nontrivial periodic solutions for the asymptotically linear hamiltonian systems with resonance at infinity abstract in this paper we are concerned with the existence of nontrivial periodic solutions of an asymptotically linear hamiltonian systems when a kind of resonance condition is satisfied we prove several new existence results via the morse theory the garlerkin methods and the moslov index theory

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

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

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

periodic solutions of delay differential systems via hamiltonian systems abstract with a new definition of the j m index theory developed in liu 2006 we give another application of this index theory in delay differential systems via hamiltonian systems where we do not need the potential function to be c 2 continuous

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

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

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 poincare bendixson theorem for monotone cyclic feedback systems with delay abstract we consider cyclic nearest neighbor systems of differential delay equations in which the coupling between neighbors possesses a monotonicity property using a discrete integer valued lyapunov function we prove that the poincare bendixson theorem holds for such systems we also obtain results on piecewise monotonicity and stability of periodic solutions of such systems

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

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

automatic construction of feedforward recurrent fuzzy systems by clustering aided simplex particle swarm optimization this paper proposes a new approach for automating the structure and parameter learning of fuzzy systems by clustering aided simplex particle swarm optimization called cspso unlike most evolutionary fuzzy systems where the structure of the fuzzy system is assigned in advance an on line fuzzy clustering approach is proposed for system structure learning this structure learning not only helps determine the number of rules automatically but also avoids the generation of highly similar fuzzy sets on each input variable in addition it improves subsequent parameter learning performance by assigning suitable initial locations of the fuzzy sets on each input variable once a new rule is generated the corresponding parameters are further tuned by the hybrid of the simplex method and particle swarm optimization pso in cspso each fuzzy system corresponds to a particle in pso and the idea of the simplex method is incorporated to improve pso searching performance to verify the performance of cspso two simulations on feedforward fuzzy systems design are performed in addition design of a recurrent fuzzy controller for a practical experiment on water bath temperature control is performed comparisons with other design approaches are also made in these examples

nontrivial periodic solutions for delay differential systems via morse theory abstract the existence of the nontrivial periodic solutions to the system of delay differential equations 1 1 x t f x t is investigated where x r n f c r n r n we prove several new existence results via morse theory and the galerkin methods

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

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

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

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

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

robust static output feedback controller synthesis using kharitonov s theorem and evolutionary algorithms this paper presents a simple but effective tuning strategy for robust static output feedback sof controllers with minimal quadratic cost in the context of multiple parametric uncertainties finding this type of controller is known to be computationally intractable using conventional techniques this is mainly due to the non convexity of the resulting control problem which has a fixed structure to solve this kind of control problem easily and directly without using any complicated mathematical manipulations we utilize kharitonov s theorem and an evolutionary algorithm ea for the resolution of the underlying constrained optimization problem using kharitonov s theorem a family of bounded robustly stable static output feedback controllers can be defined and ea is used to select the controller that ensures a minimal quadratic cost within this family the resulting tuning strategy is applicable to both stable and unstable systems without any limitations on the order of the process to be controlled a numerical study was conducted to demonstrate the validity of the proposed tuning procedure

applications of a zp index theory to periodic solutions for a class of functional differential equations abstract by means of a new geometrical index with z p group actions multiplicity results for a certain class of nonautonomous time periodic functional differential systems are obtained

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

multiplicity results for periodic solutions to delay differential equations via critical point theory abstract by the critical point theory we study the existence and multiplicity of periodic solutions to the following system of delay differential equations x t f x t r where x r n f c r n r n and r 0 is a given constant a sufficient condition on the existence and multiplicity of periodic solutions for eq is obtained to the authors knowledge this is the first time the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly

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

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

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

granular representation and granular computing with fuzzy sets in this study we introduce a concept of a granular representation of numeric membership functions of fuzzy sets which offers a synthetic and qualitative view at fuzzy sets and their ensuing processing the notion of consistency of the granular representation is formed which helps regard the problem as a certain optimization task more specifically the consistency is referred to a certain operation f which gives rise to the concept of f consistency likewise introduced is a concept of granular consistency with regard to a collection of several operations given the essential role played by logic operators in computing with fuzzy sets detailed investigations include and and or consistency as well as and or consistency of granular representations of membership functions with the logic operators implemented in the form of various t norms and t conorms the optimization framework supporting the realization of the f consistent optimization process is provided through particle swarm optimization further conceptual and representation issues impacted processing fuzzy sets are discussed as well

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

bifurcations of periodic solutions of delay differential equations abstract in this paper we develop kaplan yorke s method and consider the existence of periodic solutions for some delay differential equations we especially study hopf and saddle node bifurcations of periodic solutions with certain periods for these equations with parameters and give conditions under which the bifurcations occur we also give application examples and find that hopf and saddle node bifurcations often occur infinitely many times

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

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

distributed consensus algorithms in sensor networks quantized data and random link failures the paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures to achieve consensus dither small noise is added to the sensor states before quantization when the quantizer range is unbounded countable number of quantizer levels stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable we show that the mean squared error mse can be made arbitrarily small by tuning the link weight sequence at a cost of the convergence rate of the algorithm to study dithered consensus with random links when the range of the quantizer is bounded we establish uniform boundedness of the sample paths of the unbounded quantizer this requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer this is accomplished by splitting the state vector of the quantizer in two components one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace the proofs use maximal inequalities for submartingale and supermartingale sequences from these we derive probability bounds on the excursions of the two subsequences from which probability bounds on the excursions of the quantizer state vector follow the paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels the size of the quantization steps the desired probability of saturation and the desired level of accuracy away from consensus finally the paper illustrates the quantizer design with a numerical study

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

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

circulant matrices and differential delay equations on etudie les solutions periodiques non triviales de familles parametrisees d equations differentielles a retard

characteristic multipliers and stability of symmetric periodic solutions of x t g x t 1 on etudie l equation differentielle scalaire a retard x t g x t 1 a retroaction negative on suppose que la fonction non lineaire g est impaire et monotone on demontre que des solutions periodiques x t de type legerement oscillant satisfaisant la condition de symetrie x t x t 2 t r sont non degenerees et ont toutes des multiplicateurs de floquet non triviaux dans le cercle unite

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

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