nonlinear mathematical theory of perforated viscoelastic thin plates with its applications abstract in this paper the nonlinear mathematical theory of perforated viscoelastic thin plates by the karman s hypotheses of plates with large deflection and the boltzmann s constitutive law of linear viscoelastic materials is established one could see that the governing equations boundary conditions and constraining conditions generally are of nonlinear integro differential operator types and that they further generalize the mathematical theory for perforated elastic thin plates and could be also reduced to the existing mathematical theory of viscoelastic thin plates without holes as an application the nonlinear dynamical stability of a viscoelastic annular plate is analyzed and the effect of parameters on the stability is considered by using galerkin averaging method and numerical methods in nonlinear dynamics some helpful conclusions are obtained specially a new method calculating the lyapunov exponent spectrum of dynamical systems excited periodically is suggested by using this method the computation time can be greatly reduced

multi objective design optimization using cascade evolutionary computations the consideration of uncertainties in conjunction with the probability of violation of the constraints imposed by the design codes is examined in the framework of structural optimization the optimum design achieved based on a deterministic formulation is compared in terms of the optimum weight the probability of violation of the constraints and the probability of failure with the optimum designs achieved through a robust design formulation where the variance of the response is considered as an additional criterion the stochastic finite element problem is solved using the monte carlo simulation method combined with the latin hypercube sampling technique for improving its computational efficiency a non dominant cascade evolutionary algorithm based methodology is adopted for the solution of the multi objective optimization problem encountered in order to obtain the global pareto front curve

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

pareto optimal sensor locations for structural identification theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the objective is to optimally locate sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling for a single model class the information entropy is used as the optimality criterion for selecting the best sensor configuration for multiple model classes the problem is formulated as a multi objective optimization problem of finding the pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices a heuristic algorithm is proposed for constructing effective pareto optimal sensor configurations that are superior in terms of computational efficiency and accuracy to the pareto sensor configurations predicted by evolutionary algorithms suitable for solving general multi objective optimisation problems the theoretical developments and the effectiveness of the proposed algorithms are illustrated for a 10 dof chain like spring mass model and a 32 dof truss structure

control of the optimum synthesis process of a four bar linkage whose point on the working member generates the given path this paper presents the optimum synthesis of a four bar linkage in which the coupler point performs a path composed of rectilinear segments and a circular arc the grashof four bar linkage whose geometry provides minimum deviations from the given problem for certain parts of the crank cycle is chosen the motion of the coupler point of the four bar linkage is controlled within the given values of allowed deviations so that it is always in the prescribed environment of the given point on the observed segment the synthesis process tends to bring only those path segments that are beyond the boundaries within the prescribed boundary deviations during the synthesis allowed deviations change from the initial maximum values to the given minimum ones groups of mechanisms realising satisfactory approximation to the desired motion can be obtained by the method of controlled decrease of allowed deviations with the application of the differential evolution de algorithm

a local exploration based differential evolution algorithm for constrained global optimization abstract we propose a modified differential evolution de algorithm for constrained global optimization the modification is based on the mutation rule of de the new algorithm also incorporates a periodic local exploration technique the local technique used is a limited version of the pattern search ps method the penalty functions such as the superiority of feasible points sfp and the parameter free penalty pfp are used for handling constraints we numerically study sfp and pfp and based on a drawback observed we adapt the selection rule of de the new algorithm is tested on 45 test problems comparisons are made with some recent algorithms

a decremental stochastic fractal differential evolution for global numerical optimization the aim of hybridization in the context of evolutionary computation is to combine appropriate operators from different evolutionary computation paradigms to form a single technique that enjoys a statistically superior performance over a wide range of optimization problems this paper introduces a novel hybridization between differential evolution and update processes of the stochastic fractal search algorithm the diffusion property of the fractal search algorithm is applied in random fractals followed by two novel update processes to explore the search space more efficiently in this algorithm a diffusion process based on differential evolution algorithm is used instead of random fractals in the original stochastic fractal search algorithm a new success based scheme is used to utilize the update processes and to solve the burden of extra computations during the search this new algorithm captures the strengths of both component algorithms and produces a greater explorative power as compared to the original algorithms to verify the performance of our algorithm a challenging test suite of 30 benchmark functions from the ieee cec2014 real parameter single objective competition is used the results affirm the effectiveness and robustness of the proposed approach compared to the original stochastic fractal search and other recent state of the art algorithms the proposed algorithm enjoys a statistically superior performance over most of the tested benchmarks especially hybrid and composition test functions compared to the other contestant algorithms

vibration analysis of linear coupled thermoviscoelastic thin plates by a variational approach abstract according to the integral type constitutive relation of linear coupled thermoviscoelasticity a mathematical model of thin plates is set up by the introduction of structural functions and thermal functions in the sense of the kirchhoff s hypothesis the corresponding integral type variational formulations are presented by means of modern convolution bilinear forms as well as classical cartesian bilinear forms the ritz method in the spatial domain and the differentiating method in the temporal domain are used to approximate the mathematical model in a system of rectangular cartesian coordinates by properties of inequality and parabola the structure of dynamic solution to vibration of a thermoviscoelastic thin plate under a harmonic thermal load is studied in the space splayed by material parameter and loading parameter the influences of thermal excitation frequency mechanical relaxation time and thermal relaxation time on amplitude and phase difference of steady state vibration of a square plate are investigated by amplitude frequency analysis and phase frequency analysis double peak resonance vibration of thermoviscoelastic plates exists for given parameters

enhancing the search ability of differential evolution through orthogonal crossover differential evolution de is a class of simple yet powerful evolutionary algorithms for global numerical optimization binomial crossover and exponential crossover are two commonly used crossover operators in current popular de it is noteworthy that these two operators can only generate a vertex of a hyper rectangle defined by the mutant and target vectors therefore the search ability of de may be limited orthogonal crossover ox operators which are based on orthogonal design can make a systematic and rational search in a region defined by the parent solutions in this paper we have suggested a framework for using an ox in de variants and proposed oxde a combination of de rand 1 bin and ox extensive experiments have been carried out to study oxde and to demonstrate that our framework can also be used for improving the performance of other de variants

an incremental relaxation finite element analysis of viscoelastic problems with contact and friction abstract based on the principle of virtual work a general but effective finite element technique associated with an incremental relaxation procedure is established for the analysis of viscoelastic contact problems with friction a generalized maxwell model is used to model the viscoelastic constitutive equations of which the relaxation function is represented by the sum of a series of decaying exponential functions of time the contact behaviors are accurately performed through a transformation matrix method by the incremental relaxation procedure developed the stress of each element of the generalized maxwell model at instant t n 1 includes two parts 1 the part decaying from the stress at instant t n during the time interval t n t n 1 and 2 the incremental stress induced from the incremental strain applied at instant t n the total stress at instant t n 1 can thus be computed by the sum of the stress of the elements of the generalized maxwell model and is only dependent on the previous stress level and the incremental strain applied at instant t n hence both the total strain and displacement at each instant are not used in the total stress calculation in addition the numerical errors caused by selecting larger time increments can also be avoided finally the influence of friction on the contact traction distributed on the contact surface at various time instants is presented

single and multiobjective frame optimization by evolutionary algorithms and the auto adaptive rebirth operator abstract the constrained minimum mass problem of middle size frames is taken into account for both continuous and discrete cases with ideal without buckling effect and own gravitational load and real with both models comparing three strategies of evolutionary algorithms some proposals to obtain appropriate results in middle sized frames are exposed optimization considerations about coding and structure and the introduction of the auto adaptive rebirth operator moreover the introduction in the initial population of high quality single optimization solutions obtained via the auto adaptive rebirth operator is proposed as a way to improve the final non dominated fronts obtained in structural frame multicriteria optimization number of different cross section types as second criteria the results through three test cases 55 35 bar sized show the advantageous use of the auto adaptive rebirth operator in frame optimization

constrained optimization based on modified differential evolution algorithm this paper presents a novel constrained optimization based on modified differential evolution algorithm comde in the new algorithm a new directed mutation rule based on the weighted difference vector between the best and the worst individuals at a particular generation is introduced the new directed mutation rule is combined with the modified basic mutation strategy de rand 1 bin where only one of the two mutation rules is applied with the probability of 0 5 the proposed mutation rule is shown to enhance the local search ability of the basic differential evolution de and to get a better trade off between convergence rate and robustness two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction additionally a dynamic non linear increased crossover probability is utilized to balance the global exploration and local exploitation comde also includes a modified constraint handling technique based on feasibility and the sum of constraints violations a new dynamic tolerance technique to handle equality constraints is also adopted the effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in comde has been experimentally investigated the effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of comde have been analyzed and evaluated by different experiments numerical experiments on 13 well known benchmark test functions and five engineering design problems have shown that the new approach is efficient effective and robust the comparison results between the comde and the other 28 state of the art evolutionary algorithms indicate that the proposed comde algorithm is competitive with and in some cases superior to other existing algorithms in terms of the quality efficiency convergence rate and robustness of the final solution

adaptive memetic differential evolution with global and local neighborhood based mutation operators differential evolution de is one of the most popular optimization methods for real valued problems and a large number of its variants have been proposed so far however bringing together different ideas that already led to successful de versions is rare in the literature in the present paper a novel de algorithm is proposed in which three among the most efficient concepts already applied separately within de framework are gathered together namely 1 the adaptation of algorithm control parameters and probabilities of using different mutation strategies 2 the use of nelder mead algorithm as a local search method hybridized with de and 3 the splitting mutation into global and local models when local mutation model is based on the concept of neighborhood of individuals organized on a ring topology the performance of the novel algorithm called adaptive memetic de with global and local neighborhood based mutation operators is compared with 13 different de variants on a set of 25 popular problems which include rotated shifted and hybrid composition functions it is found that although none de algorithm outperforms all the others for the majority of problems on average the proposed approach perform better than all 13 de algorithms selected for comparison the proposed algorithm is another heuristic approach developed to solve optimization problems the question may arise whether proposing novel methods is useful as no free lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal in the last section of the paper the limitations and implications of no free lunch theorems are discussed based on rich but unfortunately frequently neglected literature a very simple continuous and differentiable minimization problem is proposed for which it is empirically verified that each among considered 14 de algorithms perform poorer than random sampling it is also empirically shown that when all considered de algorithms search for the maximum of the proposed problem they found lower minimum than de algorithms searching for the minimum such result is not unexpected according to no free lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods

an improved self adaptive constraint sequencing approach for constrained optimization problems real life optimization problems involve a number of constraints arising out of user requirements physical laws statutory requirements resource limitations etc such constraints are routinely evaluated using computationally expensive analysis i e solvers relying on finite element methods computational fluid dynamics computational electro magnetic etc existing optimization approaches adopt a full evaluation policy i e all the constraints corresponding to a solution are evaluated throughout the course of search furthermore a common sequence of constraint evaluation is used for all the solutions in this paper we introduce a novel scheme for constraint handling wherein every solution is assigned a random sequence of constraints and the evaluation process is aborted whenever a constraint is violated the solutions are sorted based on two measures i e the number of satisfied constraints and the violation measure the number of satisfied constraints takes precedence over the amount of violation and the most efficient sequence of constraint evaluation is evolved during the course of search the performance of the proposed scheme is rigorously compared with other state of the art constraint handling methods using single objective inequality constrained test problems of cec 2006 and cec 2010 the constraint handling approach is generic and can be easily used for the solution of constrained multiobjective optimization problems or even problems with equality constraints a bi objective welded beam design problem a tri objective car side impact problem and an equality constrained optimization problem of cec 2006 is solved as an illustration the results clearly highlight potential savings offered by the proposed strategy and more importantly the paper provides a detailed insight on why such a strategy performs better than others

coupled eagle strategy and differential evolution for unconstrained and constrained global optimization the performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process the fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve modern metaheuristic algorithms are generally more suitable for global optimization this paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by yang and deb in combination with the efficient differential evolution after a detailed formulation and explanation of its implementation the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks for the validation against constrained problems this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature the performance of the proposed algorithm is further compared with various state of the art algorithms in the area the optimal solutions obtained in this study are better than the best solutions obtained by the existing methods the unique search features used in the proposed algorithm are analyzed and their implications for future research are also discussed in detail

non linear mathematical model of viscoelastic thin plates with its applications in this paper the nonlinear mathematical model of viscoelastic thin plates by the karman s hypotheses of a large deflection plate and the boltzmann s law of anisotropic viscoelastic materials is established by means of the laplace transformation and its inverse as well as so called structural functions introduced in this paper in the case of isotropic viscoelastic materials with poisson s ratio v const the quasi static problems of a simply supported rectangular plate are investigated by using the galerkin method for the spatial domain and two finite difference schemes for the temporal domain it could be seen that the numerical method in this paper is very simple and has some advantages such as smaller storage and quicker computational speed

decentralized event triggered consensus with general linear dynamics the consensus problem with general linear dynamics and undirected graphs is studied in this paper by means of event triggered control strategies a novel consensus protocol is proposed where each agent implements a model of the decoupled dynamics of its neighbors under this control strategy transmission of information does not occur continuously but only at discrete points in time the approach presented in this paper provides both a decentralized control law and a decentralized communication policy we are able to design thresholds that only depend on local information and guarantee asymptotic consensus positive inter event times are guaranteed for particular cases of the linear dynamics in an extension a positive constant is added to the thresholds in order to exclude zeno behavior for general linear dynamics the difference between agents trajectories can be bounded in this case and bounds on the state disagreement are derived

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

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

solving constrained optimization problems using a novel genetic algorithm a novel genetic algorithm is described in this paper for the problem of constrained optimization the algorithm incorporates modified genetic operators that preserve the feasibility of the trial solutions encoded in the chromosomes the stochastic application of a local search procedure and a stopping rule which is based on asymptotic considerations the algorithm is tested on a series of well known test problems and a comparison is made against the algorithms c somga and donlp2

differential evolution in constrained numerical optimization an empirical study motivated by the recent success of diverse approaches based on differential evolution de to solve constrained numerical optimization problems in this paper the performance of this novel evolutionary algorithm is evaluated three experiments are designed to study the behavior of different de variants on a set of benchmark problems by using different performance measures proposed in the specialized literature the first experiment analyzes the behavior of four de variants in 24 test functions considering dimensionality and the type of constraints of the problem the second experiment presents a more in depth analysis on two de variants by varying two parameters the scale factor f and the population size np which control the convergence of the algorithm from the results obtained a simple but competitive combination of two de variants is proposed and compared against state of the art de based algorithms for constrained optimization in the third experiment the study in this paper shows 1 important information about the behavior of de in constrained search spaces and 2 the role of this knowledge in the correct combination of variants based on their capabilities to generate simple but competitive approaches

three dimensional incompressible viscoelasticity in large strains formulation and numerical approximation abstract this paper considers viscoelastic incompressible solids in large deformations a three dimensional thermodynamical model is first proposed it leads to a nonlinear variational problem which is approximated in space by mixed finite elements and in time by a first order implicit scheme this approximation is analyzed on the corresponding linearized problem finally an elimination strategy is described which reduces each step of the discrete problem to the solution of a standard hyperelastic problem to be solved by newton s method

cultured differential evolution for constrained optimization a cultural algorithm with a differential evolution population is proposed in this paper this cultural algorithm uses different knowledge sources to influence the variation operator of the differential evolution algorithm in order to reduce the number of fitness function evaluations required to obtain competitive results comparisons are provided with respect to three techniques that are representative of the state of the art in the area the results obtained by our algorithm are similar in quality to those obtained by the other approaches with respect to which it was compared however our approach requires a lower number of fitness function evaluations than the others