance the searching performance mspso groups the whole population into multiple cooperative subswarms which perform different search behaviors for the potential solutions we have found that the multiple subswarms strategy proposed in this paper is greatly helpful for finding the optimal parameters suitable for the subspaces of the t s fuzzy model our theoretical proof has also demonstrated that the cooperation among the subswarms can maintain a balance between exploration and exploitation to ensure the particles converge to stable points experimental results show that mspso performs significantly better than traditional pso algorithms on six benchmark functions with the improved mspso optifel can generate a good fuzzy system model with high accuracy and strong generalization ability

the vibration and stability of a friction guided translating string abstract eyelets capstans and cylindrical surfaces are often used in thread fiber and paper handling machinery to guide the axially moving element in addition to providing positional control these guides introduce dry friction forces that alter the vibration and stability characteristics of the system this paper examines the lateral response of a string that slides through an elastically supported dry friction guide exact expressions are derived for the linear response under free and forced conditions solutions for the eigenvalue spectrum exhibit unusual features including multiple divergence instabilities regions of flutter instability and regions of curve veering associated with mode localization a second order perturbation solution is derived to examine the behavior of the eigenvalue spectrum in regions of flutter instability and curve veering the analysis highlights the common features of these two phenomena and suggests ways to minimize vibration by adjusting various design variables the analysis also demonstrates that the eigenvalue loci in regions of flutter instability and curve veering are naturally described by a local hyperbolic approximation

singular free boundary problems and local bifurcation theory a constructive method applicable to the solution of a wide class of free boundary problems is presented a solution dependent transformation technique is introduced by considering a singular limit of the transformation a related problem to which local bifurcation theory may be applied is derived by inverting the near singular mapping between the two problems an expression for solutions of the original problem is obtained the method is illustrated by the study of a singularly perturbed elliptic equation approximate solutions are constructed and the validity of the approximations established by means of the contraction mapping theorem

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

the application of runge kutta schemes to singular initial value problems a theory for explicit runge kutta schemes applied to the initial value problem for a first order system of differential equations with a singularity of the first kind is developed it is shown that in general the order of convergence is at most two but that the usual order up to a logarithmic term can be obtained for level three and four schemes applied to specific problems 1 introduction in this paper we examine the application of explicit runge kutta schemes to the numerical solution of the problem

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

on moving continua with contacts and sliding friction modeling general properties and examples abstract many technical applications feature contacts between moving continua where the contact zone is more or less spatially fixed this contribution describes the modeling of such systems by means of weak formulations derived from hamilton s principle in a material as well as a spatial formulation furthermore linearizations about a stationary solution are carried out the arising differential operators are stated and discussed with respect to symmetry particular attention is paid to the structure and physical interpretation of the contributions arising from the contacts as well as those due to the transport motion the article closes with several examples

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

a defect correction method for unsteady conduction convection problems ii time discretization in this paper a fully discrete defect correction mixed finite element method mfem for solving the non stationary conduction convection problems in two dimension which is leaded by combining the back euler time discretization with the two step defect correction in space is presented in this method we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct these solutions on the same grid using a linearized defect correction technique the stability and the error analysis are derived the theory analysis shows that our method is stable and has a good convergence property some numerical results are also given which show that this method is highly efficient for the unsteady conduction convection problems

modeling nonlinear dynamic biological systems with human readable fuzzy rules optimized by convergent heterogeneous particle swarm abstract it is an important issue to model the dynamic biological networks from their time course response datasets which is critical to understand the system behaviors this task includes two sub tasks network structure identification and associated parameters estimation in most existing methods the two sub tasks are dealt with step by step which may result in inconsistence between them and hence inaccuracy of the final model another challenge is how to transparently understand the derived model which cannot be achieved by the traditional black box methods a human readable fuzzy rule based model denoted as mopath is developed for the identification of both structure topology and associated parameters simultaneously of a biological network within an optimization framework mopath encodes the fuzzy rules into particles of heterogeneous particle swarm optimization chpso algorithm to generate the optimal model theoretically we demonstrate that the cooperation in chpso can maintain a balance between exploration and exploitation to guarantee the particles converge to stable points which is greatly helpful for finding the optimal model consisting of both the network topology and parameters we demonstrate mopath on two dynamic biological networks and successfully generate a few human readable rules that can well represent the network with high accuracy and good robustness

travelling load response of an axially moving string abstract the classical moving load problem in which a mass traverses an elastic structure is extended to systems in which the guideway also has prescribed axial motion a monocable ropeway such as a tramway or ski lift is an example of such a traveling structure traveling load system and it is modeled herein as an axially moving string that transports an attached discrete mass between two supports the green s function methods for the two constituent systems the particle and the uniform traveling string are combined to derive a volterra integral equation with delay that governs the interaction force in the coupled system the calculated response of the traveling string particle system to arbitrary initial conditions and external excitation is compared to that predicted by the derived asymptotic solution for vanishing discrete mass repeated scattering by the particle of transverse waves in the string dominates the motion transient vibration as the particle is transported between the supports is maximized at a transport speed that can be substantially lower than the critical speed of divergence instability for the uniform traveling string agreement between responses measured in the laboratory and those predicted by the traveling structure traveling load theory supports the analysis

a novel approach to the numerical solution of boundary value problems on infinite intervals the classical numerical treatment of two point boundary value problems on infinite intervals is based on the introduction of a truncated boundary instead of infinity where appropriate boundary conditions are imposed then the truncated boundary allowing for a satisfactory accuracy is computed by trial motivated by several problems of interest in boundary layer theory here we consider boundary value problems on infinite intervals governed by a third order ordinary differential equation we highlight a novel approach to define the truncated boundary the main result is the convergence of the solution of our formulation to the solution of the original problem as a suitable parameter goes to zero in the proposed formulation the truncated boundary is an unknown free boundary and has to be determined as part of the solution for the numerical solution of the free boundary formulation a noniterative and an iterative transformation method are introduced furthermore we characterize the class of free boundary value problems that can be solved noniteratively a nonlinear flow problem involving two physical parameters and belonging to the characterized class of problems is then solved moreover the falkner skan equation with relevant boundary conditions is considered and representative results obtained by the iterative transformation method are listed for the homann flow all the obtained numerical results clearly indicate the effectiveness of our approach finally we discuss the possible extensions of the proposed approach and for the question of a priori error analysis

lie group theory and analytical solutions for the axially accelerating string problem abstract transverse vibrations of a string moving with time dependent velocity v t have been investigated analytical solutions of the problem are found using the systematic approach of lie group theory group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations from the symmetries of the partial differential equation the method for deriving exact solutions for the arbitrary velocity case is shown special cases of interest such as constant velocity constant acceleration harmonically varying velocity and exponentially decaying velocity are investigated in detail finally for a simply supported strip approximate solutions are presented for the exponentially decaying and harmonically varying cases

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

on convergence of the multi objective particle swarm optimizers several variants of the particle swarm optimization pso algorithm have been proposed in recent past to tackle the multi objective optimization mo problems based on the concept of pareto optimality although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of pso as a single objective optimizer till date to the best of our knowledge no such analysis exists for the multi objective pso mopso algorithms this paper presents a first simple analysis of the general pareto based mopso and finds conditions on its most important control parameters the inertia factor and acceleration coefficients that govern the convergence behavior of the algorithm to the optimal pareto front in the objective function space computer simulations over benchmark mo problems have also been provided to substantiate the theoretical derivations

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

a difference method for a singular boundary value problem of second order the standard three point discretization applied to the numerical solution of linear boundary value problems for second order systems with a singularity at the origin is investigated a number of numerical examples illustrating the theoretical results are presented

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

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

iterated defect correction for the solution of singular initial value problems we investigate the convergence properties of the iterated defect correction idec method based on the implicit euler rule for the solution of singular initial value problems with a singularity of the first kind we show that the method retains its classical order of convergence which means that the sequence of approximations obtained during the iteration shows gradually growing order of convergence limited by the smoothness of the data and technical details of the procedure

propagation phenomena in a bistable reaction diffusion system consideration is given to a system of reaction diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical biochemical systems these equations are of the fitzhugh nagumo type and contain three parameters for certain ranges of the parameters the system exhibits two stable singular points a singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves a complete rigorous description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity numerical results of solutions to these equations are also presented these calculations illustrate how waves are generated from initial data how they interact during collisions and how they are influenced by local disturbances and boundary conditions in one example a righltward moving

collocation for singular boundary value problems of second order the collocation methods for solving linear boundary value problems with a singularity of the first kind are investigated the stability and convergence results are established particular attention is paid to the superconvergence properties of the methods which are different as in the classical case when the singularity is not present the results are extended to the nonlinear case and illustrated by numerical examples

transient vibration of gyroscopic systems with unsteady superposed motion abstract the equation of motion for a gyroscopic system with unsteady superposed motion is derived for the prototypical problem in which motion of an oscillating particle is measured relative to a non inertial frame the resulting coefficient matrices are time dependent and skew symmetric acceleration terms are present both as coriolis acceleration and as a component of net stiffness such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems including flexible media that translate with time dependent speed following the asymptotic approach of krylov bogoliubov and mitropolsky a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the system s natural periods of oscillation first order approximations for the modal amplitude and phase are obtained in closed form the method is illustrated through two examples of technical interest a two degree of freedom model of a rotating shaft and a distributed parameter model of a moving tape or web

spline finite difference methods for singular two point boundary value problems in this paper we discuss the construction of a spline function for a class of singular two point boundary value problemx x u f x u u 0 a u 1 b 0 1 or 1 2 the boundary conditions may also be of the formu 0 0 u 1 b three point finite difference methods using the above splines are obtained for the solution of the boundary value problem these methods are of second order and are illustrated by four numerical examples

optimization of zero pole interlacing for indirect discrete approximations of noninteger order operators to realize the basic units of fractional order controllers it is necessary to approximate irrational differintegrators many methods deal with analog approximation but not many results exist for discrete approximation in this case approximations are most times poor in some frequency range or the quality of the approximation is good in a narrow frequency interval this paper proposes an indirect discretization method that takes advantage from the particle swarm optimization pso to approximate fractional order operators the method employs an heuristic procedure to optimize the interlacing of zero pole pairs on the real axis then a discretization rule is applied to obtain the discrete approximation simulation results show that the frequency response obtained by pso improves the approximation offered by other efficient and recent indirect discretization techniques

stability of the travelling wave solution of the fitzhugh nagumo system on demontre la stabilite relative au systeme complet d equations aux derivees partielles de ces ondes de propagation

asymptotically correct error estimation for collocation methods applied to singular boundary value problems we discuss an a posteriori error estimate for collocation methods applied to boundary value problems in ordinary differential equations with a singularity of the first kind as an extension of previous results we show the asymptotical correctness of our error estimate for the most general class of singular problems where the coefficient matrix is allowed to have eigenvalues with positive real parts this requires a new representation of the global error for the numerical solution obtained by piecewise polynomial collocation when applied to our problem class

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

analytical and numerical treatment of a singular initial value problem in avalanche modeling we discuss a leading edge model used in the computation of the run out length of dry flowing avalanches the model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics existence uniqueness and smoothness properties of the analytical solution are shown we also prove the existence of a unique root of the solution moreover we present a fortran 90 code for the numerical computation of the run out length the code is based on a solver for singular initial value problems which is an implementation of the acceleration technique known as iterated defect correction based on the implicit euler method

on the numerical solution of singular boundary value problems of second order by a difference method the standard three point discretization applied to the numerical solution of nonlinear boundary value problems for second order systems with a singularity of the first kind is investigated the results are extended to the boundary value problems arising in practical problems from mechanics and chemistry a number of numerical examples illustrating the theoretical results is presented

on a singular boundary value problem arising in the theory of shallow membrane caps abstract we investigate the following singular boundary value problem which originates from the theory of shallow membrane caps t 3 u t t 3 1 8 u 2 t a 0 u t b 0 t 2 4 0 lim t 0 t 3 u t 0 u 1 0 where a 0 b 0 and are given constants we show the existence of a positive solution to the above problem by means of a generalized lower and upper functions method involving limiting processes we illustrate the theory by numerical experiments in which we used the new version of the matlab code sbvp based on polynomial collocation to approximate the solution of the membrane problem

optimal solution of a class of non autonomous initial value problems with unknown singularities in this paper we are interested in a rigorous analysis of the solution of a class of initial value problems with singularities we consider scalar non autonomous ivps with separated variables and one unknown singularity in each variable which leads to four unknown events in the two dimensional space many algorithms proposed in the literature for singular ivps are practically oriented they do not avoid heuristic arguments and are often checked for efficiency by numerical experiments we design an adaptive algorithm with no heuristic steps for solving the considered problems and provide rigorous bounds on the error we show that in spite of the presence of singularities the algorithm preserves the optimal error known for the regular case lower bounds on the error of any algorithm in the case of a larger number of singularities are also discussed

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

particle swarm optimization based on intermediate disturbance strategy algorithm and its application in multi threshold image segmentation abstract particle swarm optimization pso algorithm simulates social behavior among individuals or particles flying through multidimensional search space for enhancing the local search ability of pso and guiding the search a region that had most number of the particles was defined and analyzed in detail inspired by the ecological behavior we presented a pso algorithm with intermediate disturbance searching strategy idpso which enhances the global search ability of particles and increases their convergence rates the experimental results on comparing the idpso to ten known pso variants on 16 benchmark problems demonstrated the effectiveness of the proposed algorithm furthermore we applied the idpso algorithm to multilevel image segmentation problem for shortening the computational time experimental results of the new algorithm on a variety of images showed that it can effectively segment an image faster

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

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

on the numerical solution of a class of singular two point boundary value problems abstract mono implicit runge kutta mirk formulae used in a deferred correction framework have proved to be a very effective way of solving first order systems of nonlinear two point boundary value problems we examine this general approach in detail and question whether mirk formulae are the most efficient class of runge kutta methods to use we also consider the extension of this deferred correction approach to deal with problems having a certain type of singularity at the end of the range of integration we consider the questions whether it is possible to derive mirk formulae which are applicable to such problems and whether it is in general possible to solve such problems automatically we will answer the first question in the affirmative however we will show that despite claims to the contrary appearing in the literature the answer to the second question is no