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

a primal dual active set algorithm for three dimensional contact problems with coulomb friction in this paper efficient algorithms for contact problems with tresca and coulomb friction in three dimensions are presented and analyzed the numerical approximation is based on mortar methods for nonconforming meshes with dual lagrange multipliers using a nonsmooth complementarity function for the three dimensional friction conditions a primal dual active set algorithm is derived the method determines active contact and friction nodes and at the same time resolves the additional nonlinearity originating from sliding nodes no regularization and no penalization are applied and superlinear convergence can be observed locally in combination with a multigrid method it defines a robust and fast strategy for contact problems with tresca or coulomb friction the efficiency and flexibility of the method is illustrated by several numerical examples

a hybrid particle swarm optimization with a feasibility based rule for constrained optimization during the past decade hybrid algorithms combining evolutionary computation and constraint handling techniques have shown to be effective to solve constrained optimization problems for constrained optimization the penalty function method has been regarded as one of the most popular constraint handling technique so far whereas its drawback lies in the determination of suitable penalty factors which greatly weakens the efficiency of the method as a novel population based algorithm particle swarm optimization pso has gained wide applications in a variety of fields especially for unconstrained optimization problems in this paper a hybrid pso hpso with a feasibility based rule is proposed to solve constrained optimization problems in contrast to the penalty function method the rule requires no additional parameters and can guide the swarm to the feasible region quickly in addition to avoid the premature convergence simulated annealing sa is applied to the best solution of the swarm to help the algorithm escape from local optima simulation and comparisons based on several well studied benchmarks demonstrate the effectiveness efficiency and robustness of the proposed hpso moreover the effects of several crucial parameters on the performance of the hpso are studied as well

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

switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in odes the paper provides full algorithmic details on switching to the continuation of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium bifurcation points in n dimensional odes we discuss the implementation and the performance of the algorithm in several examples including an extended lorenz 84 model and a laser system

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

adaptive memetic differential evolution with global and local neighborhood based mutation operators differential evolution de is one of the most popular optimization methods for real valued problems and a large number of its variants have been proposed so far however bringing together different ideas that already led to successful de versions is rare in the literature in the present paper a novel de algorithm is proposed in which three among the most efficient concepts already applied separately within de framework are gathered together namely 1 the adaptation of algorithm control parameters and probabilities of using different mutation strategies 2 the use of nelder mead algorithm as a local search method hybridized with de and 3 the splitting mutation into global and local models when local mutation model is based on the concept of neighborhood of individuals organized on a ring topology the performance of the novel algorithm called adaptive memetic de with global and local neighborhood based mutation operators is compared with 13 different de variants on a set of 25 popular problems which include rotated shifted and hybrid composition functions it is found that although none de algorithm outperforms all the others for the majority of problems on average the proposed approach perform better than all 13 de algorithms selected for comparison the proposed algorithm is another heuristic approach developed to solve optimization problems the question may arise whether proposing novel methods is useful as no free lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal in the last section of the paper the limitations and implications of no free lunch theorems are discussed based on rich but unfortunately frequently neglected literature a very simple continuous and differentiable minimization problem is proposed for which it is empirically verified that each among considered 14 de algorithms perform poorer than random sampling it is also empirically shown that when all considered de algorithms search for the maximum of the proposed problem they found lower minimum than de algorithms searching for the minimum such result is not unexpected according to no free lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods

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

a large deformation frictional contact formulation using nurbs based isogeometric analysis this paper focuses on the application of nurbs based isogeometric analysis to coulomb frictional contact problems between deformable bodies in the context of large deformations a mortar based approach is presented to treat the contact constraints whereby the discretization of the continuum is performed with arbitrary order nurbs as well as c0 continuous lagrange polynomial elements for comparison purposes the numerical examples show that the proposed contact formulation in conjunction with the nurbs discretization delivers accurate and robust predictions results of lower quality are obtained from the lagrange discretization as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface copyright 2011 john wiley sons ltd

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

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

nonlinear systems design by a novel fuzzy neural system via hybridization of electromagnetism like mechanism and particle swarm optimisation algorithms in this paper a hybrid of algorithms for electromagnetism like mechanisms em and particle swarm optimisation pso called hempso is proposed for use in designing a functional link based petri recurrent fuzzy neural system flprfns for nonlinear system control the flprfns has a functional link based orthogonal basis function fuzzy consequent and a petri layer to eliminate the redundant fuzzy rule for each input calculation in addition the flprfns is trained by the proposed hybrid algorithm the main innovation is that the random neighbourhood local search is replaced by a pso algorithm with an instant update strategy for particle information each particle updates its information instantaneously and in this way receives the best current information thus hempso combines the advantages of multiple agent based searching global optimisation and rapid convergence simulation results confirm that hempso can be used to perform global optimisation and offers the advantage of rapid convergence they also indicate that the flprfns exhibits high accuracy

discretizing dynamical systems with generalized hopf bifurcations we consider the discretizations of parameter dependent continuous time dynamical systems we show that the general one step methods shift a generalized hopf bifurcation and turn it into a generalized neimark sacker point we analyze the effect of discretization methods on the emanating hopf curve in particular we obtain estimates for the eigenvalues of the discretized system along this curve a detailed analysis of the discretized first lyapunov coefficient is also given the results are illustrated by a numerical example dynamical consequences are discussed

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

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

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

local numerical analysis of hopf bifurcation this paper contributes to a local numerical analysis of hopf bifurcation in the sense of a bordered systems approach however the method proposed enables us to decide about stability exchange betw

auto selection mechanism of differential evolution algorithm variants and its application abstract each type of problems such as unimodal multimodal linear non linear convex non convex and symmetrical asymmetrical has its own characteristics although various differential evolution de variants have been proposed several studies indicate that a de variant may only exhibit high solution efficiency in solving a specific type of problems but may perform poorly in others therefore an important decision is made to automatically select a suitable de variant among several chosen algorithms for solving a particular type of problems during the evolutionary process to achieve this objective an auto selection mechanism asm is introduced in this study in the asm rankings attained using friedman s test are adopted to assess the performances of de variants a learning strategy is employed to update the choice probabilities of de variants and an additional selection probability is used to alleviate the greedy selection issue three sets of benchmark test functions proposed in bbob2012 ieee cec2005 and ieee cec2014 are used to evaluate the effectiveness of the asm the performance of the proposed algorithm is also compared with that of nine state of the art de variants and four non de algorithms statistical analysis results demonstrate that the asm is an efficient and effective method that can take full advantages of multiple algorithms furthermore the asm is utilized to estimate the parameters of a heavy oil thermal cracking model experimental results indicate that the proposed algorithm outperforms the other compared algorithms in this case

an algorithm for melnikov functions and application to a chaotic rotor in this work we study a dynamical system with a complicated nonlinearity which describes oscillation of a turbine rotor and give an algorithm to compute melnikov functions for analysis of its chaotic behavior we first derive the rotor model whose nonlinear term brings difficulties to investigating the distribution and qualitative properties of its equilibria this nonlinear model provides a typical example of a system for which the homoclinic and heteroclinic orbits cannot be analytically determined in order to apply melnikov s method to make clear the underlying conditions for chaotic motion we present a generic algorithm that provides a systematic procedure to compute melnikov functions numerically substantial analysis is done so that the numerical approximation precision at each phase of the computation can be guaranteed using the algorithm developed in this paper it is straightforward to obtain a sufficient condition for chaotic motion under damping and periodic external excitation whenever the rotor parameters are given

capso centripetal accelerated particle swarm optimization meta heuristic search algorithms are developed to solve optimization problems such algorithms are appropriate for global searches because of their global exploration and local exploitation abilities swarm intelligence si algorithms comprise a branch of meta heuristic algorithms that imitate the behavior of insects birds fishes and other natural phenomena to find solutions for complex optimization problems in this study an improved particle swarm optimization pso scheme combined with newton s laws of motion the centripetal accelerated particle swarm optimization capso scheme is introduced capso accelerates the learning and convergence of optimization problems in addition the binary mode of the proposed algorithm binary centripetal accelerated particle swarm optimization bcapso is introduced for binary search spaces these algorithms are evaluated using nonlinear benchmark functions and the results are compared with the gravitational search algorithm gsa and pso in both the real and the binary search spaces moreover the performance of capso in solving the functions is compared with some well known pso algorithms in the literature the experimental results showed that the proposed methods enhance the performance of pso in terms of convergence speed solution accuracy and global optimality

contact treatment in isogeometric analysis with nurbs abstract we study nurbs based isogeometric analysis of contact problems and compare with standard c 0 continuous lagrange finite elements a knot to surface kts algorithm is developed to treat the contact constraints with nurbs contact surface discretizations qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems quantitative studies based on the hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard kts approach the improved mortar based kts algorithm delivers robust and accurate results for nurbs discretizations based on numerical examples we conclude that nurbs based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over c 0 continuous finite elements

numerical methods for the generalized hopf bifurcation the presence of a generalized hopf gh point hopf point where the first lyapunov coefficient vanishes deeply influences the qualitative behavior of a dynamical system further information on this behavior can be obtained from the second lyapunov coefficient which depends on derivatives of order up to five we describe two computational procedures implemented in the software package content to compute and numerically continue gh points this is applied to a biochemical model and two examples from neurobiology we make some comparisons between the two methods for computing gh points and discuss briefly the merits of three methods for computing curves of hopf points

a mixed formulation of mortar based frictionless contact abstract a class of mortar based frictionless contact formulations is derived based on a classical three field mixed variational framework within a penalty regularization complemented by uzawa augmentations discrete mortar constraints are naturally induced by the variational setting major aspects of earlier mortar approaches are obtained through constrained lumped or unconstrained recovery procedures for the mixed kinematic and kinetic mortar quantities from their projected counterparts two and three dimensional examples at the infinitesimal and finite deformation regimes highlight the local and global quality of the contact interactions

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

multiparametric bifurcation analysis of a basic two stage population model in this paper we investigate long term dynamics of the most basic model for stage structured populations in which the per capita transition from the juvenile into the adult class is density dependent the model is represented by an autonomous system of two nonlinear differential equations with four parameters for a single population we find that the interaction of intra adult competition and intra juvenile competition gives rise to multiple attractors one of which can be oscillatory a detailed numerical study reveals a rich bifurcation structure for this two dimensional system originating from a degenerate bogdanov takens bt bifurcation point when one parameter is kept constant depending on the value of this fixed parameter the corresponding triple critical equilibrium has either an elliptic sector or it is a topological focus which is demonstrated by the numerical normal form analysis it is shown that the canonical unfolding of the codimension three bt point reveals the underlying dynamics of

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

thermo mechanical contact problems on non matching meshes non matching meshes and domain decomposition techniques based on lagrange multipliers provide a flexible and efficient discretization technique for variational inequalities with interface constraints although mortar methods are well analyzed for variational inequalities its application to dynamic thermo mechanical contact problems with friction is still a field of active research in this work we extend the mortar approach for dynamic contact problems with coulomb friction to the thermo mechanical case we focus on the discretization and on algorithmic aspects of dynamic effects such as frictional heating and thermal softening at the contact interface more precisely we generalize the mortar concept of dual lagrange multipliers to non linear robin type interface conditions and apply local static condensation to eliminate the heat flux numerical examples in the two dimensional and the three dimensional setting illustrate the flexibility of the discretization on non matching meshes

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

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

a mixed formulation of mortar based contact with friction abstract a classical three field mixed variational formulation of frictionless contact is extended to the frictional regime the construction of the variational framework with respect to a curvilinear coordinate system naturally induces projected mortar counterparts of tangential kinetic and kinematic quantities while automatically satisfying incremental objectivity of the associated discrete penalty regularized mortar constraints mixed contact variables that contribute to the boundary value problem are then obtained through unconstrained lumped or constrained recovery approaches complemented by uzawa augmentations patch tests and surface locking studies are presented together with local and global quality monitors of the contact interactions in two and three dimensional settings at the infinitesimal and finite deformation regimes

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

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

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

computation of cusp singularities for operator equations and their discretizations we discuss the direct calculation of cusp singularities as solutions of a minimally augmented defining system which is nonsingular under the canonical cusp conditions the underlying operator equation may have any finite fredholm index and bounds on the discretization error are derived for the case of projection methods

a hybrid simplex search and particle swarm optimization for unconstrained optimization this paper proposes the hybrid nm pso algorithm based on the nelder mead nm simplex search method and particle swarm optimization pso for unconstrained optimization nm pso is very easy to implement in practice since it does not require gradient computation the modification of both the nelder mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence the main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy in a suite of 20 test function problems taken from the literature computational results via a comprehensive experimental study preceded by the investigation of parameter selection show that the hybrid nm pso approach outperforms other three relevant search techniques i e the original nm simplex search method the original pso and the guaranteed convergence particle swarm optimization gcpso in terms of solution quality and convergence rate in a later part of the comparative experiment the nm pso algorithm is compared to various most up to date cooperative pso cpso procedures appearing in the literature the comparison report still largely favors the nm pso algorithm in the performance of accuracy robustness and function evaluation as evidenced by the overall assessment based on two kinds of computational experience the new algorithm has demonstrated to be extremely effective and efficient at locating best practice optimal solutions for unconstrained optimization

numerical continuation of bifurcations of limit cycles in matlab rm cl matcont and matcont are matlab continuation packages for the interactive numerical study of a range of parameterized nonlinear dynamical systems in particular odes matcont is an interactive graphical package and rm cl matcont is a commandline version both packages allow us to compute curves of equilibria limit points hopf points limit cycles flip fold and torus bifurcation points of limit cycles we discuss computational details of the continuation of limit cycles and flip fold and torus bifurcations of limit cycles in matcont and rm cl matcont using orthogonal collocation instead of the more commonly used fully extended systems we use minimally extended systems we further describe the use of the matlab sparse matrix routines and the initialization and adaptation of the bordering vectors that are essential in minimally extended systems finally we compare the use of the minimally and the fully extended systems in the matlab environment

numerical computation of nonsimple turning points and cusps a method is developed for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters an augmented system containing the original equation is introduced for which the cusp point is an isolated solution an efficient implementation of newton s method in the finite dimensional case is presented results are given for some chemical engineering problems and this direct method is compared with some other techniques to locate cusp points

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

two dimensional mortar contact methods for large deformation frictional sliding this paper presents a mortar based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding as is widely recognized traditional node to surface contact formulations have several drawbacks in solution of deformable to deformable contact problems including lack of general patch test passage degradation of spatial convergence rates and robustness issues associated with the faceted representation of contacting surfaces the mortar finite element method initially proposed as a technique to join dissimilarly meshed domains has been shown to preserve optimal convergence rates in tied contact problems see discretization methods and iterative solvers based on domain decomposition springer verlag heidelberg 2001 for a recent review and is examined here as an alternative spatial discretization method for large sliding contact in particular a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work in recent years the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics see int j numer meth engng 1993 36 3451 however in the presence of large deformations and finite sliding one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface in this paper such a formulation is presented with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics some novel techniques are proposed to treat the non smoothness in the contact geometry and the searching required to define mortar segments a number of numerical examples illustrate the performance and accuracy of the proposed formulation copyright 2004 john wiley sons ltd

computing hopf bifurcations i this paper addresses the problems of detecting hopf bifurcations in systems of ordinary differential equations and following curves of hopf points in two parameter families of vector fields the established approach to this problem relies upon augmenting the equilibrium condition so that a hopf bifurcation occurs at an isolated regular point of the extended system we propose two new methods of this type based on classical algebraic results regarding the roots of polynomial equations and properties of kronecker products for matrices in addition to their utility as augmented systems for use with standard newton type continuation methods they are also particularly well adapted for solution by computer algebra techniques for vector fields of small or moderate dimension

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

a dual lagrange method for contact problems with regularized frictional contact conditions modelling micro slip abstract this paper presents an algorithm for solving quasi static non linear elasticity contact problems with friction in the context of rough surfaces here we want to model the transition from sticking to slipping also called micro slip in a physically correct way in order to reproduce measured frictional damping the popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size the algorithm is deduced from a perturbed lagrange formulation and combined with a serial parallel iwan model this leads to a regularized saddle point problem for which a non linear complementary function and thus a semi smooth newton method can be derived numerical examples demonstrate the applicability to industrial problems and show good agreement to experimentally obtained results

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

a stable energy conserving approach for frictional contact problems based on quadrature formulas a common approach for the numerical simulation of non linear multi body contact problems is the use of lagrange multipliers to model the contact conditions the stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes by this the spurious algorithmic oscillations in the multiplier do not occur any more which facilitates the application of the primal dual active set strategy to dynamical contact problems the new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost in addition the conservation properties of the underlying algorithm are transferred to the modified mass version different numerical examples for frictional two body contact problems illustrate the improvement in the results for the contact stresses copyright 2007 john wiley sons ltd

stable lagrange multipliers for quadrilateral meshes of curved interfaces in 3d for the discretization of coupled problems by means of mortar finite elements the choice of the discrete lagrange multiplier space is of crucial importance for the performance of the resulting numerical scheme dual lagrange multipliers offer several advantages since they can be locally eliminated in this paper the lowest order dual lagrange multipliers are extended to arbitrary quadrilateral or triangular surface grids in a first step two alternatives are provided for the case of planar interfaces for the approximation of vector fields two more modifications are given for use on curvilinear interfaces a priori results are obtained and several numerical examples are shown

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

differential evolution algorithm with separated groups for multi dimensional optimization problems the classical differential evolution de algorithm one of population based evolutionary computation methods proved to be a successful approach for relatively simple problems but does not perform well for difficult multi dimensional non convex functions a number of significant modifications of de have been proposed in recent years including very few approaches referring to the idea of distributed evolutionary algorithms the present paper presents a new algorithm to improve optimization performance namely de with separated groups de sg which distributes population into small groups defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities the performance of de sg is compared to that of eight algorithms belonging to the class of evolutionary strategies covariance matrix adaptation es particle swarm optimization comprehensive learning pso and efficient population utilization strategy pso differential evolution distributed de with explorative exploitative population families self adaptive de de with global and local neighbours and grouping differential evolution and multi algorithms amalgam the comparison is carried out for a set of 10 30 and 50 dimensional rotated test problems of varying difficulty including 10 and 30 dimensional composition functions from cec2005 although slow for simple functions the proposed de sg algorithm achieves a great success rate for more difficult 30 and 50 dimensional problems

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

vector coevolving particle swarm optimization algorithm in this paper we propose a novel vector coevolving particle swarm optimization algorithm vcpso in vcpso the full dimension of each particle is first randomly partitioned into several sub dimensions then we randomly assign either one of our newly designed scalar operators or learning operators to update the values in each sub dimension the scalar operators are designed to enhance the population diversity and avoid premature convergence in addition the learning operators are designed to enhance the global and local search ability the proposed algorithm is compared with several other classical swarm optimizers on thirty three benchmark functions comprehensive experimental results show that vcpso displays a better or comparable performance compared to the other algorithms in terms of solution accuracy and statistical results

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

estimation of particle swarm distribution algorithms combining the benefits of pso and edas this paper presents a novel framework of the estimation of particle swarm distribution algorithms epsdas the aim is to effectively combine particle swarm optimization pso with the estimation of distribution algorithms edas without losing their unique features this aim is achieved by incorporating the following mechanisms 1 selection is applied to the local best solutions in order to obtain more promising individuals for model building 2 a probabilistic model of the problem is built from the selected solutions and 3 new individuals are generated by a stochastic combination of the eda s model sampling method and the pso s particle moving mechanism to exhibit the utility of the epsda framework an extended compact particle swarm optimization ecpso is developed by combining the strengths of the extended compact genetic algorithm ecga with binary pso bpso along the lines of the suggested framework due to its effective nature of harmonizing the global search of ecga with the local search of bpso ecpso is able to discover the optimal solution in a fast and reliable manner experimental results on artificial to real world problems have adduced grounds for the effectiveness of the proposed approach

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

a primal dual active set strategy for non linear multibody contact problems abstract non conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations for the discretization of a non linear multibody contact problem we use the mortar approach with a dual lagrange multiplier space to handle the non linearity of the contact conditions we apply a primal dual active set strategy to find the actual contact zone the algorithm can be easily generalized to multibody contact problems a suitable basis transformation guarantees the same algebraic structure in the multibody situation as in the one body case using an inexact primal dual active set strategy in combination with a multigrid method yields an efficient iterative solver different numerical examples for one and multibody contact problems illustrate the performance of the method

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

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

a hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization numerous optimization methods have been proposed for the solution of the unconstrained optimization problems such as mathematical programming methods stochastic global optimization approaches and metaheuristics in this paper a metaheuristic algorithm called modified shuffled complex evolution msce is proposed where an adaptation of the downhill simplex search strategy combined with the differential evolution method is proposed the efficiency of the new method is analyzed in terms of the mean performance and computational time in comparison with the genetic algorithm using floating point representation gaf and the classical shuffled complex evolution sce ua algorithm using six benchmark optimization functions simulation results and the comparisons with sce ua and gaf indicate that the msce improves the search performance on the five benchmark functions of six tested functions

a dual lagrange method for contact problems with regularized contact conditions this paper presents an algorithm for solving quasi static non linear elasticity contact problems without friction in the context of rough surfaces here we want to model the transition from soft to hard contact in case of rough surfaces on the micro scale the popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size the algorithm is deduced from a perturbed lagrange formulation and combined with mass lumping techniques to exploit the full advantages of the duality pairing this leads to a regularized saddle point problem for which a nonlinear complementary function and thus a semi smooth newton method can be derived numerical examples demonstrate the applicability to industrial problems and show a good agreement to experimentally obtained results copyright 2014 john wiley sons ltd

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

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

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

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

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

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

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

defining functions for multiple hopf bifurcations let a u alpha f u u alpha u in r n alpha in r k be a family of real n times n matrices arising as the jacobian matrices of equilibrium solutions to the dynamical system stackrel u f u alpha an equilibrium point is called a hopf point if a has a conjugate pair of pure imaginary eigenvalues pm i omega omega 0 it is called a double hopf point if there are two such pairs pm i omega 1 pm i omega 2 and a 1 1 resonant double hopf point if in addition omega 1 omega 2 defining functions are obtained for the numerical detection computation and continuation of hopf double hopf and 1 1 resonant double hopf points they are based on a combination of matrix biproduct and bordered matrix methods example computations are done in a fairly realistic and complicated neural model problem with n 13 and k 29 however to make the methods applicable to large scale problems e g discretized boundary value problems we reduce the state space to a subspace that essentially contains the generalized eigenspaces of the eigenvalues with largest real part

a new simple fast and efficient algorithm for global optimization over continuous search space problems we propose a new stochastic global optimization method for continuous search space we chose ten benchmark functions to evaluate the ability of the proposed algorithm the results are compared with two other methods which are pso and de the proposed method obtains proper and fast solution and escapes from local optima being robust fast and needing less memory are the main features of the method optimization of non linear and non differentiable problems has been considered as an important issue for mathematicians and engineers a new stochastic global optimization method for non linear and non differentiable problems is proposed and extensively explained in this article it is a swarm based method which uses spherical boundaries in a vector search space to explore for the optimal solution having a few numbers of parameter to be adjusted being robust and fast needing small memory storage size and capability of escaping from local optima are the main features of this new algorithm to analyze and evaluate the capability of this novel method ten benchmark functions are chosen and the results are compared with two existing optimization algorithms which are differential evolution and particle swarm optimization comparisons are made based on the consistency in obtaining optimal solutions computation time and convergence profile results show the capability of the proposed method in finding a proper solution in a very short time and also escaping from local optima of the solution space

thermoelastic frictional contact problems modelling finite element approximation and numerical realization abstract in this paper frictional contact including frictional heat generation and heat transfer across the contact interface is studied a model for the behaviour of the contact interface is proposed and combined with the conventional equations of linear thermoelasticity for the bulk material of the contacting bodies a finite element discretization in space and a finite difference discretization in time are introduced and an iterative algorithm is proposed to deal with the coupled thermal mechanical nature of the problem finally several numerical examples are given

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

nonlinear mappings in problem solving and their pso based development the study is devoted to a concept and algorithmic realization of nonlinear mappings aimed at increasing the effectiveness of the problem solving method given the original input space x and a certain problem solving method m designed is a nonlinear mapping f so that the method operating in the transformed space m f x becomes more efficient the nonlinear mappings realize a transformation of x through contractions and expansions of selected regions of the original space in particular we show how a piecewise linear mapping is optimized by using particle swarm optimization pso and a suitable fitness function quantifying the objective of the problem several families of problems are investigated and illustrated through illustrative experimental results

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

numerical normalization techniques for all codim 2 bifurcations of equilibria in ode s explicit computational formulas for the coefficients of the normal forms for all codim 2 equilibrium bifurcations of equilibria in autonomous odes are derived they include second order coefficients for the bogdanov takens bifurcation third order coefficients for the cusp and fold hopf bifurcations and coefficients of the fifth order terms for the generalized hopf bautin and double hopf bifurcations the formulas are independent on the dimension of the phase space and involve only critical eigenvectors of the jacobian matrix of the right hand sides and its transpose as well as multilinear functions from the taylor expansion of the right hand sides at the critical equilibrium the normal form coefficients for the fold hopf bifurcation in the new lorenz model are computed using the derived formulas proving the existence of a nontrivial invariant set in the system

particle swarm optimization with fuss and rws for high dimensional functions abstract high dimensional optimization problems play an important role in many complex engineering area though many variants of particle swarm optimization pso have been proposed however most of them are tested and compared with dimension no larger than 300 since numerical problem with high dimension maintains a large linkage and correlation among different variables and the number of local optimum increases significantly with different dimensions this paper proposes a novel variant of pso aiming to provide a balance between exploration and exploitation capability firstly the fitness uniform selection strategy fuss with a weak selection pressure is incorporated into the standard pso secondly random walk strategy rws with four different form is designed to further enhance the exploration capability to escaping from a local optimum finally the proposed pso combined with fuss and rws is applied to seven famous high dimensional benchmark with the dimension up to 3000 simulation results demonstrate good performance of the new method in solving high dimensional multi modal problems when compared with two other variants of the pso

a molecular solution to the hitting set problem in dna based supercomputing assume that there exists a collection c of subsets of a finite set s and a positive integer k s and we need to know whether there is a subset s s with s

particle swarm optimization hybridization perspectives and experimental illustrations metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods in the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic particle swarm optimization or pso hybridization is a method of combining two or more techniques in a judicious manner such that the resulting algorithm contains the positive features of both or all the algorithms depending on the algorithm s used we made three classifications as i hybridization of pso and genetic algorithms ii hybridization of pso with differential evolution and iii hybridization of pso with other techniques where other techniques include various local and global search methods besides giving the review we also show a comparison of three hybrid pso algorithms hybrid differential evolution particle swarm optimization de pso adaptive mutation particle swarm optimization ampso and hybrid genetic algorithm particle swarm optimization ga pso on a test suite of nine conventional benchmark problems