example based learning particle swarm optimization for continuous optimization particle swarm optimization pso is a heuristic optimization technique based on swarm intelligence that is inspired by the behavior of bird flocking the canonical pso has the disadvantage of premature convergence several improved pso versions do well in keeping the diversity of the particles during the searching process but at the expense of rapid convergence this paper proposes an example based learning pso elpso to overcome these shortcomings by keeping a balance between swarm diversity and convergence speed inspired by a social phenomenon that multiple good examples can guide a crowd towards making progress elpso uses an example set of multiple global best particles to update the positions of the particles in this study the particles of the example set were selected from the best particles and updated by the better particles in the first in first out order in each iteration the particles in the example set are different and are usually of high quality in terms of the target optimization function elpso has better diversity and convergence speed than single gbest and non gbest pso algorithms which is proved by mathematical and numerical results finally computational experiments on benchmark problems show that elpso outperforms all of the tested pso algorithms in terms of both solution quality and convergence time

controller design for synchronization of an array of delayed neural networks using a controllable probabilistic pso in this paper a controllable probabilistic particle swarm optimization cppso algorithm is introduced based on bernoulli stochastic variables and a competitive penalized method the cppso algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller which is used in the synchronization of an array of delayed neural networks dnns the learning strategies occur in a random way governed by bernoulli stochastic variables the expectations of bernoulli stochastic variables are automatically updated by the search environment the proposed method not only keeps the diversity of the swarm but also maintains the rapid convergence of the cppso algorithm according to the competitive penalized mechanism in addition the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value the efficiency of the proposed cppso algorithm is demonstrated by comparing it with some well known pso algorithms on benchmark test functions with and without rotations in the end the proposed cppso algorithm is used to design the controller for the synchronization of an array of continuous time delayed neural networks

a theoretical and empirical study on unbiased boundary extended crossover for real valued representation we present a new crossover operator for real coded genetic algorithms employing a novel methodology to remove the inherent bias of pre existing crossover operators this is done by transforming the topology of the hyper rectangular real space by gluing opposite boundaries and designing a boundary extension method for making the fitness function smooth at the glued boundary we show the advantages of the proposed crossover by comparing its performance with those of existing ones on test functions that are commonly used in the literature and a nonlinear regression on a real world dataset

feature subset selection by gravitational search algorithm optimization a new method for feature subset selection in machine learning fss mgsa feature subset selection by modified gravitational search algorithm is presented fss mgsa is an evolutionary stochastic search algorithm based on the law of gravity and mass interactions and it can be executed when domain knowledge is not available a wrapper approach over naive bayes id3 k nearest neighbor and support vector machine learning algorithms is used to evaluate the goodness of each visited solution the key to the success of the mgsa is to utilize the piecewise linear chaotic map for increasing its diversity of species and to use sequential quadratic programming for accelerating local exploitation promising results are achieved in a variety of tasks where domain knowledge is not available the experimental results show that the proposed method has the ability of selecting the discriminating input features correctly and can achieve high accuracy of classification which is comparable to or better than well known similar classifier systems furthermore the mgsa is tested on ten functions provided by cec 2005 special session and compared with various modified gravitational search algorithm particle swarm optimization and genetic algorithm the obtained results confirm the high performance of the mgsa in solving various problems in optimization

an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

a new fitness estimation strategy for particle swarm optimization particle swarm optimization pso is a global metaheuristic that has been proved to be very powerful for optimizing a wide range of problems however pso requires a large number of fitness evaluations to find acceptable optimal or sub optimal solutions if one single evaluation of the objective function is computationally expensive the computational cost for the whole optimization run will become prohibitive fespso a new fitness estimation strategy is proposed for particle swarm optimization to reduce the number of fitness evaluations thereby reducing the computational cost different from most existing approaches which either construct an approximate model using data or utilize the idea of fitness inheritance fespso estimates the fitness of a particle based on its positional relationship with other particles more precisely once the fitness of a particle is known either estimated or evaluated using the original objective function the fitness of its closest neighboring particle will be estimated by the proposed estimation formula if the fitness of its closest neighboring particle has not been evaluated using the original objective function the minimum of all estimated fitness values on this position will be adopted in case of more than one particle is located at the same position the fitness of only one of them needs to be evaluated or estimated the performance of the proposed algorithm is examined on eight benchmark problems and the experimental results show that the proposed algorithm is easy to implement effective and highly competitive

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

an adaptive parameter tuning of particle swarm optimization algorithm an adaptive parameter tuning of particle swarm optimization based on velocity information apso vi algorithm is proposed in this paper the velocity convergence of particles is first analyzed and the relationship between the velocity of particle and the search failures is pointed out which reveals the reasons why pso has relative poor global searching ability then this algorithm introduces the velocity information which is defined as the average absolute value of velocity of all the particles a new strategy is presented that the inertia weight is dynamically adjusted according to average absolute value of velocity which follows a given nonlinear ideal velocity by feedback control which can avoid the velocity closed to zero at the early stage under the guide of the nonlinear ideal velocity apso vi can maintain appropriate swarm diversity and alleviate the premature convergence validly numerical experiments are conducted to compare the proposed algorithm with different variants of pso on some benchmark functions experimental results show that the proposed algorithm remarkably improves the ability of pso to jump out of the local optima and significantly enhance the convergence speed and precision

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

a new evolutionary search strategy for global optimization of high dimensional problems global optimization of high dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation the weakness of randomization based evolutionary algorithms in searching high dimensional spaces is demonstrated in this paper a new strategy sp uci is developed to treat complexity caused by high dimensionalities this strategy features a slope based searching kernel and a scheme of maintaining the particle population s capability of searching over the full search space examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that sp uci surpasses two popular algorithms particle swarm optimizer pso and differential evolution de on high dimensional problems experimental results also corroborate the argument that in high dimensional optimization only problems with well formative fitness landscapes are solvable and slope based schemes are preferable to randomization based ones

long time behavior of solutions of fisher kpp equation with advection and free boundaries we consider fisher kpp equation with advection ut uxx ux f u for x g t h t where g t and h t are two free boundaries satisfying stefan conditions this equation is used to describe the population dynamics in advective environments we study the influence of the advection coefficient on the long time behavior of the solutions we find two parameters c0 and with c0 0 which play key roles in the dynamics here c0 is the minimal speed of the traveling waves of fisher kpp equation more precisely by studying a family of the initial data 0 where is some compactly supported positive function we show that 1 in case 0 c0 there exists 0 such that spreading happens when i e u t 1 locally uniformly in r and vanishing happens when 0 i e g t h t remains bounded and u t 0 uniformly in g t h t 2 in case c0 there exists 0 such that virtual spreading happens when i e u t 0 locally uniformly in g t and u t ct 1 locally uniformly in r for some c c0 vanishing happens when 0 and in the transition case u t o t v c0 t uniformly the latter is a traveling wave with a big head near the free boundary x c0 t and with an infinite long tail on the left 3 in case c0 there exists 0 such that virtual spreading happens when and u t 0 uniformly in g t h t when 0 4 in case vanishing happens for any solution

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

feature selection using a piecewise linear network we present an efficient feature selection algorithm for the general regression problem which utilizes a piecewise linear orthonormal least squares ols procedure the algorithm 1 determines an appropriate piecewise linear network pln model for the given data set 2 applies the ols procedure to the pln model and 3 searches for useful feature subsets using a floating search algorithm the floating search prevents the nesting effect the proposed algorithm is computationally very efficient because only one data pass is required several examples are given to demonstrate the effectiveness of the proposed algorithm

approximating pareto frontier using a hybrid line search approach the aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach but it is well known that this technique sometimes fail in different aspects for determining the pareto frontier this paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point once the first pareto solution is obtained a simplified version of the former one is used in the context of pareto dominance to obtain a set of efficient points which will assure a thorough distribution of solutions on the pareto frontier in the current form the proposed technique is well suitable for problems having multiple objectives it is not limited to bi objective problems and require the functions to be continuous twice differentiable in order to assess the effectiveness of this approach some experiments were performed and compared with two recent well known population based metaheuristics namely parego and nsga ii when compared to parego and nsga ii the proposed approach not only assures a better convergence to the pareto frontier but also illustrates a good distribution of solutions from a computational point of view both stages of the line search converge within a short time average about 150ms for the first stage and about 20ms for the second stage apart from this the proposed technique is very simple easy to implement and use to solve multiobjective problems

improving particle swarm optimization using multi layer searching strategy abstract in recent years particle swarm optimization pso algorithm has been used to solve global optimization problems this algorithm is widely used as an effective optimization tool in various applications however traditional pso consists of only two searching layers and thus often results in premature convergence into the local minima thus multi layer particle swarm optimization mlpso is proposed in this paper to improve the performance of traditional pso by increasing the two layers of swarms to multiple layers the mlpso strategy increases the diversity of searching swarms to improve its performance when solving complex problems the experiment indicates that the novel approach improves the final results and the convergence speed

mpso median oriented particle swarm optimization particle swarm optimization pso is a bio inspired optimization algorithm which has been empirically demonstrated to perform well on many optimization problems however it has two main weaknesses which have restricted the wider applications of pso the algorithm can easily get trapped in the local optima and has slow convergence speed therefore improvement and or elimination of these disadvantages are the most important objective in pso research in this paper we propose median oriented particle swarm optimization mpso to carry out a global search over entire search space with accelerating convergence speed and avoiding local optima the median position of particles and the worst and median fitness values of the swarm are incorporated in the standard pso to achieve the mentioned goals the proposed algorithm is evaluated on 20 unimodal multimodal rotated and shifted high dimensional benchmark functions and the results are compared with some well known pso algorithms in the literature the results show that mpso substantially enhances the performance of the pso paradigm in terms of convergence speed and finds global or good near global optimal in the functions

regularity and asymptotic behavior of nonlinear stefan problems we study the following nonlinear stefan problem left begin aligned u t d delta u g u quad rm for x in omega t t 0 u 0 rm and u t mu nabla x u 2 quad rm for x in gamma t t 0 u 0 x u 0 x quad rm for x in omega 0 end aligned right where omega t subset mathbb r n n geqq 2 is bounded by the free boundary gamma t with omega 0 omega 0 and d are given positive constants the initial function u0 is positive in omega 0 and vanishes on partial omega 0 the class of nonlinear functions g u includes the standard monostable bistable and combustion type nonlinearities we show that the free boundary gamma t is smooth outside the closed convex hull of omega 0 and as t to infty either omega t expands to the entire mathbb r n or it stays bounded moreover in the former case gamma t converges to the unit sphere when normalized and in the latter case u to 0 uniformly when g u au bu 2 we further prove that in the case omega t expands to mathbb r n u to a b as t to infty and the spreading speed of the free boundary converges to a positive constant moreover there exists mu geqq 0 such that omega t expands to mathbb r n exactly when mu mu

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

application of particle swarm optimization based on chks smoothing function for solving nonlinear bilevel programming problem particle swarm optimization pso is a new optimization technique originating from artificial life and evolutionary computation it completes optimization through following the personal best solution of each particle and the global best value of the whole swarm pso can be used to solve nonlinear programming problems for global optimal solutions efficiently so a novel approach based on particle swarm optimization is proposed to solve nonlinear bilevel programming problem nblp in the proposed approach applying karush kuhn tucker kkt condition to the lower level problem we transform the nblp into a regular nonlinear programming with complementary constraints which is sequentially smoothed by chen harker kanzow smale chks smoothing function the pso approach is then applied to solve the smoothed nonlinear programming for getting the approximate optimal solution of the nblp problem simulations on 5 benchmark problems and practical example about watershed water trading decision making problem are made and the results demonstrate the effectiveness of the proposed method for solving nblp

an improved particle swarm optimization with double bottom chaotic maps for numerical optimization chaos theory studies the behavior of dynamical systems that are highly sensitive to their initial conditions this effect is popularly referred to as the butterfly effect small differences in the initial conditions yield widely diverging outcomes for chaotic systems rendering long term prediction impossible in general in mathematics a chaotic map is a map i e an evolution function that exhibits some sort of chaotic behavior chaotic maps occur in the study of dynamical systems and often generate fractals in this paper an improved logistic map namely a double bottom map with particle swarm optimization was applied to the test function simple pso adopts a random sequence with a random starting point as a parameter and relies on this parameter to update the positions and velocities of the particles however pso often leads to premature convergence especially in complex multi peak search problems in recent years the use of chaotic sequences in optimization techniques rather than random sequences with random seeds has been growing steadily chaotic sequences which are created by means of chaotic maps have been proven easy and fast to generate and are more easily stored then random seed processes they can improve the performance of pso due to their unpredictability double bottom maps are designed by the updating equation of pso in order to balance the exploration and exploitation capability we embedded many commonly used chaotic maps as well as our double bottom map into pso to improve performance and compared these versions to each other to demonstrate the effectiveness of the pso with the double bottom map we call this improved pso method double bottom map pso dbmpso in the conducted experiments pso dbmpso and other chaotic psos were extensively compared on 22 benchmark test functions the experimental results indicate that the performance of dbmpso is significantly better than the performance of other psos tested

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

time periodic traveling wave solutions for periodic advection reaction diffusion systems abstract we study the existence uniqueness and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection reaction diffusion systems under certain conditions we prove that there exists a maximal wave speed c such that for each wave speed c c there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system it is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co moving frame coordinate we also show that the traveling wave solutions with wave speed c c are asymptotically stable in certain sense in addition we establish the nonexistence of time periodic traveling waves with speed c c

fuzzy portfolio selection models with value at risk based on fuzzy value at risk var this paper proposes a new portfolio selection model psm called the var based fuzzy psm var fpsm compared with the existing fpsms the var can directly reflect the greatest loss of a selected case under a given confidence level in this study when the security returns are taken as trapezoidal triangular and gaussian fuzzy numbers several crisp equivalent models of the var fpsm are derived which can be handled by any linear programming solvers in general situations an improved particle swarm optimization algorithm on the basis of fuzzy simulation is designed to search for the approximate optimal solutions to illustrate the proposed model and the behavior of the improved particle swarm optimization algorithm two numerical examples are provided and the results are discussed furthermore the proposed algorithm is compared with some existing approaches to fuzzy portfolio selection such as the genetic algorithm and simulated annealing

numerical calculation of incomplete gamma functions by the trapezoidal rule the trapezoidal rule is applied to the numerical calculation of a known integral representation of the complementary incomplete gamma function a x in the regiona 0 since this application of the rule is not standard a careful investigation of the remainder terms using the euler maclaurin formula is carried out the outcome is a simple numerical procedure for obtaining values of incomplete gamma functions with surprising accuracy in the stated region

all dimension neighborhood based particle swarm optimization with randomly selected neighbors particle swarm optimization pso is widely used for solving various optimization problems since it has few parameters and is easy to implement however canonical pso generally suffers from premature convergence because it usually loses diversity too rapidly during the evolutionary process to improve the performance of pso on complex problems an all dimension neighborhood based pso with randomly selected neighbors learning strategy adn rsn pso is proposed in this study the randomly selected neighbors rsn learning strategy is adopted in the early stage of pso to enhance the swarm diversity while the all dimension neighborhood adn strategy is utilized in the later stage to accelerate the convergence rate the adn strategy enhances the local search capability around the global best solution in a dimension by dimension manner and the search distance is adapted by shrinking and random expansion operators experimental results show that adn pso can improve the exploitation capability of the global version of pso to test the performance of the proposed adn rsn pso comparison tests on the cec2013 test suite are carried out the comparison results reveal that adn rsn pso outperforms other peer pso variants in the end the proposed adn rsn pso is applied to the radar system design problem to demonstrate its potential in real life applications

an intelligent augmentation of particle swarm optimization with multiple adaptive methods over the last two decades the newly developed optimization technique particle swarm optimization pso has attracted great attention two common criticisms exist first most existing psos are designed for a specific search space thus an algorithm performing well on a diverse set of problems is lacking secondly pso suffers premature convergence to address the first issue we propose to augment pso via the fusion of multiple search methods an intelligent selection mechanism is developed based on an effectiveness index to trigger appropriate search methods in this research two search techniques are studied a non uniform mutation based method and an adaptive sub gradient method we further improve the proposed pso using adaptive cauchy mutation to prevent premature convergence as a result an augmented pso with multiple adaptive methods pso mam is proposed the performance of pso mam is tested on 43 functions uni modal multi modal non separable shifted rotated noisy and mis scaled functions the results are compared in terms of solution quality and convergence speed with 10 published pso methods the experimental results demonstrate pso mam outperforms the comparison algorithms on 36 out of 43 functions we conclude while promising there is still room for improving pso mam on complex multi modal functions e g rotated multi modal functions

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

efficient least angle regression for identification of linear in the parameters models least angle regression as a promising model selection method differentiates itself from conventional stepwise and stagewise methods in that it is neither too greedy nor too slow it is closely related to l1 norm optimization which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability in this paper we propose an efficient least angle regression algorithm for model selection for a large class of linear in the parameters models with the purpose of accelerating the model selection process the entire algorithm works completely in a recursive manner where the correlations between model terms and residuals the evolving directions and other pertinent variables are derived explicitly and updated successively at every subset selection step the model coefficients are only computed when the algorithm finishes the direct involvement of matrix inversions is thereby relieved a detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency compared with the original approach where the well known efficient cholesky decomposition is involved in solving least angle regression three artificial and real world examples are employed to demonstrate the effectiveness efficiency and numerical stability of the proposed algorithm

a diffusive logistic equation with a free boundary and sign changing coefficient in time periodic environment abstract this paper concerns a diffusive logistic equation with a free boundary and sign changing intrinsic growth rate in heterogeneous time periodic environment in which the variable intrinsic growth rate may be very negative in a suitable large region see conditions h1 h2 4 3 such a model can be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front in the case of higher space dimensions with radial symmetry and when the intrinsic growth rate has a positive lower bound this problem has been studied by du guo peng 11 they established a spreading vanishing dichotomy the sharp criteria for spreading and vanishing and estimate of the asymptotic spreading speed in the present paper we show that the above results are retained for our problem

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

multi objective robust pid controller tuning using two lbests multi objective particle swarm optimization in this paper two lbests multi objective particle swarm optimization 2lb mopso is applied to design multi objective robust proportional integral derivative pid controllers for two mimo systems namely distillation column plant and longitudinal control system of the super maneuverable f18 harv fighter aircraft multi objective robust pid controller design problem is formulated by minimizing integral squared error ise and balanced robust performance criteria during the search 2lb mopso can focus on small regions in the parameter space in the vicinity of the best existing fronts as the lbests are chosen from the top fronts in a non domination sorted external archive of reasonably large size the offspring obtained can be more diverse with good fitness the performance of various optimal pid controllers is compared in terms of the sum of ise and balanced robust performance criteria for the purpose of comparison 2lb mopso nsga ii as well as earlier reported riccati iga and osa methods are considered the performance of pid controllers obtained using 2lb mopso is better than that of others in addition hypervolume based comparisons are carried out to show the superior performance of 2lb mopso over nsga ii the results reveal that 2lb mopso yields better robustness and consistency in terms of the sum of ise and balanced robust performance criteria than various optimal pid controllers

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

across neighborhood search for numerical optimization population based search algorithms pbsas including swarm intelligence algorithms sias and evolutionary algorithms eas are competitive alternatives for solving complex optimization problems and they have been widely applied to real world optimization problems in different fields in this study a novel population based across neighborhood search ans is proposed for numerical optimization ans is motivated by two straightforward assumptions and three important issues raised in improving and designing efficient pbsas in ans a group of individuals collaboratively search the solution space for an optimal solution of the optimization problem considered a collection of superior solutions found by individuals so far is maintained and updated dynamically at each generation an individual directly searches across the neighborhoods of multiple superior solutions with the guidance of a gaussian distribution this search manner is referred to as across neighborhood search the characteristics of ans are discussed and the concept comparisons with other pbsas are given the principle behind ans is simple moreover ans is easy for implementation and application with three parameters being required to tune extensive experiments on 18 benchmark optimization functions of different types show that ans has well balanced exploration and exploitation capabilities and performs competitively compared with many efficient pbsas related matlab codes used in the experiments are available from http guohuawunudt gotoip2 com publications html

on an advection reaction diffusion competition system with double free boundaries modeling invasion and competition of aedes albopictus and aedes aegypti mosquitoes abstract based on the invasion of the aedes albopictus mosquitoes and the competition between ae albopictus and ae aegypti mosquitoes in the united states we consider an advection reaction diffusion competition system with two free boundaries consisting of an invasive species ae albopictus with density u and a local species ae aegypti with density v in which u invades the environment with leftward front x g t and rightward front x h t in the case that the competition between the two species is strong weak and species v wins over species u the solution u v converges uniformly to the semi positive equilibrium 0 1 while the two fronts satisfy that lim t g t h t g h r in the case that the competition between the two species is weak we show that when the advection coefficients are less than fixed thresholds there are two scenarios for the long time behavior of solutions i when the initial habitat h 0 4 1 2 1 and the initial value of u is sufficiently small the solution u v converges uniformly to the semi positive equilibrium 0 1 with the two fronts g h r ii when the initial habitat h 0 4 1 2 1 the solution u v converges locally uniformly to the interior equilibrium with the two fronts g h r in addition we propose an upper bound and a lower bound for the asymptotic spreading speeds of the leftward and rightward fronts numerical simulations are also provided to confirm our theoretical results

the spreading front of invasive species in favorable habitat or unfavorable habitat abstract spatial heterogeneity and habitat characteristic are shown to determine the asymptotic profile of the solution to a reaction diffusion model with free boundary which describes the moving front of the invasive species a threshold value r 0 fr d t is introduced to determine the spreading and vanishing of the invasive species we prove that if r 0 fr d t 0 1 for some t 0 0 the spreading must happen while if r 0 fr d 0 1 the spreading is also possible our results show that the species in the favorable habitat can establish itself if the diffusion is slow or the occupying habitat is large in an unfavorable habitat the species dies out if the initial value of the species is small however big initial number of the species is benefit for the species to survive when the species spreads in the whole habitat the asymptotic spreading speed is given some implications of these theoretical results are also discussed

a rank based particle swarm optimization algorithm with dynamic adaptation the particle swarm optimization pso technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space this paper presents a variation on the standard pso algorithm called the rank based particle swarm optimizer or pso r a n k employing cooperative behavior of the particles to significantly improve the performance of the original algorithm in this method in order to efficiently control the local search and convergence to global optimum solution the c best particles are taken to contribute to the updating of the position of a candidate particle the contribution of each particle is proportional to its strength the strength is a function of three parameters strivness immediacy and number of contributed particles all particles are sorted according to their fitness values and only the c best particles will be selected the value of c decreases linearly as the iteration increases a time varying inertia weight decreasing non linearly is introduced to improve the performance pso r a n k is tested on a commonly used set of optimization problems and is compared to other variants of the pso algorithm presented in the literature as a real application pso r a n k is used for neural network training the pso r a n k strategy outperformed all the methods considered in this investigation for most of the functions experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness

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

finknn a fuzzy interval number k nearest neighbor classifier for prediction of sugar production from populations of samples this work introduces finknn a k nearest neighbor classifier operating over the metric lattice of conventional interval supported convex fuzzy sets we show that for problems involving populations of measurements data can be represented by fuzzy interval numbers fins and we present an algorithm for constructing fins from such populations we then present a lattice theoretic metric distance between fins with arbitrary shaped membership functions which forms the basis for finknn s similarity measurements we apply finknn to the task of predicting annual sugar production based on populations of measurements supplied by hellenic sugar industry we show that finknn improves prediction accuracy on this task and discuss the broader scope and potential utility of these techniques

heterogeneous local model networks for time series prediction the approaches of local modeling have emerged as one of the promising methods of time series prediction by use of the divide and conquer method local models can exploit state dependent features to approximate a subset of training data accurately however the generalization performance of local model networks is subject to the proper selection of model parameters in this paper we present a new method for local model construction for the noisy time series prediction the proposed method uses the principal component analysis pca and cross validation technique to construct an optimal input vector for each local model a heuristic learning rule is also proposed to update the mixture of experts network structure which determines the confidence level of local prediction model the proposed method has been tested with noisy mackey glass time series and sunspot series

nonlinear model validation using correlation tests new higher order correlation tests which use model residuals combined with system inputs and outputs are presented to check the validity of a general class of nonlinear models the new method is illustrated by testing both simple and complex nonlinear system models

evolutionary programming based on non uniform mutation a new evolutionary programming using non uniform mutation instead of gaussian cauchy and levy mutations is proposed evolutionary programming with non uniform mutation nep has the merits of searching the space uniformly at the early stage and very locally at the later stage during the programming for a suite of 14 benchmark problems nep outperforms the improved evolutionary programming using mutation based on levy probability distribution ilep for multimodal functions with many local minima while being comparable to ilep in performance for unimodal and multimodal functions with only a few minima the detailed theoretical analysis of the executing process of nep and the expected step size on non uniform mutation are given

chaotic catfish particle swarm optimization for solving global numerical optimization problems abstract chaotic catfish particle swarm optimization c catfishpso is a novel optimization algorithm proposed in this paper c catfishpso introduces chaotic maps into catfish particle swarm optimization catfishpso which increase the search capability of catfishpso via the chaos approach simple catfishpso relies on the incorporation of catfish particles into particle swarm optimization pso the introduced catfish particles improve the performance of pso considerably unlike other ordinary particles the catfish particles initialize a new search from extreme points of the search space when the gbest fitness value global optimum at each iteration has not changed for a certain number of consecutive iterations this results in further opportunities of finding better solutions for the swarm by guiding the entire swarm to promising new regions of the search space and accelerating the search the introduced chaotic maps strengthen the solution quality of pso and catfishpso significantly the resulting improved pso and catfishpso are called chaotic pso c pso and chaotic catfishpso c catfishpso respectively pso c pso catfishpso c catfishpso as well as other advanced pso procedures from the literature were extensively compared on several benchmark test functions statistical analysis of the experimental results indicate that the performance of c catfishpso is better than the performance of pso c pso catfishpso and that c catfishpso is also superior to advanced pso methods from the literature

term and variable selection for non linear system identification the purpose of variable selection is to pre select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection it is required that the selected significant variables alone should sufficiently represent the system generally not all the model terms which are produced by combining different variables make an equal contribution to the system output and terms which make little contribution can be omitted a parsimonious representation which contains only the significant terms can often be obtained without the loss of representational accuracy by eliminating the redundant terms based on these observations a new variable and term selection algorithm is proposed in this paper the term detection algorithm can be applied to the general class of non linear modelling problems which can be expressed as a linear in the parameters form the variable selection procedure is based on locally linea

a multi objective portfolio selection model with fuzzy value at risk ratio considering nonstatistical uncertainties and or insufficient historical data in security return forecasts fuzzy set theory has been applied in the past decades to build portfolio selection models meanwhile various risk measurements such as variance entropy and value at risk have been proposed in fuzzy environments to evaluate investment risks from different perspectives sharpe ratio also known as the reward to variability ratio which measures the risk premium per unit of the nonsystematic risk asset deviation has received great attention in modern portfolio theory in this study the sharpe ratio in fuzzy environments is introduced whereafter a fuzzy value at risk ratio is proposed compared with sharpe ratio value at risk ratio is an index with dimensional knowledge that reflects the risk premium per unit of the systematic risk the greatest loss under a given confidence level on the basis of the two ratios a multi objective model is built to evaluate their joint impact on portfolio selection then the proposed model is solved by a fuzzy simulation based multi objective particle swarm optimization algorithm where the global best of each iteration is determined by an improved dominance times based method finally the algorithm superiority is justified via comparing with existing solvers on benchmark problems and the model effectiveness is exemplified by using three case studies on portfolio selection

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

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

an improved particle swarm optimization algorithm an improved particle swarm optimization ipso is proposed in this paper in the new algorithm a population of points sampled randomly from the feasible space then the population is partitioned into several sub swarms each of which is made to evolve based on particle swarm optimization pso algorithm at periodic stages in the evolution the entire population is shuffled and then points are reassigned to sub swarms to ensure information sharing this method greatly elevates the ability of exploration and exploitation simulations for three benchmark test functions show that ipso possesses better ability to find the global optimum than that of the standard pso algorithm compared with pso ipso is also applied to identify the hydrologic model the results show that ipso remarkably improves the calculation accuracy and is an effective global optimization to calibrate hydrologic model

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

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

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

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

a modified particle swarm optimization algorithm with applications abstract in this paper firstly a modified particle swarm optimization algorithm mpso is developed in which the mean value of past optimal positions for each particle and the mutation operation are considered for avoiding premature in the optimization test mpso performs better than particle swarm optimization algorithm pso then mpso is applied to solve four portfolio optimization models with the real data from the hong kong stock market and optimal values are obtained when the number of swarm n 80 160 respectively finally actual return rates of these models are calculated in numerical experiments and it is illustrated from these graphs of actual return rates that when considering higher return cai s model performs better in short term investment

on some free boundary problems of the prey predator model abstract in this paper we investigate some free boundary problems for the lotka volterra type prey predator model in one space dimension the main objective is to understand the asymptotic behavior of the two species prey and predator spreading via a free boundary we prove a spreading vanishing dichotomy namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment or they fail to establish and die out in the long run the long time behavior of solution and criteria for spreading and vanishing are also obtained finally when spreading successfully we provide an estimate to show that the spreading speed if exists cannot be faster than the minimal speed of traveling wavefront solutions for the prey predator model on the whole real line without a free boundary

piecewise linear identification of non linear systems methods of identifying a series of piecewise linear models which approximate to a non linear system over some operating range are investigated spatial linear models and models with signal dependent parameters are considered

on solving the double loading problem using a modified particle swarm optimization we consider in this paper a double loading problem dlp an np hard optimization problem of extreme economic relevance in industrial areas the problem consists in loading items into bins then stowing bins in a set of compartments the main objective is to minimize the number of used bins we state the mathematical model as well as a modified binary particle swarm optimization with ffd initialization that outperforms state of the art approaches carried out on a large testbed instances

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

on a reaction diffusion equation with robin and free boundary conditions this paper studies the following problem ut uxx f u 0 0 u 0 t bux 0 t t 0 u h t t 0 h t ux h t t t 0 h 0 h0 u x 0 x 0 x h0 where f is an unbalanced bistable nonlinearity b 0 0 and is a compactly supported c2 function we prove that there exists 0 such that vanishing happens when 0 and u t converges as t to 0 uniformly in 0 h t spreading happens when i e h t c t tends to a constant for some c 0 u t converges to a positive stationary solution locally uniformly in 0 and to a traveling semi wave with speed c near x h t in the transition case when u t v t h2 0 h t tends to 0 as t where t is a maximum point of u t and v is the unique even positive solution of v f v 0 subject to v 0 moreover with respect to b and f t pln t q o 1 for some p 0 and q r or t z for some root z of v z bv z

backtracking search optimization algorithm for numerical optimization problems this paper introduces the backtracking search optimization algorithm bsa a new evolutionary algorithm ea for solving real valued numerical optimization problems eas are popular stochastic search algorithms that are widely used to solve non linear non differentiable and complex numerical optimization problems current research aims at mitigating the effects of problems that are frequently encountered in eas such as excessive sensitivity to control parameters premature convergence and slow computation in this vein development of bsa was motivated by studies that attempt to develop simpler and more effective search algorithms unlike many search algorithms bsa has a single control parameter moreover bsa s problem solving performance is not over sensitive to the initial value of this parameter bsa has a simple structure that is effective fast and capable of solving multimodal problems and that enables it to easily adapt to different numerical optimization problems bsa s strategy for generating a trial population includes two new crossover and mutation operators bsa s strategies for generating trial populations and controlling the amplitude of the search direction matrix and search space boundaries give it very powerful exploration and exploitation capabilities in particular bsa possesses a memory in which it stores a population from a randomly chosen previous generation for use in generating the search direction matrix thus bsa s memory allows it to take advantage of experiences gained from previous generations when it generates a trial preparation this paper uses the wilcoxon signed rank test to statistically compare bsa s effectiveness in solving numerical optimization problems with the performances of six widely used ea algorithms pso cmaes abc jde clpso and sade the comparison which uses 75 boundary constrained benchmark problems and three constrained real world benchmark problems shows that in general bsa can solve the benchmark problems more successfully than the comparison algorithms

improved structure optimization for fuzzy neural networks fuzzy neural network based inference systems are well known universal approximators which can produce linguistically interpretable results unfortunately their dimensionality can be extremely high due to an excessive number of inputs and rules which raises the need for overall structure optimization in the literature various input selection methods are available but they are applied separately from rule selection often without considering the fuzzy structure this paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously first a method is developed to select the most significant rules along with a refinement stage to remove unnecessary correlations an improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model leading to a balanced tradeoff between interpretability and accuracy simulation results confirm the efficacy of the proposed method

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

a dominance tree and its application in evolutionary multi objective optimization most contemporary multi objective evolutionary algorithms moeas store and handle a population with a linear list and this may impose high computational complexities on the comparisons of solutions and the fitness assignment processes this paper presents a data structure for storing the whole population and their dominating information in moeas this structure called a dominance tree dt is a binary tree that can effectively and efficiently store three valued relations namely dominating dominated or non dominated among vector values this paper further demonstrates dt s potential applications in evolutionary multi objective optimization with two cases the first case utilizes the dt to improve nsga ii as a fitness assignment strategy the second case demonstrates a dt based moea called a dtea which is designed by leveraging the favorable properties of the dt the simulation results show that the dt improved nsga ii is significantly faster than nsga ii meanwhile dtea is much faster than spea2 nsga ii and an improved version of nsga ii on the other hand in regard to converging to the pareto optimal front and maintaining the diversity of solutions dt improved nsga ii and dtea are found to be competitive with nsga ii and spea2

a new pso algorithm with random c d switchings abstract this paper investigates the overall convergence analysis and proposes a novel random c d switchings pso algorithm with random switchings between convergence operator and divergence operator with respect to the standard pso algorithm its convergence analysis provides a fundamental theory of selecting convergence operator and divergence operator during the process of finding the suboptimal or global solution the random switchings between two typical operators namely operator c and operator d which are two different ways to update velocities of all particles are conducted by a so called convergence ratio parameter which can determine the tradeoff between exploration ability and exploitation ability from the quantitative perspective numerical results on several benchmark functions demonstrate the following observations 1 the proper convergence ratio is closely related to the landscape of objective function the dimension of solution space and the number of local optimums 2 small convergence ratio setting to 0 60 or 0 65 may benefit the optimization problem which has many local optimums in the high dimensional space while large convergence ratio setting to 0 85 or 0 9 is probably helpful for the optimization problem with few local optimums or flat landscape

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

short term scheduling of cascade reservoirs using an immune algorithm based particle swarm optimization this paper presents a new approach for short term hydropower scheduling of reservoirs using an immune algorithm based particle swarm optimization ia pso ia pso is employed by coupling the immune information processing mechanism with the particle swarm optimization algorithm in order to achieve a better global solution with less computational effort with the ia pso technique the hydro electrical optimization model of reservoirs is formulated as a high dimensional dynamic nonlinear and stochastic global optimization problem of a multi reservoir hydropower system the purpose of the proposed methodology is to maximize total hydropower production here it is applied to a reservoir system on the qingjiang river in the yangtze watershed that consists of two reservoirs the results are compared with the results obtained through conventional operation method the dynamic programming and the standard pso algorithm from the comparative results it is found that the ia pso approach provides the most globally optimum solution at a faster convergence speed

a novel metaheuristic for multi objective optimization problems vs algorithm is modified and multi objective vs movs has been proposed movs algorithm has been tested on 36 different benchmark problems along with 4 other algorithms obtained results show that movs is a very successful and competitive algorithm this study investigates a multi objective vortex search algorithm movs by modifying the single objective vortex search algorithm or vs the vs is a metaheuristic based algorithm that uses a new adaptive step size adjustment strategy to improve the performance of the search process search mechanism of the vs is inspired by the vortex pattern so it is called a vortex search algorithm the original vs is an improved way of solving single objective continuous problems to improve the movs algorithm the vs algorithm is enhanced with added calculation approaches such as fast nondominated sorting and crowding distance in order to identify the degree of non dominance of the solutions and the densities of their occurrence in addition a crossover operation is added to the movs algorithm in order to enhance the pareto front convergence capacity of the solutions finally to spread the solutions more successfully over the pareto front it has been randomly produced using the inverse incomplete gamma function using a parameter between 0 and 1 the proposed movs algorithm is tested against 36 different benchmark problems together with nsgaii mocell ibea and moea d algorithms the test results indicate that the movs algorithm achieves a better performance on accuracy and convergence speed than any other algorithms when comparisons are made against several test problems and they also show that it is a competitive algorithm

a new metaheuristic for numerical function optimization vortex search algorithm abstract in this study a new single solution based metaheuristic namely the vortex search vs algorithm is proposed to perform numerical function optimization the proposed vs algorithm is inspired from the vortex pattern created by the vortical flow of the stirred fluids to provide a good balance between the explorative and exploitative behavior of a search the proposed method models its search behavior as a vortex pattern by using an adaptive step size adjustment scheme the proposed vs algorithm is tested over 50 benchmark mathematical functions and the results are compared to both the single solution based simulated annealing sa and pattern search ps and population based particle swarm optimization pso2011 and artificial bee colony abc algorithms a wilcoxon signed rank test is performed to measure the pair wise statistical performances of the algorithms the results of which indicate that the proposed vs algorithm outperforms the sa ps and abc algorithms while being competitive with the pso2011 algorithm

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

a finite time particle swarm optimization algorithm for odor source localization abstract this paper is concerned with a finite time particle swarm optimization algorithm for odor source localization first a continuous time finite time particle swarm optimization fpso algorithm is developed based on the continuous time model of the particle swarm optimization pso algorithm since the introduction of a nonlinear damping item the proposed continuous time fpso algorithm can converge over a finite time interval furthermore in order to enhance its exploration capability a tuning parameter is introduced into the proposed continuous time fpso algorithm the algorithm s finite time convergence is analyzed by using the lyapunov approach second the discrete time fpso algorithm is obtained by using a given dicretization scheme the corresponding convergence condition is derived by using a linear matrix inequality lmi approach finally the features and performance of the proposed fpso algorithm are illustrated by using two ill posed functions and twenty five benchmark functions respectively in numerical simulation results the problem of odor source localization is presented to validate the effectiveness of the proposed fpso algorithm

a new separation measure for improving the effectiveness of validity indices many validity indices have been proposed for quantitatively assessing the performance of clustering algorithms one limitation of existing indices is their lack of generalizability due to their dependence on the specific algorithms and structures of the data space to handle large scale datasets with arbitrary structures this research study proposes a new cluster separation measure for improving the effectiveness of existing validity indices this is achieved by partitioning the original data space into a grid based structure which allows the introduction of a new measurement for assessing the true data distribution between any two clusters instead of the distance between the two cluster prototypes to validate the effectiveness of the proposed separation measure we adopt two commonly used validity indices the davies bouldin s function db and tibshirani s gap statistic gs these indices are denoted as r db 1 and r gs 1 for clusters with sphere shaped structures and r db 2 and r gs 2 for irregular shaped structures this integration enables the indices to evaluate both partitional algorithms and hierarchical algorithms partitional algorithms including c means cm fuzzy c means fcm and hierarchical algorithms including dbscan and clique are used to test the performance of the new indices two synthetic datasets with spherical structures and four synthetic datasets with irregular shapes are first compared five real datasets from the uci machine learning repository are then used to further test the measure s performance the experimental results provide evidence that the new indices outperform the original indices

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

enhancing pso methods for global optimization the particle swarm optimization pso method is a well established technique for global optimization during the past years several variations of the original pso have been proposed in the relevant literature because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms in this work we propose three modifications of the original pso method in order to increase the speed and its efficiency that can be applied independently in almost every pso variant these modifications are a a new stopping rule b a similarity check and c a conditional application of some local search method the proposed were tested using three popular pso variants and a variety test functions we have found that the application of these modifications resulted in significant gain in speed and efficiency

a quantum behaved particle swarm optimization with memetic algorithm and memory for continuous non linear large scale problems abstract quantum behaved particle swarm optimization qpso a novel variant of pso inspired by quantum mechanics is a global convergence guaranteed algorithm which outperforms the original pso in search ability and has fewer parameters to control but as many other psos it is easy to fall into local optimum in solving high dimensional complex optimization problems this paper proposes an improved qpso algorithm for continuous non linear large scale problems based on memetic algorithm and memory mechanism the memetic algorithm is used to make all particles each particle corresponding to a memetic gain some experience through a local search before being involved in the evolutionary process and the memory mechanism is used to introduce a so called bird kingdom with memory capacity both of which can improve the global search ability of the algorithm another difference compared to the previous qpsos is that we let each dimension of a particle update with the same random number thus increasing the speed of convergence and enhancing the ability of local search numerical experiments are conducted to compare the proposed algorithm with different variants of pso and other swarm intelligence algorithms the experimental results show the superiority of the proposed approach on benchmark test functions

variable selection algorithm for the construction of mimo operating point dependent neurofuzzy networks an input variable selection procedure is introduced for the identification and construction of multi input multi output mimo neurofuzzy operating point dependent models the algorithm is an extension of a forward modified gram schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting the proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice based modeling algorithms such as radial basis function neurofuzzy networks enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm

stochastic numerical treatment for solving troesch s problem abstract in this article the numerical techniques are presented for the solution of troesch s problem based on neural networks optimized with three different methods including particle swarm optimization pso active set as and pso hybridized with as pso as algorithms the variable transformation is applied in order to convert the original problem to a transformed problem which is relatively less stiff to solve feed forward artificial neural networks are used to model the transformed problem learning of adjustable parameters is made with pso as and pso as algorithms the proposed methodologies are applied to a number of cases for stiff and non stiff boundary value problems the comparative analyses are carried out with other standard numerical solutions as well as approximate analytical solver