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

two point distortion for univalent functions abstract we discuss two point distortion inequalities for not necessarily normalized univalent functions f on the unit disk d by a two point distortion inequality we mean an upper or lower bound on the euclidean distance f a f b in terms of d d a b the hyperbolic distance between a and b and the quantities 1 a 2 f a 1 b 2 f b the expression 1 z 2 f z measures the infinitesimal length distortion at z when f is viewed as a function from d with hyperbolic geometry to the complex plane c with euclidean geometry we present a brief overview of the known two point distortion inequalities for univalent functions and obtain a new family of two point upper bounds that refine the classical growth theorem for normalized univalent functions

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

loops and branches of coexistence states in a lotka volterra competition model abstract a two species lotka volterra competition diffusion model with spatially inhomogeneous reaction terms is investigated the two species are assumed to be identical except for their interspecific competition coefficients viewing their common diffusion rate as a parameter we describe the bifurcation diagram of the steady states including stability in terms of two real functions of we also show that the bifurcation diagram can be rather complicated namely given any two positive integers l and b the interspecific competition coefficients can be chosen such that there exist at least l bifurcating branches of positive stable steady states which connect two semi trivial steady states of the same type they vanish at the same component and at least b other bifurcating branches of positive stable steady states that connect semi trivial steady states of different types

asymmetric diffusion in a two patch consumer resource system abstract this paper considers a two patch system with consumer diffusion which characterizes laboratory experiments and includes exploitable resources using dynamical systems theory we exhibit global dynamics of the one patch subsystem and show existence of stable positive equilibria in the two patch system based on rigorous analysis we demonstrate that heterogeneously distributed resources with asymmetric diffusion can support higher total population abundance than those with symmetric diffusion or without diffusion a novel finding of this work is that the asymmetric diffusion can make heterogeneously distributed resources support higher total population abundance than homogeneously distributed resources even with species diffusion which extends previous theory meanwhile we reveal that intermediate asymmetry is favorable for total population abundance while extremely large or extremely small asymmetry is unfavorable our results are consistent with experimental observations and provide new insights numerical simulations confirm and extend the results

on the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms although evolutionary algorithms eas have some operators which let them explore the whole search domain still they get trapped in local minima when multimodality of the objective function is increased to improve the performance of eas many optimization techniques or operators have been introduced in recent years however it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions some of which have been noted in previous research and solutions to eliminate them have been proposed in this article we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some eas such as covariance matrix adaptation evolution strategy cma es this method based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions is considered as a robust and efficient method however as far as black box optimization problems are considered no special trend in the behavior of the objective function can be assumed consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems to improve the performance of cma es the elite search sub algorithm is introduced and implemented in the basic algorithm importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end

effect of a protection zone in the diffusive leslie predator prey model abstract in this paper we consider the diffusive leslie predator prey model with large intrinsic predator growth rate and investigate the change of behavior of the model when a simple protection zone 0 for the prey is introduced as in earlier work y du j shi a diffusive predator prey model with a protection zone j differential equations 229 2006 63 91 y du x liang a diffusive competition model with a protection zone j differential equations 244 2008 61 86 we show the existence of a critical patch size of the protection zone determined by the first dirichlet eigenvalue of the laplacian over 0 and the intrinsic growth rate of the prey so that there is fundamental change of the dynamical behavior of the model only when 0 is above the critical patch size however our research here reveals significant difference of the model s behavior from the predator prey model studied in y du j shi a diffusive predator prey model with a protection zone j differential equations 229 2006 63 91 with the same kind of protection zone we show that the asymptotic profile of the population distribution of the leslie model is governed by a standard boundary blow up problem and classical or degenerate logistic equations

an sqp method for general nonlinear programs using only equality constrained subproblems in this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints compared with an older version p spellucci han s method without solving qp in a auslender w oettli j stoer eds optimization and optimal control lecture notes in control and information sciences vol 30 springer berlin 1981 pp 123 141 it is much simpler to implement and allows any kind of changes of the working set in every step our method relies on a strong regularity condition as far as it is applicable the new approach is superior to conventional sqp methods as demonstrated by extensive numcrical tests 1998 the mathematical programming society inc published by elsevier science b v

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

effects of a degeneracy in the competition model part i classical and generalized steady state solutions abstract we study the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of we show that there exists a critical number such that if then the model behaves similarly to the well studied classical competition model where all the coefficient functions are positive constants but when new phenomena occur our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative but can be qualitative as well in part i here we mainly study two kinds of steady state solutions which determine the dynamics of the model one consists of finite functions while the other consists of generalized functions which satisfy u v 0 on the part of the domain that b x vanishes but are positive and finite on the rest of the domain and are determined by certain boundary blow up systems the research is continued in part ii where these two kinds of steady state solutions will be used to determine the dynamics of the model

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

convergence in competition models with small diffusion coefficients abstract it is well known that for reaction diffusion 2 species lotka volterra competition models with spatially independent reaction terms global stability of an equilibrium for the reaction system implies global stability for the reaction diffusion system this is not in general true for spatially inhomogeneous models we show here that for an important range of such models for small enough diffusion coefficients global convergence to an equilibrium holds for the reaction diffusion system if for each point in space the reaction system has a globally attracting hyperbolic equilibrium this work is planned as an initial step towards understanding the connection between the asymptotics of reaction diffusion systems with small diffusion coefficients and that of the corresponding reaction systems

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

realization of prescribed patterns in the competition model we demonstrate that for any prescribed set of finitely many disjoint closed subdomains d1 dm of a given spatial domain in rn if d1 d2 a1 a2 c d e are positive continuous functions on and b x is identically zero on d d1 dm and positive in the rest of then for suitable choices of the parameters and all small e 0 the competition model ut x t d1 x u x t a1 x u e 1b x 1 u2 c x uv vt x t d2 x v x t a2 x v e x v2 e 1d x uv x t 0 under natural boundary conditions on possesses an asymptotically stable positive steady state solution ue ve that has pattern d that is roughly speaking as e 0 ue converges to a positive function over d while it converges to 0 over the rest of on the other hand ve converges to 0 over d but converges to some positive function in the rest of in other words the two competing species ue and ve become spatially segregated as e 0 with ue concentrating on d and ve concentrating on d

a diffusive competition model with a protection zone this paper is concerned with a two species diffusive competition model with a protection zone for the weak competitor our mathematical results imply that when the protection zone is above a certain critical patch size determined by the birth rate of the weak competitor the weak species almost always survives but it cannot survive when the protection zone is below the critical size and its competitor is strong enough while this is the main feature of the model the actual dynamical behavior of the reaction diffusion system is more complicated the key to reveal the main feature of the system lies in a detailed analysis of the attracting regions of its steady state solutions our mathematical analysis shows that compared with the predator prey model discussed in yihong du junping shi a diffusive predator prey model with a protect zone j differential equations 226 2006 63 91 the protection zone has some essentially different effects on the fine dynamics of the competition model

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

spatial heterogeneity of resources versus lotka volterra dynamics abstract the problem is motivated by a consideration of two phenotypes of a species in a strongly heterogenous spatial environment the phenotypes vary in their diffusion rates and interspecific interactions the aim is to investigate the relative strengths of the diffusion and reaction effects the problem is thus of competing species type but there are many questions which arise which are not covered by standard theory we investigate in particular the stability of the equilibria and the existence of coexistence solutions with emphasis on cases where the spatial variation of the environment becomes large we discuss briefly the implications of our results for the principle of competitive exclusions and for the question of the evolution of diffusion discussed in dockery et al j math biol 37 1998 61 83

a semilinear parabolic system for migration and selection in population genetics abstract the semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated the population occupies a finite habitat of arbitrary dimensionality and shape the selection coefficients depend on position the drift and diffusion coefficients may do so for two alleles the scalar case the global analysis of d henry 1981 geometric theory of semilinear parabolic equations lecture notes in mathematics vol 840 springer verlag berlin is extended from homogeneous isotropic migration corresponding to the laplacian to arbitrary migration corresponding to an arbitrary elliptic operator for multiple alleles sufficient conditions are given for the global loss of an allele that is nowhere the fittest in the case of no dominance with at least one change in the direction of selection sufficient conditions are established for global convergence to a stable equilibrium with all the intermediate alleles absent and one or two extreme alleles present sufficient conditions on the migration pattern for casting the elliptic operator into variational form are proved in this case the above results become more explicit

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

diffusion effect and stability analysis of a predator prey system described by a delayed reaction diffusion equations in this paper we consider a delayed reaction diffusion equations which describes a two species predator prey system with diffusion terms and stage structure by using the linearization method and the method of upper and lower solutions we study the local and global stability of the constant equilibria respectively the results show that the free diffusion of the delayed reaction diffusion equations has no effect on the populations when the diffusion is too slow otherwise the free diffusion has a certain influence on the populations however the influence can be eliminated by improving the parameters to satisfy some suitable conditions

qualitative analysis of a lotka volterra predator prey system with migration abstract two species lotka volterra predator prey models are analyzed we study some qualitative criteria such as stability the existence of a coexistence equilibrium for the models for system with migration criteria are derived for the asymptotic behaviors with 0 or

evolution of a semilinear parabolic system for migration and selection in population genetics abstract the semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated the population occupies a finite habitat of arbitrary dimensionality and shape i e a bounded open domain in rd the selection coefficients depend on position and may depend on the gene frequencies the drift and diffusion coefficients may depend on position sufficient conditions are given for the global loss of an allele and for its protection from loss a sufficient condition for the existence of at least one internal equilibrium is also offered and the profile of any internal equilibrium in the zero migration limit is obtained

uniqueness and complete dynamics in heterogeneous competition diffusion systems in this paper we study the interactions between diffusion and heterogeneity of the environment in the classical diffusive lotka volterra competition systems in the weak competition case we establish the uniqueness hence the global asymptotic stability of coexistence steady states under various circumstances and thereby we obtain a complete understanding of the change in dynamics when one of the interspecific competition coefficients is small

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

hybrid harmony search and artificial bee colony algorithm for global optimization problems harmony search hs is one of the newest and the easiest to code music inspired heuristics for optimization problems in order to enhance the accuracy and convergence rate of harmony search a hybrid harmony search is proposed by incorporating the artificial bee colony algorithm abc the artificial bee colony algorithm is a new swarm intelligence technique inspired by intelligent foraging behavior of honey bees the abc and its variants are used to improve harmony memory hm to compare and analyze the performance of our proposed hybrid algorithms a number of experiments are carried out on a set of well known benchmark global optimization problems the effects of the parameters about the hybrid algorithms are discussed by a uniform design experiment numerical results show that the proposed algorithms can find better solutions when compared to hs and other heuristic algorithms and are powerful search algorithms for various global optimization problems

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

unbounded connected component of the positive solution set of nonlinear operator equation and its applications abstract in this paper by using global bifurcation theories we obtain some results for structure of positive solution set of some nonlinear equations with parameters as a result we obtain some existence results for positive solutions of the nonlinear operator equation the main result can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinearities are positone

dynamics of a diffusive competition model in spatially heterogeneous environment abstract we discuss the effects of dispersal rate and spatial heterogeneity on population dynamics via a diffusive lotka volterra competition model under homogeneous dirichlet boundary conditions by the theory of monotone dynamical system we show that in the weak competition case for some ranges of dispersal rate of competing species 1 if dispersal rate of competing species 2 is sufficiently small there exists a unique coexistence steady state of the model which is globally asymptotically stable moreover for certain ranges of dispersal rate of competing species 1 we derive the limit behavior of the coexistence steady state as dispersal rate of competing species 2 tends to zero on the other hand we demonstrate that for some larger scopes of dispersal rate of competing species 1 if dispersal rate of competing species 2 is small enough there is no coexistence steady state whereas one of the semi trivial steady states of the model is globally asymptotically stable

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

an intelligent global harmony search approach to continuous optimization problems abstract harmony search algorithm is a meta heuristic optimization method imitating the music improvisation process where musicians improvise their instruments pitches searching for a perfect state of harmony to solve continuous optimization problems more efficiently this paper presents an improved harmony search algorithm using the swarm intelligence technique applying the proposed algorithm to several well known benchmark problems it is shown that it can find better solutions in comparison with both basic harmony search algorithms and improved harmony search algorithms such as the self adaptive global best harmony search as well as novel global harmony search furthermore a study on the effect of changing the parameters of the proposed algorithm on its performance is carried out finally the proper values of the algorithm parameters are suggested

spatially heterogeneous lotka volterra competition abstract this paper studies the dynamics of the spatially heterogeneous diffusive lotka volterra competing species model it focuses special attention in ascertaining the linear stability and multiplicity of the coexistence steady states one of our main findings establishes that as soon as any steady state solution of the non spatial model is linearly unstable somewhere in the inhabiting territory any steady state of the spatial counterpart perturbing from it therein as the diffusion rates d 1 d 2 move away from 0 must be linearly unstable from this general principle one can derive a number of rather astonishing consequences as the multiplicity of the coexistence steady states when the non spatial model exhibits founder control competition somewhere in say bi even if bi is negligible empirically actually this is the first available multiplicity result for small diffusion rates finally based on a celebrated identity by m picone 1910 we are able to establish a new rather striking uniqueness result valid for general spatially heterogeneous models

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

a singular perturbation result in competition theory abstract this paper establishes a generalized version of the singular perturbation results given by v hutson et al 10 theorem 4 1 and x he and w m ni 6 theorem 4 2 iii in particular it ascertains the limiting profiles of the coexistence states of the classical lotka volterra model for two competing species as the diffusion coefficients approximate zero they are provided by the global attractors of the underlying non spatial model whenever they exist

two point distortion bounds for biholomorphic mappings of the ball in cn abstract lower and upper two point distortion bounds for families f of biholomorphic mappings on the unit ball b of c n are given in terms of the trace order of the linear invariant family generated by f bounds on ratios involving the derivative and jacobian of the mappings in f and the caratheodory distance on b by two point distortion bounds we mean estimates on f b f a for a b b and f f this immediately results in growth bounds for such mappings a contrast is drawn between these bounds and two point distortion bounds in terms of the norm order of the generated linear invariant family as part of our work we develop a lower distortion bound for automorphisms of b that may be of independent interest

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

a diffusive predator prey model with a protection zone in this paper we study the effects of a protection zone 0 for the prey on a diffusive predator prey model with holling type ii response and no flux boundary condition we show the existence of a critical patch size described by the principal eigenvalue d 0 of the laplacian operator over 0 with homogeneous dirichlet boundary conditions if the protection zone is over the critical patch size i e if d 0 is less than the prey growth rate then the dynamics of the model is fundamentally changed from the usual predator prey dynamics in such a case the prey population persists regardless of the growth rate of its predator and if the predator is strong then the two populations stabilize at a unique coexistence state if the protection zone is below the critical patch size then the dynamics of the model is qualitatively similar to the case without protection zone but the chances of survival of the prey species increase with the size of the protection zone as generally expected our mathematical approach is based on bifurcation theory topological degree theory the comparison principles for elliptic and parabolic equations and various elliptic estimates

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

global dynamics of the lotka volterra competition diffusion system diffusion and spatial heterogeneity i in the first part of this series of three papers we investigate the combined effects of diffusion spatial variation and competition ability on the global dynamics of a classical lotka volterra competition diffusion system we establish the main results that determine the global asymptotic stability of semitrivial as well as coexistence steady states hence a complete understanding of the change in dynamics is obtained immediately our results indicate confirm that when spatial heterogeneity is included in the model diffusion driven exclusion could take place when the diffusion rates and competition coefficients of both species are chosen appropriately 2015 wiley periodicals inc

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

the effects of diffusion and spatial variation in lotka volterra competition diffusion system ii the general case abstract it is well known that the interactions between diffusion and spatial heterogeneity could create very interesting phenomena in this series of two papers using the classical lotka volterra competition system we will illustrate the combined effects of dispersal and spatial variations on the outcome of the competition in part i with the total resources being fixed at exactly the same level we first show that a heterogeneous distribution of resources is usually superior to its homogeneous counterpart in the presence of diffusion then we study the more general case when both species have heterogeneous carrying capacities but still with the same total resources limiting behaviors of co existence steady states as the dispersal rates tend to 0 or are also obtained in part ii we continue our investigation but under much broader situations including different strengths and distributions of the resources and with different competition abilities

effects of a degeneracy in the competition model part ii perturbation and dynamical behaviour this is the second part of our study on the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of in part i we mainly discussed the existence of two kinds of steady state solutions of this system namely the classical steady states and the generalized steady states here we use these solutions to determine the dynamics of the model we do this with the help of the perturbed model where b x is replaced by b x e which itself is a classical competition model this approach also reveals the interesting relationship between the steady state solutions both classical and generalized of the above system and that of the perturbed system

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

large diffusivity and asymptotic behavior in parabolic systems abstract for systems of reaction diffusion equations with neumann boundary conditions it is shown that the solutions are asymptotic to the solutions of an ordinary differential equation if the diffusivity is large the methods apply also to reaction diffusion systems with time delays

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

fish hook shaped global bifurcation branch of a spatially heterogeneous cooperative system with cross diffusion abstract in this paper we will consider the following strongly coupled cooperative system in a spatially heterogeneous environment with neumann boundary condition u u u b x v 0 x 1 k x u v v v d x u 0 x u v 0 x where is a bounded domain in r n n 1 with smooth boundary k is a positive constant and are real constants which may be non positive b x 0 and d x 0 are continuous functions in x is a smooth positive function in with x 0 is the outward unit normal vector on and for the case 0 we show that if is small and k is large a spatial segregation of x and b x can cause the positive solution curve to form an unbounded fish hook shaped curve with parameter for the case 0 if is small and k is large and the cooperative effect is strong for species u and very weak for species v then the positive solution set also forms an unbounded fish hook shaped continuum these results are quite different from those of predator prey systems and the cooperative system under dirichlet boundary condition both of which can form a bounded continuum our results deduce that the spatial heterogeneity of environments can produce multiple coexistence states our method of analysis is based on the bifurcation theory and the lyapunov schmidt procedure

on a lotka volterra competition diffusion advection system homogeneity vs heterogeneity abstract as we know interactions between movement and environmental heterogeneity could create very interesting phenomena in population dynamics in this paper based on a lotka volterra competition diffusion advection system we try to reveal the combined effect of movement and spatial variations on the outcome of competition for the purpose of comparison we suppose that the total resources for two populations are fixed at the same level but one distribution is even across space while the other one not our main results suggest that the contest between heterogeneous and homogeneous distribution is very complex either one of the two competitors becomes the final single winner exclusion or both populations coexist eventually coexistence depending closely on the movement rates and the shape of the given resource

asymptotic behavior of the principal eigenvalue for cooperative periodic parabolic systems and applications abstract the effects of spatial heterogeneity on population dynamics have been studied extensively however the effects of temporal periodicity on the dynamics of general periodic parabolic reaction diffusion systems remain largely unexplored as a first attempt to understand such effects we analyze the asymptotic behavior of the principal eigenvalue for linear cooperative periodic parabolic systems with small diffusion rates as an application we show that if a cooperative system of periodic ordinary differential equations has a unique positive periodic solution which is globally asymptotically stable then the corresponding reaction diffusion system with either the neumann or regular oblique derivative boundary condition also has a unique positive periodic solution which is globally asymptotically stable provided that the diffusion coefficients are sufficiently small the role of temporal periodicity spatial heterogeneity and their combined effects with diffusion will be studied in subsequent papers for further understanding and illustration

asymptotic profiles of steady states for a diffusive sis epidemic model with mass action infection mechanism abstract mass action and standard incidence are two major infection mechanisms in modelling spread of infectious diseases spatial heterogeneity plays an important role in spread of infectious diseases and hence motivates and advocates diffusive models for disease dynamics by analyzing a diffusive sis model with the standard incidence infection mechanism some recent works 2 12 have investigated the asymptotical profiles of the endemic steady state for large and small diffusion rates and the results show that controlling the diffusion rate of the susceptible individuals can help eradicate the infection while controlling the diffusion rate of the infectious individuals cannot this paper aims to reveal the difference between the two infection mechanisms in a spatially heterogeneous environment to this end we consider a diffusive sis model of the same structure but with the mass action infection adopted and explore the asymptotic profiles of the endemic steady state for small and large diffusion rates it turns out that the new model poses some new challenges due to the nonlocal term in the equilibrium problem and the unboundedness of the nonlinear term our results on this new model reveal some fundamental differences between the two transmission mechanisms in such spatial models which may provide some implications on disease modelling and controls

on the basic reproduction number of reaction diffusion epidemic models the basic reproduction number r 0 serves as a threshold parameter of many epidemic models for disease extinction or spread the purpose of this paper is to investigate r 0 for spatial reaction