a new meta heuristic algorithm for continuous engineering optimization harmony search theory and practice most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point these algorithms however reveal a limited approach to complicated real world optimization problems if there is more than one local optimum in the problem the result may depend on the selection of an initial point and the obtained optimal solution may not necessarily be the global optimum this paper describes a new harmony search hs meta heuristic algorithm based approach for engineering optimization problems with continuous design variables this recently developed hs algorithm is conceptualized using the musical process of searching for a perfect state of harmony it uses a stochastic random search instead of a gradient search so that derivative information is unnecessary various engineering optimization problems including mathematical function minimization and structural engineering optimization problems are presented to demonstrate the effectiveness and robustness of the hs algorithm the results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms 2004 elsevier b v all rights reserved

windowed fourier phase completeness and signal reconstruction it is established that a signal either continuous or discrete is determined up to a multiplicative constant by its windowed fourier phase wfp at any frequency this result indicates that the wfp contains richer information than zero crossings and peaks it also provides insight into why wfp based image matching may achieve highly accurate and stable results to experimentally demonstrate the completeness of the wfp an algorithm is developed to reconstruct signals from the wfp

two parameter tuned meta heuristics for a discounted inventory control problem in a fuzzy environment highlightsa nearly real world mp mp inventory control problem under discounts and budget constraints is investigated the required storages space is considered a fuzzy number the goal is to find the optimal ordered quantities of the products a hsa is developed to solve the complex problem in this paper a nearly real world multi product multi period inventory control problem under budget constraint is investigated where shortages in combination with backorders and lost sales are considered for each product the ordered quantities of products are delivered in batch sizes with a known number of boxes each containing a pre specified number of products some products are purchased under an all unit discount policy and others are purchased under an incremental quantity discount with fuzzy discount rates the goal is to find the optimal ordered quantities of products such that not only the total inventory cost but also the required storage space considered as a fuzzy number to store the products is minimized the weighted linear sum of objectives is applied to generate a single objective model for the bi objective problem at hand and a harmony search algorithm is developed to solve the complex inventory problem as no benchmarks are available to validate the obtained results a particle swarm optimization algorithm is employed to solve the problem in addition to validate the results given by the harmony search method the parameters of both algorithms are tuned using both taguchi and response surface methodology rsm finally to assess the performance of the proposed algorithms some numerical examples are generated and the results are compared statistically

acceleration of limit periodic continued fractions by the t m transformation we consider limit periodic continued fractions b 0 a 1 1 a n 1 where lim n a n a is finite and not on the ray 1 4 of the negative real axis using related properties of continued fractions we obtain the t m process considered by gray and clark and the process considered by w j thron and h waadeland it follows the possibility of choosing the best process according to the convergence behaviour of the sequences a n

nonlinearities in stereoscopic phase differencing exploiting the quasi linear relationship between local phase and disparity phase differencing registration algorithms provide a fast powerful means for disparity estimation unfortunately these phase differencing techniques suffer a significant impediment phase nonlinearities in regions of phase nonlinearity the signals under consideration possess properties that invalidate the use of phase for disparity estimation this paper uses the amenable properties of gaussian white noise images to analytically quantify these properties the improved understanding gained from this analysis enables us to better understand current methodologies for detecting regions of phase instability most importantly we introduce a new more effective means for identifying these regions based on the second derivative of phase

image representation by one bit fourier phase theory sampling and coherent image model the problem of recovering an image from its fourier transform phase quantized to one bit or equivalently finding the locations of the zero crossings of the real part of the fourier transform is addressed theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band limited image it is then shown that sampling in the frequency domain presents a major obstacle to obtaining good reconstruction results the one bit fourier phase reconstruction problem is then considered when the original image is coherent i e the image phase is random and highly uncorrelated examples are given which demonstrate that the information loss produced by frequency sampling is not as severe as that in the nonclassical problem motivated by digital phase only holograms a known random diffuser is used as the image phase and a well known iterative reconstruction procedure is extended to incorporate the knowledge of the image phase at each stage of the iteration this reconstruction method produces good image quality by using a few iterations unlike its noncoherent counterpart

optimization of sparse linear arrays using harmony search algorithms a sparse linear array composed of a uniformly spaced core subarray and an extended sparse subarray is synthesized using a harmony search hs and an exploratory harmony search ehs algorithms the optimal solution is searched by changing the amplitudes of all the elements and the positions of the extended elements under a set of practical constraints performance of the ehs the hs a genetic algorithm ga and a particle swarm optimization pso algorithm has also been compared in synthesizing these sparse linear arrays

image matching using the windowed fourier phase a theoretical framework is presented in which windowed fourier phase wfp is introduced as the primary matching primitive zero crossings and peaks correspond to special values of the phase the wfp is quasi linear and dense and its spatial period and slope are controlled by the scale this framework has the following important characteristics 1 matching primitives are available almost everywhere to convey dense disparity information in every channel either coarse or fine 2 the false target problem is significantly mitigated 3 the matching is easier uniform and can be performed by a network suitable for parallel computer architecture 4 the matching is fast since very few iterations are needed in fact the wfp is so informative that the original signal can be uniquely determined up to a multiplicative constant by the wfp in any channel the use of phase as matching primitive is also supported by some existing psychophysical and neurophysiological studies an implementation of the proposed theory has shown good results from synthesized and natural images

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

an improved adaptive binary harmony search algorithm harmony search hs inspired by the music improvisation process is a new meta heuristic optimization method and has been successfully used to tackle the optimization problems in discrete or continuous space although the standard hs algorithm is able to solve binary coded optimization problems the pitch adjustment operator of hs is degenerated in the binary space which spoils the performance of the algorithm based on the analysis of the drawback of the standard hs an improved adaptive binary harmony search abhs algorithm is proposed in this paper to solve the binary coded problems more effectively various adaptive mechanisms are examined and investigated and a scalable adaptive strategy is developed for abhs to enhance its search ability and robustness the experimental results on the benchmark functions and 0 1 knapsack problems demonstrate that the proposed abhs is efficient and effective which outperforms the binary harmony search the novel global harmony search algorithm and the discrete binary particle swarm optimization in terms of the search accuracy and convergence speed

reconstructions from zero crossings in scale space in computer vision the one parameter family of images obtained from the laplacian of a gaussian filtered version of the image parameterized by the width of the gaussian has proved to be a useful data structure for the extraction of feature data in particular the zero crossings of this so called scale space data are associated with edges and have been proposed by d marr 1982 and others as the basis of a representation of the image data the question arises as to whether the representation is complete and stable the authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations they formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error and they present results showing that the reconstruction is possible but can be unstable they further show that the method applies when gradient data along the zero crossings are included in the representation and they demonstrate empirically that the reconstruction is then stable

a tabu harmony search based approach to fuzzy linear regression we propose an unconstrained global continuous optimization method based on tabu search and harmony search to support the design of fuzzy linear regression flr models tabu and harmony search strategies are used for diversification and intensification of flr respectively the proposed approach offers the flexibility to use any kind of an objective function based on client s requirements or requests and the nature of the dataset and then attains its minimum error moreover we elaborate on the error produced by this method and compare it with the errors resulting from the other known estimation methods to study the performance of the method three categories of datasets are considered numeric inputs symmetric fuzzy outputs symmetric fuzzy inputs symmetric fuzzy outputs and numeric inputs asymmetric fuzzy outputs through a series of experiments we demonstrate that in terms of the produced error with different model fitting measurements the proposed method outperforms or is pareto equivalent to the existing methods reported in the literature

a novel meta heuristic optimization algorithm inspired by group hunting of animals hunting search a novel optimization algorithm is presented inspired by group hunting of animals such as lions wolves and dolphins although these hunters have differences in the way of hunting they are common in that all of them look for a prey in a group the hunters encircle the prey and gradually tighten the ring of siege until they catch the prey in addition each member of the group corrects its position based on its own position and the position of other members if the prey escapes from the ring hunters reorganize the group to siege the prey again several benchmark numerical optimization problems constrained and unconstrained are presented here to demonstrate the effectiveness and robustness of the proposed hunting search hus algorithm the results indicate that the proposed method is a powerful search and optimization technique it yields better solutions compared to those obtained by some current algorithms when applied to continuous problems

an improved harmony search algorithm for solving optimization problems this paper develops an improved harmony search ihs algorithm for solving optimization problems ihs employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search hs algorithm in this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented the ihs algorithm has been successfully applied to various benchmarking and standard engineering optimization problems numerical results reveal that the proposed algorithm can find better solutions when compared to hs and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems

harmony search algorithm with dynamic control parameters abstract harmony search hs is a population based meta heuristic imitating the music improvisation process which has been successfully applied to optimization problems in recent years this paper presents an effective harmony search algorithm for solving global continuous optimization problems the proposed method presents a novel improvisation process which is different from the classical hs in two aspects firstly the candidate harmony is chosen from the harmony memory by a tournament selection rule so that the harmonies with better fitness will have more opportunities to be used in generating new harmonies secondly two key control parameters pitch adjustment rate par and bandwidth distance bw are adjusted dynamically with respect to the evolution of the search process and the different search spaces of the optimization problems numerical results demonstrate that the proposed algorithm performs much better than the existing hs variants in terms of the solution quality and the stability

novel meta heuristic algorithms for clustering web documents clustering the web documents is one of the most important approaches for mining and extracting knowledge from the web recently one of the most attractive trends in clustering the high dimensional web pages has been tilt toward the learning and optimization approaches in this paper we propose novel hybrid harmony search hs based algorithms for clustering the web documents that finds a globally optimal partition of them into a specified number of clusters by modeling clustering as an optimization problem first we propose a pure harmony search based clustering algorithm that finds near global optimal clusters within a reasonable time then we hybridize k means and harmony clustering in two ways to achieve better clustering experimental results reveal that the proposed algorithms can find better clusters when compared to similar methods and also illustrate the robustness of the hybrid clustering algorithms

novel derivative of harmony search algorithm for discrete design variables calculus has widespread applications in science and engineering optimization is one of its major subjects where a problem can be mathematically formulated and its optimal solution is determined by using derivatives however this calculus based derivative technique can only be applied to real valued or continuous valued functions rather than discrete valued functions while there are many situations where design variables contain not continuous values but discrete values by nature in order to consider these realistic design situations this study proposes a novel derivative for discrete design variables based on a harmony search algorithm detailed analysis shows how this new stochastic derivative works in the bench mark function and fluid transport network design hopefully this new derivative as a fundamental technology will be utilized in various science and engineering problems

global best harmony search harmony search hs is a new meta heuristic optimization method imitating the music improvisation process where musicians improvise their instruments pitches searching for a perfect state of harmony a new variant of hs called global best harmony search ghs is proposed in this paper where concepts from swarm intelligence are borrowed to enhance the performance of hs the performance of the ghs is investigated and compared with hs and a recently developed variation of hs the experiments conducted show that the ghs generally outperformed the other approaches when applied to ten benchmark problems the effect of noise on the performance of the three hs variants is investigated and a scalability study is conducted the effect of the ghs parameters is analyzed finally the three hs variants are compared on several integer programming test problems the results show that the three approaches seem to be an efficient alternative for solving integer programming problems 2007 elsevier inc all rights reserved

a self adaptive global best harmony search algorithm for continuous optimization problems this paper presents a self adaptive global best harmony search sghs algorithm for solving continuous optimization problems in the proposed sghs algorithm a new improvisation scheme is developed so that the good information captured in the current global best solution can be well utilized to generate new harmonies the harmony memory consideration rate hmcr and pitch adjustment rate par are dynamically adapted by the learning mechanisms proposed the distance bandwidth bw is dynamically adjusted to favor exploration in the early stages and exploitation during the final stages of the search process extensive computational simulations and comparisons are carried out by employing a set of 16 benchmark problems from literature the computational results show that the proposed sghs algorithm is more effective in finding better solutions than the state of the art harmony search hs variants

successive modifications of limit periodic continued fractions it is well known that limit periodic continued fractions can be accelerated by modifications using converging factors in this paper the repeated use of modifications is studied in the case of a constant converging factor and in the case of aitken s d 2 process based on these modifications a method for controlling the error is proposed

chaotic harmony search algorithms harmony search hs is one of the newest and the easiest to code music inspired heuristics for optimization problems like the use of chaos in adjusting note parameters such as pitch dynamic rhythm duration tempo instrument selection attack time etc in real music and in sound synthesis and timbre construction this paper proposes new hs algorithms that use chaotic maps for parameter adaptation in order to improve the convergence characteristics and to prevent the hs to get stuck on local solutions this has been done by using of chaotic number generators each time a random number is needed by the classical hs algorithm seven new chaotic hs algorithms have been proposed and different chaotic maps have been analyzed in the benchmark functions it has been detected that coupling emergent results in different areas like those of hs and complex dynamics can improve the quality of results in some optimization problems it has been also shown that some of the proposed methods have somewhat increased the solution quality that is in some cases they improved the global searching capability by escaping the local solutions

geometric selective harmony search abstract this paper presents a new variant of the harmony search algorithm called geometric selective harmony search the main differences between the proposed variant and the original formulation of harmony search are the integration of a selection procedure in the improvisation phase a new memory consideration process that makes use of a recombination operator and the integration of a new mutation operator we compare geometric selective harmony search with the original harmony search with another existing variant called improved harmony search and with two existing selection based harmony search algorithms the experimental study was conducted on 20 benchmark problems belonging to the cec 2010 suite one of the most well known state of the art benchmark sets the results show that geometric selective harmony search outperforms the other studied methods with statistical significance in almost all the considered benchmark problems

hybridizing harmony search algorithm with different mutation operators for continuous problems abstract harmony search hs is a recent ea inspired by musical improvisation process to seek a pleasing harmony mutation is a vital component used in evolutionary algorithms ea where a value in the population is randomly selected to be altered to improve the evolution process the original hs algorithm applies an operation similar to mutation during the random consideration operator during random selection operator a value within the range of the decision variable is selected randomly to explore different areas in the search space this paper aims at experimentally evaluating the performance of hs algorithm after replacing the random consideration operator in the original hs with five different mutation methods the different variations of hs are experimented on standard benchmark functions in terms of final obtained solution and convergence speed the results show that using polynomial mutation improves the performance of the hs algorithm for most of the used functions

global dynamic harmony search algorithm gdhs this paper presents a new modification of harmony search hs algorithm to improve its accuracy and convergence speed and eliminates setting parameters that have to be defined before optimization process and it is difficult to predict fixed values for all kinds of problems the proposed algorithm is named global dynamic harmony search gdhs in this modification all the key parameters are changed to dynamic mode and there is no need to predefine any parameters also the domain is changed to dynamic mode to help a faster convergence two experiments with large sets of benchmark functions are executed to compare the proposed algorithms with other ones in the first experiment 15 benchmark problems are used to compare the proposed algorithm with other similar algorithms based on the harmony search method and in the second experiment 47 benchmark problems are used to compare the performance of the gdhs with other algorithms from different families including ga pso de and abc algorithms results showed that the proposed algorithm outperforms the other algorithms considering the point that the gdhs does not require any predefined parameter

on the acceleration of limit periodic continued fractions a continued fraction c f k a n 1 is called limit periodic if mathop lim limits n to infty a n a fora anda 1 4 a 0 thron waadeland 1980 examined a modification of a limit periodic c f for accelerating the convergence this acceleration remains modest if thea n converge only logarithmically thus it is proposed to apply an euler summability method to the series equivalent to the c f properties of the equivalent function are derived these properties are used for choosing appropriate parameters for the summability method such that a considerable acceleration can be expected even if thea n converge logarithmically

hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems this study presents a hybrid harmony search algorithm hhsa to solve engineering optimization problems with continuous design variables although the harmony search algorithm hsa has proven its ability of finding near global regions within a reasonable time it is comparatively inefficient in performing local search in this study sequential quadratic programming sqp is employed to speed up local search and improve precision of the hsa solutions moreover an empirical study is performed in order to determine the impact of various parameters of the hsa on convergence behavior various benchmark engineering optimization problems are used to illustrate the effectiveness and robustness of the proposed algorithm numerical results reveal that the proposed hybrid algorithm in most cases is more effective than the hsa and other meta heuristic or deterministic methods

a novel modified differential evolution algorithm for constrained optimization problems a novel modified differential evolution algorithm nmde is proposed to solve constrained optimization problems in this paper the nmde algorithm modifies scale factor and crossover rate using an adaptive strategy for any solution if it is at a standstill its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions we can obtain satisfactory feasible solutions for constrained optimization problems by combining the nmde algorithm and a common penalty function method experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems and it can be an efficient alternative to solving constrained optimization problems

randomness as source for inspiring solution search methods music based approaches abstract as the world progresses towards industrialization engineering problems become increasingly complex and it becomes even more difficult to optimize these problems the reason for this is the increasing complexity of variables dimensions space complexity and time complexity in order to be able to cope with such a situation randomized intelligent optimization and search algorithms are proposed to optimize numerical benchmarking problems multi objective problems and solve difficult problems including a large number of variables dimensions constraints and objectives metaheuristic random search and optimization methods are widely used to search and find the most appropriate solutions for large scale optimization problems in an acceptable time they are general purposed methods that can be efficiently applied to optimization and search problems without too much modification to accommodate a specific probing metaheuristic optimization algorithms are generally categorized as physics music sociology biology swarm mathematics plant chemistry sports water and hybrid based although most of the intelligent metaheuristic methods are inspired by physics and biology concepts activities rules and processes in music can be an inspiration source of new intelligent optimization and search techniques that is why novel and efficient music inspired intelligent optimization and search methods having effective exploitation and exploration capabilities have been proposed in this paper music based metaheuristic optimization algorithms were gathered and analyzed for the first time harmony search and its versions melody search algorithm and method of musical composition have been examined in detail furthermore their performances have been compared within both unconstrained numerical benchmark functions and constrained problems and the obtained results from music based algorithms have been comparatively studied

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

a note on teaching learning based optimization algorithm teaching learning based optimization tlbo seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances it is reported that it outperforms some of the well known metaheuristics regarding constrained benchmark functions constrained mechanical design and continuous non linear numerical optimization problems such a breakthrough has steered us towards investigating the secrets of tlbo s dominance this paper reports our findings on tlbo qualitatively and quantitatively through code reviews and experiments respectively our findings have revealed three important mistakes regarding tlbo 1 at least one unreported but important step 2 incorrect formulae on a number of fitness function evaluations and 3 misconceptions about parameter less control additionally unfair experimental settings conditions were used to conduct experimental comparisons e g different stopping criteria the experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy the ultimate goal of this paper is to provide reminders for metaheuristics researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects and to allow fair comparisons of the tlbo algorithm to be made with other metaheuristic algorithms

a heuristic approach to find the global optimum of function this paper presents the modified ant colony optimization maco based algorithm to find global optimum algorithm is based on that solution space of problem is restricted by the best solution of the previous iteration furthermore the proposed algorithm is that variables of problem are optimized concurrently this algorithm was tested on some standard test functions and successful results were obtained its performance was compared with the other algorithms and observed to be better

a hybrid pso ga algorithm for constrained optimization problems the main objective of this paper is to present a hybrid technique named as a pso ga for solving the constrained optimization problems in this algorithm particle swarm optimization pso operates in the direction of improving the vector while the genetic algorithm ga has been used for modifying the decision vectors using genetic operators the balance between the exploration and exploitation abilities have been further improved by incorporating the genetic operators namely crossover and mutation in pso algorithm the constraints defined in the problem are handled with the help of the parameter free penalty function the experimental results of constrained optimization problems are reported and compared with the typical approaches exist in the literature as shown the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature furthermore experimental results indicate that the proposed approach may yield better solutions to engineering problems than those obtained by using current algorithms

global best harmony search algorithm with control parameters co evolution based on pso and its application to constrained optimal problems a global best harmony search algorithm with control parameters co evolution based on particle swarm optimization pso ce ghs is proposed in pso ce ghs two control parameters i e harmony memory considering rate and pitch adjusting rate are encoded to be a symbiotic individual of original individual i e harmony vector harmony search operators are applied to evolve the original population and pso is applied to co evolve the symbiotic population thus with the evolution of the original population in pso ce ghs the symbiotic population is dynamically and self adaptively adjusted and the real time optimum control parameters are obtained the proposed pso ce ghs algorithm has been applied to various benchmark functions and constrained optimal problems the results show that the proposed algorithm can find better solutions when compared to hs and its variants

signal reconstruction from fourier transform sign information in this paper we present new results on the reconstruction of signals from only the sign of the real part of the fourier transform specifically we develop new theoretical results which state conditions under which two dimensional signals are uniquely specified to within a scale factor with this information and show that these conditions include a broad class of signals furthermore we apply this result to the problem of reconstructing two dimensional signals from their zero crossings we also present two algorithms for reconstructing a signal from sign information in either the time or frequency domain

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