fast implementation of the continuous wavelet transform with integer scales we describe a fast noniterative algorithm for the evaluation of continuous spline wavelet transforms at any integer scale m in this approach the input signal and the analyzing wavelet are both represented by polynomial splines the algorithm uses a combination of moving sum and zero padded filters and its complexity per scale is o n where n is the signal length the computation is exact and the implementation is noniterative across scales we also present examples of spline wavelets exhibiting properties that are desirable for either singularity detection first and second derivative operators or gabor like time frequency signal analysis

tabu search applied to global optimization abstract a new algorithm called enhanced continuous tabu search ects is proposed for the global optimization of multiminima functions it results from an adaptation of combinatorial tabu search which aims to follow as close as possible glover s basic approach in order to cover a wide domain of possible solutions our algorithm first performs the diversification it locates the most promising areas by fitting the size of the neighborhood structure to the objective function and its definition domain when the most promising areas are located the algorithm continues the search by intensification within one promising area of the solution space the efficiency of ects is thoroughly tested by using a set of benchmark multimodal functions of which global and local minima are known ects is compared to other published versions of continuous tabu search and to some alternative algorithms like simulated annealing we point out two main advantages of ects first its principle is rather basic directly inspired from combinatorial tabu search secondly it shows a good performance for functions having a large number of variables more than 10

neural network learning with global heuristic search a novel hybrid global optimization go algorithm applied for feedforward neural networks nns supervised learning is investigated the network weights are determined by minimizing the traditional mean square error function the optimization technique called lptau nm combines a novel global heuristic search based on lptau low discrepancy sequences of points and a simplex local search the proposed method is initially tested on multimodal mathematical functions and subsequently applied for training moderate size nns for solving popular benchmark problems finally the results are analyzed discussed and compared with such as from backpropagation bp levenberg marquardt and differential evolution methods

global optimization based on novel heuristics low discrepancy sequences and genetic algorithms abstract in this paper a new heuristic hybrid technique for bound constrained global optimization is proposed we developed iterative algorithm called glp s that uses genetic algorithms lp low discrepancy sequences of points and heuristic rules to find regions of attraction when searching a global minimum of an objective function subsequently nelder mead simplex local search technique is used to refine the solution the combination of the three techniques genetic algorithms lp o low discrepancy search and simplex search provides a powerful hybrid heuristic optimization method which is tested on a number of benchmark multimodal functions with 10 150 dimensions and the method properties applicability convergence consistency and stability are discussed in detail

a sequential niching memetic algorithm for continuous multimodal function optimization abstract this work discusses a sequential niching algorithm for multiple optimal determination the procedure consists of a sequence of genetic algorithms ga runs which incorporate a gradient based hill climbing algorithm and make use of a derating function and of niching and clearing techniques to promote the occupation of different niches in the function to be optimized thus the algorithm searches the solution space eliminating from the fitness landscape previously located peaks forcing the individuals to converge into unoccupied niches an effective search of the solution space is stimulated incorporating in the algorithm stages dedicated to find new promising domains in the variable space and stages that exploits the located promising regions unlike other algorithms the efficiency of the sequential niching memetic algorithm snma proposed in this work is not highly sensitive to the niche radius performance measurements with 37 standard test functions of dimensions ranging from 1 to 100 show that the snma has very good scalability and outperforms other algorithms in accurately locating multiple optima both global and local

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

the gradient evolution algorithm this study presents a new metaheuristic method that is derived from the gradient based search method in an exact optimization method the gradient is used to find extreme points as well as the optimal point this study modifies a gradient method and creates a metaheuristic method that uses a gradient theorem as its basic updating rule this new method named gradient evolution explores the search space using a set of vectors and includes three major operators vector updating jumping and refreshing vector updating is the main updating rule in gradient evolution the search direction is determined using the newton raphson method vector jumping and refreshing enable this method to avoid local optima in order to evaluate the performance of the gradient evolution method three different experiments are conducted using fifteen test functions the first experiment determines the influence of parameter settings on the result it also determines the best parameter setting there follows a comparison between the basic and improved metaheuristic methods the experimental results show that gradient evolution performs better than or as well as other methods such as particle swarm optimization differential evolution an artificial bee colony and continuous genetic algorithm for most of the benchmark problems tested

filter design and comparison for two fast cwt algorithms the continuous wavelet transform cwt is a powerful technique for signal analysis direct cwt computation by fft requires o n log sub 2 n operations per scale where n is the data length the a trous algorithm and the shensa 1992 algorithm are two fast methods to compute cwt recursively that require only o n operations per scale both of them can be described by the multiresolution analysis mra structure but with different mra filters this paper proposes methods to design the mra filters of the two algorithms to improve their accuracy on cwt computation we begin with the formulation of the cwt computation error using the mra structure the mra filters of the two algorithms are then designed to minimize the error in either algorithm both the lowpass and bandpass mra filters can be optimized the a trous algorithm has closed form solutions for the two filters the shensa algorithm on the other hand has an analytic solution for the bandpass filter only finding the optimum lowpass filter requires a multidimensional numerical search simulation studies show that by using the proposed optimum filters the shensa algorithm in general outperforms the a trous algorithm

genetic and nelder mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions abstract a hybrid method combining two algorithms is proposed for the global optimization of multiminima functions to localize a promising area likely to contain a global minimum it is necessary to well explore the whole search domain when a promising area is detected the appropriate tools must be used to exploit this area and obtain the optimum as accurately and quickly as possible both tasks are hardly performed through only one method we propose an algorithm using two processes each one devoted to one task global metaheuristics such as simulated annealing tabu search and genetic algorithms gas are efficient to localize the best areas on the other hand local search methods are classically available in particular the hill climbing e g the quasi newton method and the nelder mead simplex search ss therefore we worked out an hybrid method called continuous hybrid algorithm cha performing the exploration with a ga and the exploitation with a nelder mead ss to evaluate the efficiency of cha we implemented a set of benchmark functions and compared our results to the ones supplied by other competitive methods

memory induced anomalous dynamics emergence of diffusion subdiffusion and superdiffusion from a single random walk model we present a random walk model that exhibits asymptotic subdiffusive diffusive or superdiffusive behavior in different parameter regimes this appears to be an instance of a single random walk model leading to all three forms of behavior by simply changing parameter values furthermore the model offers the great advantage of analytical tractability our model is non markovian in that the next jump of the walker is probabilistically determined by the history of past jumps it also has elements of intermittency in that one possibility at each step is that the walker does not move at all this rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior

limit theorems for a random walk with memory perturbed by a dynamical system we introduce a new random walk with unbounded memory obtained as a mixture of the elephant random walk and the dynamic random walk which we call the dynamic elephant random walk derw as a consequence of this mixture the distribution of the increments of the resulting random process is time dependent we prove a strong law of large numbers for the derw and in a particular case we provide an explicit expression for its speed finally we give sufficient conditions for the central limit theorem and the law of the iterated logarithm to hold

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

global optimization using a genetic algorithm with hierarchically structured population this paper applies a genetic algorithm with hierarchically structured population to solve unconstrained optimization problems the population has individuals distributed in several overlapping clusters each one with a leader and a variable number of support individuals the hierarchy establishes that leaders must be fitter than its supporters with the topological organization of the clusters following a tree computational tests evaluate different population structures population sizes and crossover operators for better algorithm performance a set of known benchmark test problems is solved and the results found are compared with those obtained from other methods described in the literature namely two genetic algorithms a simulated annealing a differential evolution and a particle swarm optimization the results indicate that the method employed is capable of achieving better performance than the previous approaches in regard as the two criteria usually employed for comparisons the number of function evaluations and rate of success the method also has a superior performance if the number of problems solved is taken into account

the discrete wavelet transform wedding the a trous and mallat algorithms two separately motivated implementations of the wavelet transform are brought together it is observed that these algorithms are both special cases of a single filter bank structure the discrete wavelet transform the behavior of which is governed by the choice of filters in fact the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact moreover it is shown that the commonly used lagrange a trous filters are in one to one correspondence with the convolutional squares of the daubechies filters for orthonormal wavelets of compact support a systematic framework for the discrete wavelet transform is provided and conditions are derived under which it computes the continuous wavelet transform exactly suitable filter constraints for finite energy and boundedness of the discrete transform are also derived relevant signal processing parameters are examined and it is observed that orthonormality is balanced by restrictions on resolution

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

fast fir algorithms for the continuous wavelet transform from constrained least squares new algorithms for the continuous wavelet transform are developed that are easy to apply each consisting of a single pass finite impulse response fir filter and several times faster than the fastest existing algorithms the single pass filter named wt fir 1 is made possible by applying constraint equations to least squares estimation of filter coefficients which removes the need for separate low pass and high pass filters non dyadic two scale relations are developed and it is shown that filters based on them can work more efficiently than dyadic ones example applications to the mexican hat wavelet are presented

a dynamic clustering based differential evolution algorithm for global optimization a dynamic clustering based differential evolution algorithm cde for global optimization is proposed to improve the performance of the differential evolution de algorithm with population evolution cde algorithm gradually changes from exploring promising areas at the early stages to exploiting solution with high precision at the later stages experiments on 28 benchmark problems including 13 high dimensional functions show that the new method is able to find near optimal solutions efficiently compared with other existing algorithms cde improves solution accuracy with less computational effort

weighted multivariate mean square error for processes optimization a case study on flux cored arc welding for stainless steel claddings a mathematical programming technique developed recently that optimizes multiple correlated characteristics is the multivariate mean square error mmse the mmse approach has obtained noteworthy results by avoiding the production of inappropriate optimal points that can occur when a method fails to take into account a correlation structure where the mmse approach is deficient however is in cases where the multiple correlated characteristics need to be optimized with varying degrees of importance the mmse approach in treating all responses as having the same importance is unable to attribute the desired weights this paper thus introduces a strategy that weights the responses in the mmse approach the method called the weighted multivariate mean square error wmmse utilizes a weighting procedure that integrates principal component analysis pca and response surface methodology rsm in doing so wmmse obtains uncorrelated weighted objective functions from the original responses after being mathematically programmed these functions are optimized by employing optimization algorithms we applied wmmse to optimize a stainless steel cladding application executed via the flux cored arc welding fcaw process four input parameters and eight response variables were considered stainless steel cladding which carries potential benefits for a variety of industries takes low cost materials and deposits over their surfaces materials having anti corrosive properties optimal results were confirmed which ensured the deposition of claddings with defect free beads exhibiting the desired geometry and demonstrating good productivity indexes

fitting of tabu search to optimize functions of continuous variables summarytabu search ts is a stochastic global optimization procedure which proved e cient to solve variouscombinatorialoptimizationproblems however veryfewworksdealwithitsapplicationtoglobalminimiz ationof functions dependingon continuous variables the aim of this paper is to proposean adaptation oftstotheoptimizationofcontinuousfunctions andtostudytheinsuenceofthemainalgorithmparameterson the convergence towards the optimum in particular the application of ts to function optimizationinvolves the de nition of the current solution neighbourhood and the management of the tabu list thee ciency of ts applied to continuous global optimization has been tested in detail by using classicalmultimodal functions for which minima are known 1997 by john wiley sons ltd key words tabu search global optimization continuous variables 1 introductionthe underlying principles of tabu search ts were rst exposed by glover 1 2 more recentlyoverviewsaboutts and itsimplementationin various eldshavebeenproposed forinstancebyhertz

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

rapid computation of the continuous wavelet transform by oblique projections we introduce a fast simple method for computing the real continuous wavelet transform cwt the approach has the following attractive features it achieves o n complexity per scale the filter coefficients can be analytically obtained by a simple integration and the algorithm is faster than a least squares approach with negligible loss in accuracy our method is to use p wavelets per octave and to approximate them with their oblique projection onto a space defined by a compactly supported scaling function the wavelet templates are expanded to larger sizes octaves using the two scale relation and zero padded filtering error bounds are presented to justify the use of an oblique projection over an orthogonal one all the filters are fir with the exception of one filter which is implemented using a fast recursive algorithm

a niche hybrid genetic algorithm for global optimization of continuous multimodal functions a niche hybrid genetic algorithm nhga is proposed in this paper to solve continuous multimodal optimization problems more efficiently accurately and reliably it provides a new architecture of hybrid algorithms which organically merges the niche techniques and nelder mead s simplex method into gas in the new architecture the simplex search is first performed in the potential niches which likely contain a global optimum to locate the promising zones within search space quickly and reliably then another simplex search is used to quickly discover the global optimum in the located promising zones the proposed method not only makes the exploration capabilities of gas stronger through niche techniques but also has more powerful exploitation capabilities by using simplex search so it effectively alleviates premature convergence and improves weak exploitation capacities of gas a set of benchmark functions is used to demonstrate the validity of nhga and the role of every component of nhga numerical experiments show that the nhga may efficiently and reliably obtain a more accurate global optimum for the complex and high dimension multimodal optimization problems it also demonstrates that the new hybrid architecture is potential and can be used to generate more potential hybrid algorithms

real coded genetic algorithm with uniform random local search genetic algorithms are efficient global optimizers but they are weak in performing fine grained local searches in this paper the local search capability of genetic algorithm is improved by hybridizing real coded genetic algorithm with uniform random local search to form a hybrid real coded genetic algorithm termed rcgau the incorporated local technique is applied to all newly created offspring so that each offspring solution is given the opportunity to effectively search its local neighborhood for the best local optimum numerical experiments show that the performance of rcga is remarkably improved by the uniform random local search technique

non levy stable random walk propagators for a non markovian walk with both superdiffusive and subdiffusive regimes abstract one of the most important quantities of interest in the theory of diffusion and transport is the random walk propagator for markovian processes such as the standard brownian random walk and levy flights the functional form of the random walk propagator is well understood similarly for certain kinds of simple non markovian processes such as levy walks the problem can be mapped to a solvable markovian model however more complicated non markovian walks pose a challenge here we study a non markovian model that is rich enough to exhibit superdiffusion normal diffusion and subdiffusion regimes kumar harbola and lindenberg 2010 we numerically estimate propagators for this model and obtain good fits with a family of non levy propagators based on the tsallis q exponential function we conclude that stops and restrictions play similar roles in the long time limit of the propagator

quantitative fourier analysis of approximation techniques i interpolators and projectors we present a general fourier based method that provides an accurate prediction of the approximation error as a function of the sampling step t our formalism applies to an extended class of convolution based signal approximation techniques which includes interpolation generalized sampling with prefiltering and the projectors encountered in wavelet theory we claim that we can predict the l sup 2 approximation error by integrating the spectrum of the function to approximate not necessarily bandlimited against a frequency kernel e spl omega that characterizes the approximation operator this prediction is easier yet more precise than was previously available our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function our error prediction is exact for stationary processes as well as for bandlimited signals we apply this method to the comparison of standard interpolation and approximation techniques our method has interesting implications for approximation theory in particular we use our results to obtain some new asymptotic expansions of the error as t spl rarr 0 as well as to derive improved upper bounds of the kind found in the strang fix 1971 theory we finally show how we can design quasi interpolators that are near optimal in the least squares sense

continuous scatter search an analysis of the integration of some combination methods and improvement strategies scatter search is an evolutionary method that shares with genetic algorithms a well known evolutionary approach the employment of a combination method that combines the features of two parent vectors to form several offspring furthermore it uses improvement strategies to efficiently produce the local tuning of the solutions an important aspect concerning scatter search is the trade off between the exploration abilities of the combination method and the exploitation capacity of the improvement mechanism in this paper we deal with a continuous version of the scatter search which works directly with vectors of real components our objective is to study the balance between the reliability induced by the combination method and the accuracy levels provided by the improvement mechanism in continuous scatter search to do this we analyse two combination methods that may be applied to continuous scatter search 1 the blx a operator which is one of the most effective combination methods for real coded genetic algorithms and 2 the average combination method which is the classical combination method for continuous scatter search we investigate the interrelations that exist between

a tabu search approach for the minimum sum of squares clustering problem in this paper a tabu search based clustering approach called ts clustering is proposed to deal with the minimum sum of squares clustering problem in the ts clustering algorithm five improvement operations and three neighborhood modes are given the improvement operation is used to enhance the clustering solution obtained in the process of iterations and the neighborhood mode is used to create the neighborhood of tabu search the superiority of the proposed method over some known clustering techniques is demonstrated for artificial and real life data sets

directional dyadic wavelet transforms design and algorithms we propose a simple and efficient technique for designing translation invariant dyadic wavelet transforms dwts in two dimensions our technique relies on an extension of the work of duval destin et al 1993 where dyadic decompositions are constructed starting from the continuous wavelet transform the main advantage of this framework is that it allows for a lot of freedom in designing two dimensional 2 d dyadic wavelets we use this property to construct directional wavelets whose orientation filtering capabilities are very important in image processing we address the efficient implementation of these decompositions by constructing approximate qmfs through an l sup 2 optimization we also propose and study an efficient implementation in the fourier domain for dealing with large filters

integrated crossover rules in real coded genetic algorithms abstract modifications in crossover rules and localization of searches are suggested to the real coded genetic algorithms for continuous global optimization central to our modifications is the integration of different crossover rules within the genetic algorithm numerical experiments using a set of 50 test problems indicate that the resulting algorithms are considerably better than the previous version considered and offer a reasonable alternative to many currently available global optimization algorithms especially for problems requiring direct search type methods

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

an intelligent genetic algorithm designed for global optimization of multi minima functions many practical problems often lead to large non convex non linear programming problems that have multi minima the global optimization algorithms of these problems have received much attention over the last few years generally stochastic algorithms are suitable for these problems but not efficient when there are too many minima genetic algorithms are stochastic search approaches based on randomized operators such as selection crossover and mutation inspired by the natural reproduction and evolution of the living creatures however the existing genetic algorithms cannot solve global optimization of multi minima functions effectively a new algorithm called intelligent genetic algorithm iga is proposed for the global optimization of multi minima functions iga integrates many cross operator mutation operator and reattempt operation it can select the appropriate cross operator mutation operator or reattempt operation according to the current optimization result it converges to the global optimization solution without the influence of random searching process at first this paper introduces the foundation for designing intelligent genetic algorithm secondly this paper reports on the development of an intelligent genetic algorithm approach for global optimization problems thirdly the proposed method is illustrated by means of some numerical examples finally the conclusions of this study are drawn with possible directions for subsequent studies the feasibility the efficiency and the effectiveness of iga are tested in detail through a set of benchmark multi modal functions of which global and local minima are known the experimental results suggest that results from iga are better than results from other methods in conclusion the performance of iga is better than that of other methods iga results are satisfactory for all the functions

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem