a ga based fuzzy modeling approach for generating tsk models this paper proposes a new genetic based modeling method for building simple and well defined tsk models with scatter type input partitions our approach manages all attributes characterizing the structure of a tsk model simultaneously particularly it determines the number of rules the input partition the participating inputs in each rule and the consequent parameters the model building process is divided into two phases in phase one the structure learning task is formulated as a multi objective optimization problem which is resolved using a novel genetic based structure learning gbsl scheme apart from the mean square error mse and the number of rules three additional criteria are introduced in the fitness function for measuring the quality of the partitions optimization of these measures leads to models with representative rules small overlapping and efficient data cover in order to obtain models with accurate data fitting and good local performance the consequent parameters are determined using a local mse function while the overall model is evaluated on the basis of a global mse function the search capabilities of the suggested structure learning scheme are significantly enhanced by including a highly effective local search operator implemented by a micro genetic algorithm and four problem specific operators finally a genetic based parameter learning gbpl scheme is suggested in phase two which performs fine tuning of the initial models obtained after structure learning the performance of the proposed modeling approach is evaluated using a static example and a well known dynamic benchmark problem simulation results demonstrate that our models outperform those suggested by other methods with regard to simplicity model structure and accuracy

design and analysis of a fuzzy proportional integral derivative controller abstract this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional integral pi plus a derivative d controller first the fuzzy pi d controller is derived from the conventional continuous time linear pi d controller then the fuzzification control rule base and defuzzification in the design of the fuzzy controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pi d controller which has the same linear structure in the proportional integral and derivative parts but has nonconstant gains the proportional integral and derivative gains are nonlinear functions of the input signals the new fuzzy pi d controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self tuning control capability computer simulation results have demonstrated the advantages of the fuzzy controller particularly when the process to be controlled is nonlinear after a brief stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are shown to compare with the conventional pi d controller computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance

discrete breathers in a two dimensional fermi pasta ulam lattice using asymptotic methods we investigate whether discrete breathers are supported by a two dimensional fermi pasta ulam lattice a scalar one component two dimensional fermi pasta ulam lattice is shown to model the charge stored within an electrical transmission lattice a third order multiple scale analysis in the semi discrete limit fails since at this order the lattice equations reduce to the 2 1 dimensional cubic nonlinear schrodinger nls equation which does not support stable soliton solutions for the breather envelope we therefore extend the analysis to higher order and find a generalised 2 1 dimensional nls equation which incorporates higher order dispersive and nonlinear terms as perturbations we find an ellipticity criterion for the wave numbers of the carrier wave numerical simulations suggest that both stationary and moving breathers are supported by the system calculations of the energy show the expected threshold behaviour whereby the energy of breathers does em not go to zero with the amplitude we find that the energy threshold is maximised by stationary breathers and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

discrete breathers in honeycomb fermi pasta ulam lattices we consider the two dimensional fermi pasta ulam lattice with hexagonal honeycomb symmetry which is a hamiltonian system describing the evolution of a scalar valued quantity subject to nearest neighbour interactions using multiple scale analysis we reduce the governing lattice equations to a nonlinear schrodinger nls equation coupled to a second equation for an accompanying slow mode two cases in which the latter equation can be solved and so the system decoupled are considered in more detail firstly in the case of a symmetric potential we derive the form of moving breathers we find an ellipticity criterion for the wavenumbers of the carrier wave together with asymptotic estimates for the breather energy the minimum energy threshold depends on the wavenumber of the breather we find that this threshold is locally maximised by stationary breathers secondly for an asymmetric potential we find stationary breathers which even with a quadratic nonlinearity generate no second harmonic component in the breather plots of all our findings show clear hexagonal symmetry as we would expect from our lattice structure finally we compare the properties of stationary breathers in the square triangular and honeycomb lattices

mixed discrete fuzzy multiobjective programming for engineering optimization using hybrid genetic algorithm although much attention has been focused on the development and applications of fuzzy optimization multiobjective programming and mixed discrete optimization methods separately fuzzy multiobjective optimization problems in mixed discrete design space have not been addressed in the literature it is mainly because of the lack of mature and robust theories of mixed discrete and multiobjective optimization in most practical applications designers often encounter problems involving imprecise or fuzzy information multiple objectives and mixed discrete design variables a new method is presented in which the fuzzy formulation and game theory techniques are combined with a mixed discrete hybrid genetic algorithm for solving mixed dixcrete fuzzy multiobjective programming problems three example problems dealing with the optimal designs of a two bar truss a conical convective spine and a 25 bar truss demonstrate that the method can be flexibly and effectively applied to various kinds of engineering design problems to obtain more realistic and satisfactory results in an imprecise environment nomenclature d fuzzy feasible solution domain d f avorable search direction fiti x fitness function fi x ith objective function f max i upper bound of ith objective function f min i l ower bound of ith objective function g j allowable interval of the constraint function g j g j x jth inequality constraint function k number of objective functions m size of the population m number of inequality constraints n total number of design variables nd number of discrete design variables nq number of discrete design variables with equal spacing x design vector x c centroid of the composite polygon xw v ertex with the lowest fitness value xi ith design variable d x membership function of the design vector fi x membership function of the ith objective gj x membership function of the jth constraint

selecting fuzzy if then rules for classification problems using genetic algorithms this paper proposes a genetic algorithm based method for selecting a small number of significant fuzzy if then rules to construct a compact fuzzy classification system with high classification power the rule selection problem is formulated as a combinatorial optimization problem with two objectives to maximize the number of correctly classified patterns and to minimize the number of fuzzy if then rules genetic algorithms are applied to this problem a set of fuzzy if then rules is coded into a string and treated as an individual in genetic algorithms the fitness of each individual is specified by the two objectives in the combinatorial optimization problem the performance of the proposed method for training data and test data is examined by computer simulations on the iris data of fisher

fuzzy modeling of high dimensional systems complexity reduction and interpretability improvement fuzzy modeling of high dimensional systems is a challenging topic this paper proposes an effective approach to data based fuzzy modeling of high dimensional systems an initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema redundant rules are removed based on a fuzzy similarity measure then the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method during optimization rules that have a very low firing strength are deleted finally interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization the resulting fuzzy system generated by this method has the following distinct features 1 the fuzzy system is quite simplified 2 the fuzzy system is interpretable and 3 the dependencies between the inputs and the output are clearly shown this method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data

kinetic relations and the propagation of phase boundaries in solids this paper treats the dynamics of phase transformations in elastic bars the specific issue studied is the compatibility of the field equations and jump conditions of the one dimensional theory of such bars with two additional constitutive requirements a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition a special elastic material with a piecewise linear non monotonic stress strain relation is considered and the riemann problem for this material is analyzed for a large class of initial data it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities

stationary breather modes of generalized nonlinear klein gordon lattices this paper studies the form of stationary breather modes in discrete generalized nonlinear klein gordon equations with symmetric and non symmetric potential energy functions in the case of static breathers the discrete nature of the spatial dimension has a much more subtle effect on the breather than the moving breather mode this effect is analysed using a variety of approximating partial differential equations whose solutions are found by using an extended multiple scales asymptotic approach to reduce the equation to a nonlinear schrodinger equation at leading order and more complex equations at higher order where secularity conditions are required to fully specify the solution as well as the much studied discrete sine gordon equation the methods are demonstrated on a discrete nonlinear klein gordon equation with second neighbour interactions and non symmetric on site potential new partial differential equations which approximate these lattice systems are also proposed and analysed

finding multiple solutions to general integer linear programs integer linear programming ilp problems occur frequently in many applications in practice alternative optima are useful since they allow the decision maker to choose from multiple solutions without experiencing any deterioration in the objective function this study proposes a general integer cut to exclude the previous solution and presents an algorithm to identify all alternative optimal solutions of an ilp problem numerical examples in real applications are presented to demonstrate the usefulness of the proposed method

fuzzy coco a cooperative coevolutionary approach to fuzzy modeling co evolutionary algorithms have received increased attention in the past few years within the domain of evolutionary computation in this paper we combine the search power of co evolutionary computation with the expressive power of fuzzy systems and introduce a novel algorithm called fuzzy coco fuzzy cooperative coevolution we demonstrate the efficacy of fuzzy coco by applying it to a hard real world problem breast cancer diagnosis obtaining the best results to date while expending less computational effort than previous processes analyzing our results we derive guidelines for setting the algorithm parameters given a hard problem to solve we hope fuzzy coco proves to be a powerful tool in the fuzzy modeler toolkit

including a simplicity criterion in the selection of the best rule in a genetic fuzzy learning algorithm learning algorithms can obtain very useful descriptions of several problems many different alternative descriptions can be generated in many cases a simple description is preferable since it has a higher possibility of being valid in unseen cases and also it is usually easier to understand by a human expert thus the main idea of this paper is to propose simplicity criteria and to include them in a learning algorithm in this case the learning algorithm will reward the simplest descriptions we study simplicity criteria in the selection of fuzzy rules in the genetic fuzzy learning algorithm called slave

ten years of genetic fuzzy systems current framework and new trends fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains currently there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms the objective of this paper is to provide an account of genetic fuzzy systems with special attention to genetic fuzzy rule based systems after a brief introduction to models and applications of genetic fuzzy systems the field is overviewed new trends are identified a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated and open questions that remain to be addressed in the future are raised the paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems

compact and transparent fuzzy models and classifiers through iterative complexity reduction in our previous work 2000 we showed that genetic algorithms gas provide a powerful tool to increase the accuracy of fuzzy models for both systems modeling and classification in addition to these results we explore the ga to find redundancy in the fuzzy model for the purpose of model reduction an aggregated similarity measure is applied to search for redundancy in the rule base description as a result we propose an iterative fuzzy identification technique starting with data based fuzzy clustering with an overestimated number of local models the ga is then applied to find redundancy among the local models with a criterion based on maximal accuracy and maximal set similarity after the reduction steps the ga is applied with another criterion searching for minimal set similarity and maximal accuracy this results in an automatic identification scheme with fuzzy clustering rule base simplification and constrained genetic optimization with low human intervention the proposed modeling approach is then demonstrated for a system identification and a classification problem

ga fuzzy modeling and classification complexity and performance the use of genetic algorithms gas and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature authors have focused on various aspects of these randomized techniques and a whole scale of algorithms have been proposed we comment on some recent work and describe a new and efficient two step approach that leads to good results for function approximation dynamic systems modeling and data classification problems first fuzzy clustering is applied to obtain a compact initial rule based model then this model is optimized by a real coded ga subjected to constraints that maintain the semantic properties of the rules we consider four examples from the literature a synthetic nonlinear dynamic systems model the iris data classification problem the wine data classification problem and the dynamic modeling of a diesel engine turbocharger the obtained results are compared to other recently proposed methods

effect of rule weights in fuzzy rule based classification systems this paper examines the effect of rule weights in fuzzy rule based classification systems each fuzzy if then rule in our classification system has antecedent linguistic values and a single consequent class we use a fuzzy reasoning method based on a single winner rule in the classification phase the winner rule for a new pattern is the fuzzy if then rule that has the maximum compatibility grade with the new pattern when we use fuzzy if then rules with certainty grades the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade in this paper the effect of rule weights is illustrated by drawing classification boundaries using fuzzy if then rules with without certainty grades it is also shown that certainty grades play an important role when a fuzzy rule based classification system is a mixture of general rules and specific rules through computer simulations we show that comprehensible fuzzy rule based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy if then rules with certainty grades

an optimal design of neuro flc by lamarckian co adaptation of learning and evolution this paper proposes a new design method of neuro flc by the lamarckian co adaptation scheme that incorporates the backpropagation learning into the ga evolution in an attempt to find optimal design parameters fuzzy rule base and membership functions of application specific flc the design parameters are determined by evolution and learning in a way that the evolution performs the global search and makes inter flc parameter adjustments in order to obtain both the optimal rule base having high covering value and small number of useful fuzzy rules and the optimal membership functions having small approximation error and good control performance while the learning performs the local search and makes intra flc parameter adjustments by interacting each flc with its environment the proposed co adaptive design method produces better approximation ability because it includes the backpropagation learning in every generation of ga evolution shows better control performance because the used cog defuzzifier does compute the crisp value accurately and requires small workspace because the optimization procedure of fuzzy rule base and membership functions is performed concurrently by an integrated fitness function on the same fuzzy partition simulation results show that the lamarckian co adapted flc produces the most superior one among the differently generated flcs in all aspects such as the number of fuzzy rules the approximation error and the average tracing distance

discrete breathers in a two dimensional spring mass lattice we consider a two dimensional spring mass lattice with square symmetry in which each particle experiences a nonlinear onsite potential and nonlinear nearest neighbour interactions at equilibrium the particles are equally spaced in both the horizontal and vertical directions and all springs are unextended motivated by the work of marin et al 1998 phys lett a 248 225 9 2001 phys lett a 281 21 5 we seek a solution in which most of the breather s energy is focused along three chains we construct an asymptotic approximation to the breather using the method of multiple scales to describe the coherent oscillations in the three main chains that constitute the discrete breather we reduce the equation of motion to a nonlinear schrodinger equation for the leading order term and find a family of solutions which encompasses both stationary and moving bright soliton solutions we use numerical simulations of the lattice to verify the shape and velocity of breathers and find that while stationary breathers are found to persist for long times moving breathers decay by radiating energy in the direction perpendicular to their motion

finding relevant attributes and membership functions fuzzy systems that automatically derive fuzzy if then rules from numeric data have been developed most have to predefine membership functions in order to learn hong and lee proposed a general learning method that automatically derives fuzzy if then rules and membership functions from a set of given training examples using a decision table all available attributes were included in the decision table and the initial membership functions for each attribute were built according to the predefined smallest unit although hong and lee s method accurately derives the fuzzy if then rules and final membership functions the decision table and the initial membership functions are complex if there are many attributes or if the predefined unit is small we improve hong and lee s method by first selecting relevant attributes and building appropriate initial membership functions these attributes and membership functions are then used in a decision table to derive final fuzzy if then rules and membership functions experimental results on iris data show that the proposed method effectively induces membership functions and fuzzy if then rules

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

genetically optimized fuzzy polynomial neural networks with fuzzy set based polynomial neurons in this paper we propose and investigate a new category of neurofuzzy networks fuzzy polynomial neural networks fpnn endowed with fuzzy set based polynomial neurons fspns we develop a comprehensive design methodology involving mechanisms of genetic optimization and genetic algorithms gas in particular the conventional fpnns developed so far are based on the mechanisms of self organization fuzzy neurocomputing and evolutionary optimization the design of the network exploits the fspns as well as the extended group method of data handling gmdh let us stress that in the previous development strategies some essential parameters of the networks such as the number of input variables the order of the polynomial the number of membership functions and a collection of the specific subset of input variables being available within the network are provided by the designer in advance and kept fixed throughout the overall development process this restriction may hamper a possibility of developing an optimal architecture of the model the design proposed in this study addresses this issue the augmented and genetically developed fpnn gfpnn results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional fpnns the ga based design procedure being applied at each layer of the fpnn leads to the selection of the most suitable nodes or fspns available within the fpnn in the sequel two general optimization mechanisms are explored first the structural optimization is realized via gas whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method based learning the performance of the gfpnn is quantified through experimentation in which we use a number of modeling benchmarks synthetic and experimental data being commonly used in fuzzy or neurofuzzy modeling the obtained results demonstrate the superiority of the proposed networks over the models existing in the references

the vss approach to the model reference control of nonminimum phase linear plants a nontrivial application of the discontinuous control system theory based on filippov s solution concept is presented the problem addressed is the model reference output feedback control of linear plants with non hurwitzian numerator in the transfer function a solution in the case of known systems is presented first an error state equation whose state is accessible is then derived for the case in which the plant parameters are unknown in the case in which some bounds on the plant characteristics are supposed known a pair of discontinuous signals acting on both the plant and the model is chosen causing the error state to vanish asymptotically

genetic algorithm based optimal fuzzy controller design in the linguistic space in this paper a genetic algorithm ga based optimal fuzzy controller design is proposed the design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule the inputs of the controller after scaling are utilized by the index function for computing the output linguistic value this linguistic value can then be used to map the suitable fuzzy control actions this proposed novel fuzzy control rule has crisp input and fuzzified output characteristics the index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables two types of index functions both linear and nonlinear are introduced for controlling systems with different degrees of nonlinearity the parameters of the index function are obtained by applying a simple ga with a suitable fitness function various controlled systems result in various parameter sets depending on their dynamics under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions several simulation examples are given to verify the performance of the proposed ga based fuzzy controller

towards a globally stable direct adaptive control scheme for not necessarily minimum phase systems a direct adaptive control scheme for not necessarily minimum phase systems is presented the algorithm is based on simultaneous identification of input and output prediction models this leads to a bilinear parameter estimation problem for which a least squares criterion minimization is proposed this framework makes it possible to establish global convergence without any extra condition we give an example to illustrate the practical features

global solutions to the equations of a ginzburg landau theory for structural phase transitions in shape memory alloys abstract global existence of smooth solutions is proved for the system of partial differential equations governing the dynamics of martensic phase transitions in shape memory alloys the free energy is assumed in ginzburg landau form and nonconvex in the order parameter

hierarchical genetic fuzzy systems abstract this paper introduces a hierarchical evolutionary approach to optimize the parameters of takagi sugeno ts fuzzy systems the approach includes a least squares method to determine the parameters of nonlinear consequents a pruning procedure is developed to avoid redundancy in each rule consequent and to achieve proper representation flexibility the performance of the hierarchical evolutionary approach is evaluated using function approximation and classification problems they demonstrate that the evolutionary algorithm working together with optimization and pruning procedures provides structurally simple fuzzy systems whose performance seems to be better than the ones produced by alternative approaches

computing improved optimal solutions to max min flexible constraint satisfaction problems abstract the formal framework for decision making in a fuzzy environment is based on a general max min bottleneck like optimization problem proposed by zadeh it is also the basis for extending the constraint satisfaction paradigm of artificial intelligence to accommodating flexible or prioritized constraints this paper surveys refinements of the ordering of solutions supplied by the max min formulation namely the discrimin partial ordering and the leximin complete preordering a general algorithm is given which computes all maximal solutions in the sense of these relations it also sheds light on the structure of the set of best solutions moreover classes of problems for which there is a unique best discrimin and leximin solution are exhibited namely continuous problems with convex domains and so called isotonic problems noticeable examples of such problems are fuzzy linear programming problems and fuzzy pert like scheduling problems

localized excitations in two dimensional hamiltonian lattices we analyze the origin and features of localized excitations in a discrete two dimensional hamiltonian lattice the lattice obeys discrete translational symmetry and the localized excitations exist because of the presence of nonlinearities we connect the presence of these excitations with the existence of local integrability of the original n degree of freedom system on the basis of this explanation we make several predictions about the existence and stability of these excitations this work is an extension of previously published results on vibrational localization in one dimensional nonlinear hamiltonian lattices phys rev e 49 1994 836 thus we confirm earlier suggestions about the generic property of hamiltonian lattices to exhibit localized excitations independent on the dimensionality of the lattice

nonlinear waves in shallow honeycomb lattices the linear spectrum and corresponding bloch modes of shallow honeycomb lattices near dirac points are investigated via perturbation theory the dispersion relation is found to have threefold degeneracy at leading order with eigenvalue splitting at the following two orders i e the threefold eigenvalue splits into single and double values multiscale perturbation methods are employed to describe the nonlinear dynamics of the associated wave envelopes the dynamics of the envelope depends on different asymptotic balances whereupon a three level nonlinear dirac type equation or a two level nonlinear dirac equation is derived the analysis agrees well with direct numerical simulations

combining gp operators with sa search to evolve fuzzy rule based classifiers abstract the genotype phenotype encoding of fuzzy rule bases in ga along with their corresponding crossover and mutation operators can be used by other search schemes improving the behavior of these last ones as a practical consequence of this a simulated annealing based method for inducting both parameters and structure of a fuzzy classifier has been developed the adjacency operator in sa has been replaced with a macromutation taken from tree shaped genotype gas we will show that results of sa search are similar to those of gp in both the efficiency of the learned classifiers and in its linguistic interpretability while the memory consumption of the learning process is lower

fuzzy modeling with hybrid systems in this paper we present different approaches to the problem of fuzzy rules extraction by using a combination of fuzzy clustering and genetic algorithms as the main tools this combination of techniques let us define a hybrid system by which we can have different approaches in a fuzzy modeling process for example we can obtain a first approximation to the fuzzy rules that describe the system behavior represented by a collection of raw data without any assumption about the structure of the data using a fuzzy clustering technique and subsequently these rules can be tuned using a genetic algorithm alternatively this genetic algorithm can be used in order to generate and tune the fuzzy rules directly from the data with or without some priori information finally their performances are compared

kinetic relations for a lattice model of phase transitions the aim of this article is to analyse travelling waves for a lattice model of phase transitions specifically the fermi pasta ulam chain with piecewise quadratic interaction potential first for fixed sufficiently large subsonic wave speeds we rigorously prove the existence of a family of travelling wave solutions second it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails third our constructive approach provides a very good approximate travelling wave solution

genetic optimization of fuzzy networks abstract a novel fuzzy network controller is introduced which is interesting from both a theoretical and a practical viewpoint it is similar to a radial basis function neural network contains structured information and may be characterized by a few parameters only for training of these networks with experiments or by examples a nonstandard genetic algorithm is applied using a real valued parameter encoding scheme and an appropriate cross over the adaptation of a direct fuzzy controller for a simple system illustrates the procedure in a second example the integrated design and optimization approach is shown for a typical industrial controller stabilizing a laboratory size magnetic levitation system it includes nonlinear components for fuzzy anti windup

effective hamiltonian for travelling discrete breathers hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers however solutions which look like moving discrete breathers for some time are not difficult to observe in numerics in this paper we propose an abstract framework for the description of approximate travelling discrete breathers in hamiltonian chains of oscillators the method is based on the construction of an effective hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers error estimate on the approximate dynamics is also studied the concept of the peierls nabarro barrier can be made clear in this framework we illustrate the method with two simple examples namely the salerno model which interpolates between the ablowitz ladik lattice and the discrete nonlinear schrodinger system and the fermi pasta ulam chain

breathers on diatomic fermi pasta ulam lattices we prove the existence of breathers spatially localized and time periodic oscillations in diatomic fermi pasta ulam fpu chains with arbitrary mass ratio this completes an existence result by livi spicci and mackay valid for large mass ratio the problem is formulated as a mapping in a loop space and analyzed via a discrete spatial centre manifold reduction plane wave solutions of the linearized system have frequencies in a higher optic band or a lower acoustic band for frequencies close to band edges all small amplitude solutions of the nonlinear system lie on a finite dimensional centre manifold which reduces the problem locally to the study of a finite dimensional mapping for good parameter values the map admits homoclinic orbits to 0 corresponding to discrete breathers when the fpu interaction potential satisfies a hardening condition we find breathers with frequencies slightly above the optic band or in the gap slightly above the acoustic band for a potential satisfying the opposite softening condition we obtain breathers with frequencies in the gap slightly below the optic band 2004 elsevier b v all rights reserved

design of a ga based fuzzy pid controller for non minimum phase systems in this paper a fuzzy pid controller is investigated on the basis of genetic algorithms gas to eliminate the undershoot of a nonminimum phase nmp system and to improve the transient response at the same time the proposed controller employs a two stage control structure where the fuzzy pi controller is reasonably used to cancel out the effect of unstable zeros and the fuzzy pd controller is introduced for the reason of reducing the overshoot the fuzzy control rules for both controllers are evolved and determined by the gas it is demonstrated by computer simulations in which satisfactory performance can be achieved even if the system is under perturbed conditions

hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule based systems genetic algorithms and evolution strategies are combined in order to build a multi stage hybrid evolutionary algorithm for learning constrained approximate mamdani type knowledge bases from examples the genetic algorithm niche concept is used in two of the three stages composing the learning process with the purpose of improving the accuracy of the designed fuzzy rule based systems the proposed genetic fuzzy rule based system is used to solve an electrical engineering problem and the results obtained are compared with other methods presenting different characteristics

a proposal for improving the accuracy of linguistic modeling we propose accurate linguistic modeling a methodology to design linguistic models that are accurate to a high degree and may be suitably interpreted this approach is based on two main assumptions related to the interpolative reasoning developed by fuzzy rule based systems a small change in the structure of the linguistic model based on allowing the linguistic rule to have two consequents associated and a different way to obtain the knowledge base based on generating a preliminary fuzzy rule set composed of a large number of rules and then selecting the subset of them best cooperating moreover we introduce two variants of an automatic design method for these kinds of linguistic models based on two well known inductive fuzzy rule generation processes and a genetic process for selecting rules the accuracy of the proposed methods is compared with other linguistic modeling techniques with different characteristics when solving of three different applications

variable structure approach to the pole assignment control of non minimum phase systems in this paper a possible merge between the theory of variable structure control systems and that of model reference adaptive control is presented with reference to a pole assignment control problem in the presence of uncertain non minimum phase systems affected by bounded disturbances the control scheme proposed is characterized by a simple first order fixed compensator introduced in parallel to the plant so that the parallel connection turns out to be a relative degree one system with a not necessarily hurwitz numerator by a set of tunable state variable filters along with an all pass filter which allows us to avoid any unstable pole zero cancellation in the presence of a non hurwitz plant numerator by applying discontinuous control actions with an all pass filter it is possible to force a signal which plays the role of output error to zero keeping the amplitude of all the control signals bounded and solving a pole assignment problem the main novelty of this work consists in the analysis of t

coupling genetic algorithm with a grid search method to solve mixed integer nonlinear programming problems abstract a new hybrid algorithm is being introduced for solving mixed integer nonlinear programming minlp problems which arise from study of many real life engineering problems such as the minimum cost development of oil fields and the optimization of a multiproduct batch plant this new algorithm employs both the genetic algorithm and a modified grid search method interfacing in such a way that the resulting hybrid algorithm is capable of solving many minlp problems efficiently and accurately testings indicate that this algorithm is efficient and robust even for some ill conditioned problems with nonconvex constraints

simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms this paper examines the applicability of genetic algorithms ga s in the simultaneous design of membership functions and rule sets for fuzzy logic controllers previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions however the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology when ga s have been used to develop both it has been done serially e g design the membership functions and then use them in the design of the rule set this however means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently ga s are fully capable of creating complete fuzzy controllers given the equations of motion of the system eliminating the need for human input in the design loop this new method has been applied to two problems a cart controller and a truck controller beyond the development of these controllers we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules

modeling uncertainty in reservoir loss functions using fuzzy sets imprecision involved in the definition of reservoir loss functions is addressed using fuzzy set theory concepts a reservoir operation problem is solved using the concepts of fuzzy mathematical programming membership functions from fuzzy set theory are used to represent the decision maker s preferences in the definition of shape of loss curves these functions are assumed to be known and are used to model the uncertainties linear and nonlinear optimization models are developed under fuzzy environment a new approach is presented that involves development of compromise reservoir operating policies based on the rules from the traditional optimization models and their fuzzy equivalents while considering the preferences of the decision maker the imprecision associated with the definition of penalty and storage zones and uncertainty in the penalty coefficients are the main issues addressed through this study the models developed are applied to the green reservoir kentucky simulations are performed to evaluate the operating rules generated by the models considering the uncertainties in the loss functions results indicate that the reservoir operating policies are sensitive to change in the shapes of loss functions

genetic feature selection in a fuzzy rule based classification system learning process for high dimensional problems abstract the inductive learning of a fuzzy rule based classification system frbcs is made difficult by the presence of a large number of features that increases the dimensionality of the problem being solved the difficulty comes from the exponential growth of the fuzzy rule search space with the increase in the number of features considered in the learning process in this work we present a genetic feature selection process that can be integrated in a multistage genetic learning method to obtain in a more efficient way frbcss composed of a set of comprehensible fuzzy rules with high classification ability the proposed process fixes a priori the number of selected features and therefore the size of the search space of candidate fuzzy rules the experimentation carried out using sonar example base shows a significant improvement on simplicity precision and efficiency achieved by adding the proposed feature selection processes to the multistage genetic learning method or to other learning methods

discrete breathers in a two dimensional hexagonal fermi pasta ulam lattice we consider a two dimensional fermi pasta ulam fpu lattice with hexagonal symmetry using asymptotic methods based on small amplitude ansatz at third order we obtain a eduction to a cubic nonlinear schr o dinger equation nls for the breather envelope however this does not support stable soliton solutions so we pursue a higher order analysis yielding a generalised nls which includes known stabilising terms we present numerical results which suggest that long lived stationary and moving breathers are supported by the lattice we find breather solutions which move in an arbitrary direction an ellipticity criterion for the wavenumbers of the carrier wave symptotic estimates for the breather energy and a minimum threshold energy below which breathers cannot be found this energy threshold is maximised for stationary breathers and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed several of the results obtained are similar to those obtained for the square fpu lattice butt wattis em j phys a bf 39 4955 2006 though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics and the isotropy of the generalised nls equation

fuzzy nonlinear programming for mixed discrete design optimization through hybrid genetic algorithm many practical engineering optimization problems involve discrete or integer design variables and often the design decisions are to be made in a fuzzy environment in which the statements might be vague or imprecise a mixed discrete fuzzy nonlinear programming approach that combines the fuzzy formulation with a hybrid genetic algorithm is proposed in this paper this method can find a globally compromise solution for a mixed discrete fuzzy optimization problem even when the objective function is nonconvex and nondifferentiable in the construction of the objective membership function an error from the early research work is corrected and the right conclusion has been made the illustrative examples demonstrate that more reliable and satisfactory results can be obtained through the present method

three objective genetics based machine learning for linguisitc rule extraction abstract this paper shows how a small number of linguistically interpretable fuzzy rules can be extracted from numerical data for high dimensional pattern classification problems one difficulty in the handling of high dimensional problems by fuzzy rule based systems is the exponential increase in the number of fuzzy rules with the number of input variables another difficulty is the deterioration in the comprehensibility of fuzzy rules when they involve many antecedent conditions our task is to design comprehensible fuzzy rule based systems with high classification ability this task is formulated as a combinatorial optimization problem with three objectives to maximize the number of correctly classified training patterns to minimize the number of fuzzy rules and to minimize the total number of antecedent conditions we show two genetic algorithm based approaches one is rule selection where a small number of linguistically interpretable fuzzy rules are selected from a large number of prespecified candidate rules the other is fuzzy genetics based machine learning where rule sets are evolved by genetic operations these two approaches search for non dominated rule sets with respect to the three objectives

a genetic learning process for the scaling factors granularity and contexts of the fuzzy rule based system data base abstract in this contribution we propose a new method to automatically learn the knowledge base of a fuzzy rule based system by finding an appropriate data base using a genetic algorithm and considering a simple generation method to derive the rule base our genetic process learns all the components of the data base number of labels working ranges and membership function shapes for each linguistic variable using a non linear scaling function to adapt the fuzzy partition contexts

genetic programming for model selection of tsk fuzzy systems this paper compares a genetic programming gp approach with a greedy partition algorithm lolimot for structure identification of local linear neuro fuzzy models the crisp linear conclusion part of a takagi sugeno kang tsk fuzzy rule describes the underlying model in the local region specified in the premise the objective of structure identification is to identify an optimal partition of the input space into gaussian axis orthogonal fuzzy sets the linear parameters in the rule consequent are then estimated by means of a local weighted least squares algorithm lolimot is an incremental tree construction algorithm that partitions the input space by axis orthogonal splits in each iteration it greedily adds the new model that minimizes the classification error gp performs a global search for the optimal partition tree and is therefore able to backtrack in case of sub optimal intermediate split decisions we compare the performance of both methods for function approximation of a highly non linear two dimensional test function and an engine characteristic map

switching type fuzzy controller design by genetic algorithms in this paper we propose an effective method to select the parameters of the switching type fuzzy controller by using the genetic algorithm so that a high performance of the overall system s response can be achieved the proposed fitness function contains three performance measures the rise time overshoot and steady state error so that the selected parameters by the proposed method can simultaneously improve the transient response and the steady state response based on the direction of the fitness function an inverted pendulum control design problem is given to illustrate the validity of the proposed method

solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity we study the existence and stability of localized states in the discrete nonlinear schrodinger equation on two dimensional nonsquare lattices the model includes both the nearest neighbor and long range interactions for the fundamental strongly localized soliton the results depend on the coordination number i e on the particular type of lattice the long range interactions additionally destabilize the discrete soliton or make it more stable if the sign of the interaction is respectively the same as or opposite to the sign of the short range interaction we also explore more complicated solutions such as twisted localized modes and solutions carrying multiple topological charge vortices that are specific to the triangular and honeycomb lattices in the cases when such vortices are unstable direct simulations demonstrate that they typically turn into zero vorticity fundamental solitons

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