hybrid variable fidelity optimization by using a kriging based scaling function solving design problems that rely on very complex and computationally expensive calculations using standard optimization methods might not be feasible given design cycle time constraints variable fidelity methods address this issue by using lower fidelity models and a scaling function to approximate the higher fidelity models in a provably convergent framework in the past scaling functions have mainly been either first order multiplicative or additive corrections these are being extended to second order in this investigation variable metric approaches for calculating second order scaling information are developed a kriging based scaling function is introduced to better approximate the high fidelity response on a more global level an adaptive hybrid method is also developed in this investigation the adaptive hybrid method combines the additive and multiplicative approaches so that the designer does not have to determine which is more suitable prior to optimization the methodologies developed in this research are compared to existing methods using two demonstration problems the first problem is analytic whereas the second involves the design of a supercritical high lift airfoil the results demonstrate that the krigingbased scaling methods improve computational expense by lowering the number of high fidelity function calls required for convergence the results also indicate the hybrid method is both robust and effective

multiplicity results for asymptotically linear elliptic problems at resonance in this paper several new multiplicity results for asymptotically linear elliptic problem at resonance are obtained via morse theory and minimax methods some new observations on the critical groups of a local linking type critical point are used to deal with the resonance case at 0

multiplicity results for some elliptic systems near resonance with a nonprincipal eigenvalue abstract some multiplicity results of solutions are obtained for a class of elliptic systems which are near resonance with a nonprincipal eigenvalue by the classical saddle point theorem and a local saddle point theorem in critical point theory

optimal forecast combinations under general loss functions and forecast error distributions existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss under this loss function empirical studies have generally found that equally weighted combined forecasts lead to better performance than estimates of optimal forecast combination weights which in turn outperform the best individual predictions we show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed we characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights we also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise

dirichlet problems with double resonance and an indefinite potential abstract we consider semilinear dirichlet problems with an unbounded and indefinite potential and with a caratheodory reaction we assume that asymptotically at infinity the problem exhibits double resonance using variational methods together with morse theory and flow invariance arguments we prove multiplicity theorems producing three five six or seven nontrivial smooth solutions in most multiplicity theorems we provide precise sign information for all the solutions established

constraint handling in genetic search using expression strategies a traditional penalty function formulation for treatment of nonlinear constrained optimization problems in genetic search has been shown to be extremely sensitive to user specified schedules of selecting penalty parameters the sensitivity of such an approach is manifested in a biasing of the search toward suboptimal designs and a general increase in the number of function evaluations required to obtain a converged design alternative methods are described for handling constraints that are motivated by the fact that the structure of both feasible and infeasible designs is generally present in the population of designs at any generation of search a preconditionin g of the infeasible designs prior to the genetic transformations by an expression operation that is conceptually analogous to the theory of dominant and recessive genes in genetics is shown to be highly effective in evolving feasible solutions and with savings of computational resource two alternative implementations of this approach are described and a comparison is made of numerical efficiency vis a vis the penalty function based approach

trust region model management in multidisciplinary design optimization a common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques the use of approximation strategies is designed to reduce the number of detailed costly computer simulations required during optimization while maintaining the pertinent features of the design problem this paper overviews the current state of the art in model management strategies for approximate optimization model management strategies coordinate the interaction between the optimization and the fidelity of the approximation models so as to ensure that the process converges to a solution of the original design problem approximations play an important role in multidisciplinary design optimization mdo by offering system behavior information at a relatively low cost most approximate mdo strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence the move limits or trust region are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information in order to insure convergence of the sequence of approximate optimizations to a karush kuhn tucker solution a trust region model management or move limit strategy is required in this paper recent developments in approximate mdo strategies and issues of trust region model management in mdo are reviewed

stacking sequence optimization of simply supported laminates with stability and strain constraints an integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented the design variables that define the stacking sequence of the laminate are ply identity zero one integers the buckling constraint is linear in terms of the ply identity design variables but strains are nonlinear functions of these variables a linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm examples of graphite epox y plates under biaxial compression are presented optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure

an elliptic resonance problem with multiple solutions in this paper we study the existence of multiple nontrivial solutions for a semilinear elliptic equation at resonance by the minimax methods and morse theory

existence and multiplicity for solutions of neumann problem for semilinear elliptic equations the existence and multiplicity results are obtained for solutions of neumann problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

the existence of infinitely many solutions of a class of nonlinear elliptic equations with neumann boundary condition for both resonance and oscillation problems abstract in this paper we study and discuss nonlinear elliptic equations with neumann boundary condition for both resonance and oscillation problem and obtain new results on the exactly infinitely many positive and negative solutions which are all nonconstant the study of problem 1 1 are based on the variational methods and critical point theory we prove the conclusion by using sub sup solution method mountain pass theorem in order intervals leray schauder degree theory and more theory

asymptotically linear elliptic equations without nonresonance conditions abstract in this paper we are concerned with the existence of nontrivial solutions of a semilinear elliptic equation when the nonresonance condition at infinity is not satisfied we consider a strongly resonant case in the first part and a sort of resonance under density assumptions in the second part

pairs of nontrivial solutions for resonant neumann problems abstract we study a semilinear neumann problem which is resonant at with respect to any eigenvalue different from the first and the second eigenvalue of n the negative neumann laplacian using a combination of variational methods with morse theoretic techniques we show that the problem has at least two nontrivial smooth solutions

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

continuum structural topology design with genetic algorithms the genetic algorithm ga an optimization technique based on the theory of natural selection is applied to structural topology design problems after reviewing the ga and previous research in structural topology optimization we describe a binary material void design representation that is encoded in ga chromosome data structures this representation is intended to approximate a material continuum as opposed to discrete truss structures four examples showing the broad utility of the approach and representation are then presented a fifth example suggests an alternate representation that allows continuously variable material density concluding discussion suggests recommended uses of the technique and describes ongoing and possible future work

approximation based global optimization strategy for structural synthesis the methodology involves the solution of a sequence of high quality approximate problems using a global optimization algorithm the global optimization algorithm implemented consists of a branch and hound strategy based on the interval evaluation of the objective function and constraint functions combined with a local feasible directions algorithm the approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables

multiple solutions for semilinear resonance elliptic problems with nonconstant coefficients at infinity in this paper we study a class of semilinear elliptic equations which are completely resonant with nonconstant coefficients at origin and at infinity by applying morse theory and minimax method we obtain the existence of multiple nontrivial solutions for the equations

global convergence of a class of trust region algorithms for optimization with simple bounds this paper extends the known excellent global convergence properties of trust region algorithms for unconstrained optimization to the case where bounds on the variables are present weak conditions on the accuracy of the hessian approximations are considered it is also shown that when the strict complementarily condition holds the proposed algorithms reduce to an unconstrained calculation after finitely many iterations allowing a fast asymptotic rate of convergence

multiple solutions and sign changing solutions of a class of nonlinear elliptic equations with neumann boundary condition in this paper we study and discuss nonlinear elliptic equations with neumann boundary condition for oscillation problem we obtain infinitely many positive and negative solutions of 1 1 which are all nonconstant and get at least two nonconstant solutions in every order interval under resonance case moreover we yield infinitely many sign changing solutions of 1 1 under some assumptions furthermore we give a precise description of critical groups of some kinds of critical points we draw the conclusions by using sub sup solution method mountain pass theorem in order intervals leray schauder degree theory and morse theory

genetic search an approach to the nonconvex optimization problem principles of genetics and natural selection are adapted into a search procedure for function optimization such methods are based on a randomized selection from that restricted region of the design space that yields and improvement in the objective function an implementation of the approach to a class of problems in structural optimization with demonstrated nonconvexities or disjointness is discussed in the paper the principal drawback of the method is an increase in function evaluations necessary to locate an optimum possible strategies to overcome this limitation are presented

implicit multigrid algorithms for incompressible turbulent flows on unstructured grids an implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described the foundation of the code is a backward euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned generalized minimal residual gmres technique for the gmres calculations several techniques are investigated for forming the matrix vector product convergence acceleration is achieved through a multigrid scheme that uses nonnested coarse grids that are generated using a technique described in the present paper convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four element airfoil viscous results which are compared with experimental data include the turbulent flow over a naca 4412 airfoil a three element airfoil for which mach number effects are investigated and three dimensional flow over a wing with a partial span flap

solutions to a gradient system with resonance at both zero and infinity in this paper we study the existence and multiplicity of nontrivial solutions for a gradient system with resonance at both zero and infinity via morse theory

multiple solutions for semilinear elliptic boundary value problems with double resonance abstract in this paper we study the multiplicity of nontrivial solutions of semilinear elliptic boundary value problems which may be double resonance near infinity between two consecutive eigenvalues of with zero dirichlet boundary data the methods we use here are morse theory minimax methods and bifurcation theory

genetic algorithms in truss topological optimization the present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms in developing near optimal topologies of load bearing truss structures the problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space the development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness the approach is an adaptation of the ground structure method of topology optimization and is implemented in a two level genetic algorithm based search in this process the kinematic stability constraints are imposed at one level followed by the treatment of response constraints at a second level of optimization singular value decomposition is used to assess the kinematic stability constraints at the first level of design and results in the creation of a finite number of increasing weight stable topologies member sizing is then introduced at a second level of design where minimal weight and response constraints on stresses displacements and buckling are simultaneously considered at this level the only admissible topologies are those identified during the first stage and any stable combination thereof the design variable representation scheme allows for both the removal and addition of structural members during optimization

tests for conditional ellipticity in multivariate garch models tests are proposed for the assumption that the conditional distribution of a multivariate garch process is elliptic these tests are of kolmogorov smirnov and cramer von mises type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution the asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions it is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the euclidean norm of the innovations therefore a conditional monte carlo procedure is used to actually carry out the tests the validity of this resampling scheme is formally justified results on the behavior of the new tests in finite samples are included along with comparisons with other tests

combining global and local approximations a method based on a linear approximation to a scaling factor designated the global local approximation gla method is presented and shown capable of extending the range of usefulness of derivative based approximations to a more refined model the gla approach refines the conventional scaling factor by means of a linearly varying rather than constant scaling factor the capabilities of the method are demonstrated for a simple beam example with a crude and more refined fem model 6 refs

a common tabu search algorithm for the global optimization of engineering problems abstract a novel common tabu algorithm for global optimizations of engineering problems is presented the robustness and efficiency of the presented method are evaluated by using standard mathematical functions and by solving a practical engineering problem the numerical results show that the proposed method is i superior to the conventional tabu search algorithm in robustness and ii superior to the simulated annealing algorithm in efficiency

structural damage detection based on static and modal analysis the present paper describes an approach for structural damage assessment that has its basis in methods of system identification response of a damaged structure differs from predictions obtained from an analytical model of the original structure where the analytical model is typically a finite element representation the out put error approach of system identification is employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response structural damage is represented by changes in element stiffness matrices resulting from variations in geometry or material properties of the structure during damage measurements of static deflections and vibration modes are used in the identification procedure the identification methodology is implemented for representative structural systems principal shortcomings in the proposed approach and methods to circumvent these problems are also discussed of obtaining poor results these difficulties are clearly evi denced by the results obtained smith and hendricks8 follow a similar approach using two different identification methods to identify the stiffness matrix based on the minimum deviation approach and using eigenmodes as experimental data similar difficulties are re ported in their work the entries of the stiffness matrix corre sponding to the damaged members do show considerable vari ations however entries corresponding to undamaged members are also affected thereby making the damage detec tion process more uncertain the analysis of changes in the stiffness matrix is typically cumbersome may not always yield correct answers and does not permit the determination of the extent of damage this paper presents an approach that is designed to circum vent the problems just discussed the output error method or structural identification9 is used wherein the analytical model is refined to minimize the difference between the predicted and measured response of the structure iterative nonlinear pro gramming methods are employed to determine a solution to the unconstrained optimization problem damage is repre sented by reduction in the elastic extensional and shear moduli of the element and those are designated as the design varia bles of the problem the use of static structural displacements as the measured response is a departure from the standard practice of using eigenmodes alone for the identification pro blem numerical evidence clearly indicates that when eigen modes alone are used for identification the location and ex tent of damage predicted by the optimization approach is dependent on the number of modes used to match the measured and the predicted response higher modes are diffi cult to determine and measure and the use of static displace ments obtained by a loading that simulates higher modes is proposed as a solution to this problem the paper also presents an implementation of the proposed damage assessment strategies with special focus on problems of practical significance in this context the use of incomplete modal or static displacement information in the identification problem is discussed further the approach of treating the modulus of each structural element as an independent design variable results in a large dimensionality problem this results in significant computational costs when using a gradient based nonlinear programming algorithm for function minimization the use of a reduced set of dominant design variables and the construction of equivalent reduced order models for damage assessment are explored with some success

use of kriging models to approximate deterministic computer models the use of kriging models for approximation and metamodel based design and optimization has been steadily on the rise in the past decade the widespread usage of kriging models appears to be hampered by 1 the lack of guidance in selecting the appropriate form of the kriging model 2 computationally efficient algorithms for estimating the model s parameters and 3 an effective method to assess the resulting model s quality in this paper we compare 1 maximum likelihood estimation mle and cross validation cv parameter estimation methods for selecting a kriging model s parameters given its form and 2 and an r 2 of prediction and the corrected akaike information criterion for assessing the quality of the created kriging model permitting the comparison of different forms of a kriging model these methods are demonstrated with six test problems finally different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

sensitivity of complex internally coupled systems a method is presented for computing sensitivity derivatives with respect to independent input variables for complex internally coupled systems while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis the method entails two alternative algorithms the first is based on the classical implicit function theorem formulated on residuals of governing equations and the second develops the system sensitivity equations in a new form using the partial local sensitivity derivatives of the output with respect to the input for each part of the system a few application examples are presented to illustrate the discussion the method has potential to answer the what if questions by presenting engineers wigi sensitivity information on design tradeoffs to guide human judgment and formal optimization in addition the method is compatible with the modern technology of distributed computing as well as traditional division of design tasks among groups of specialists in the design process the capability to quantify the effects of proposed design changes may provide the basis for a mathematical model of design

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

multiple solutions for boundary value problems of second order difference equations with resonance in this paper we study the existence of multiple solutions for boundary value problems of second order difference equations with resonance at both infinity and zero by using morse theory critical point theory minimax methods and bifurcation theory

gaussian functional regression for output prediction in this paper we introduce a gaussian functional regression gfr technique that integrates multi fidelity models with model reduction to efficiently predict the input output relationship of a high fidelity model the gfr method combines the high fidelity model with a low fidelity model to provide an estimate of the output of the high fidelity model in the form of a posterior distribution that can characterize uncertainty in the prediction a reduced basis approximation is constructed upon the low fidelity model and incorporated into the gfr method to yield an inexpensive posterior distribution of the output estimate as this posterior distribution depends crucially on a set of training inputs at which the high fidelity models are simulated we develop a greedy sampling algorithm to select the training inputs our approach results in an output prediction model that inherits the fidelity of the high fidelity model and has the computational complexity of the reduced basis approximation numerical results are presented to demonstrate the proposed approach

shape optimization of 2d structures using simulated annealing the goal of this study is to obtain globally optimum shapes for two dimensional structures subject to quasi static loads and restraints for this purpose a technique is proposed using which the volume or weight of a structure can be minimized the emphasis is on how one can define the shape precisely and find a shape that accurately reflects the globally optimum shape as design constraints stresses developed in the structure should not exceed the maximum allowable stress and connectivity of the structure should not be lost during shape changes optimization is achieved by a stochastic search algorithm called direct simulated annealing dsa which seeks the global minimum through randomly generated configurations in order to obtain random configurations a boundary variation technique is used in this technique a set of key points is chosen and connected by cubic splines to describe the boundary of the structure whenever the positions of the key points are changed in random directions a new shape is obtained thus coordinates of the key points serve as design variables in order to apply the optimization procedure a general computer code was developed using ansys parametric design language a number of cases were examined to test its effectiveness the results show that this technique can be applied to two dimensional shape optimization problems with high reliability even for cases where the entire free boundary is allowed to vary 2007 elsevier b v all rights reserved

nonparametric checks for single index models in this paper we study goodness of fit testing of single index models the large sample behavior of certain score type test statistics is investigated as a by product we obtain asymptotically distribution free maximin tests for a large class of local alternatives furthermore characteristic function based goodness of fit tests are proposed which are omnibus and able to detect peak alternatives simulation results indicate that the approximation through the limit distribution is acceptable already for moderate sample sizes applications to two real data sets are illustrated

existence and multiplicity results for classes of elliptic resonant problems in this paper we prove some new existence results of nontrivial solutions for classes of elliptic resonant problems we also establish several multiplicity results the methods used here are based on combining the minimax methods and the morse theory especially some new observations on the critical groups of a local linking type degenerate critical point

nonlinear elliptic equations with a jumping reaction abstract we study a nonlinear nonhomogeneous dirichlet problem driven by the sum of a p laplacian and a laplacian 2 p and a jumping nonlinearity under very general conditions on the reaction and without using the fucik spectrum we show that the problem has at least three nontrivial solutions and we provide sign information for all of them our approach uses critical point theory truncation and comparison techniques and morse theory

multiple solutions to a robin problem with indefinite weight and asymmetric reaction abstract the existence of two nontrivial smooth solutions to a semilinear robin problem with indefinite unbounded potential and asymmetric nonlinearity f is established both crossing and resonance are allowed a third nonzero solution exists provided f is c 1 proofs exploit variational methods truncation techniques and morse theory

the effect of simulation order on level accuracy and power of monte carlo tests we discuss the effect of simulation order on level accuracy and power of monte carlo tests in a very general setting both parametric problems with or without nuisance parameters and nonparametric problems are treated by a single unifying argument it is shown that if the level of a monte carlo test is known only nominally not precisely then the level error of a monte carlo test is an order of magnitude less than that of the corresponding asymptotic test this result is available whenever the test statistic is asymptotically pivotal even if the number of simulations is held fixed as the sample size n increases it implies that monte carlo methods are a real alternative to asymptotic methods we also show that even if the number of simulations is held fixed a monte carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n 12 from the null

unique continuation for elliptic operators a geometric variational approach dans un sous ensemble connexe ouvert de r n n 3 on considere l equation d ordre 2 lu div a x u b x u v x u 0 ou a x a id j x est une matrice symetrique reelle on etudie les proprietes d unicite de l operateur

a tabu search hooke and jeeves algorithm for unconstrained optimization this paper addresses the problem of finding the global minimum of a nonconvex function a new hybrid algorithm for this problem based on tabu search is developed it is hybrid in the sense that search directions are generated using tabu search strategy and then they are used in an optimization algorithm the algorithm is tested on some standard test functions and its performance is compared with existing algorithms computational results show that the proposed algorithm is very efficient and robust

semilinear elliptic problems near resonance with a nonprincipal eigenvalue abstract we consider the dirichlet problem for the equation u u f x u h x in a bounded domain where f has a sublinear growth and h l 2 we find suitable conditions on f and h in order to have at least two solutions for near to an eigenvalue of a typical example to which our results apply is when f x u behaves at infinity like a x u q 2 u with m a x 0 and 1 q 2

nontrivial critical points for asymptotically quadratic function abstract in this paper we study the existence of nontrivial critical points as applications we study the existence of nontrivial solutions of the dirichelet problem for nonlinear elliptic pde and periodic boundary value problem for nonlinear ope

infinitely many solutions for a class of semilinear elliptic equations abstract in this paper we find some new conditions to ensure the existence of infinitely many nontrivial solutions for the dirichlet boundary value problems of the form u a x u g x u in a bounded smooth domain conditions s 1 s 3 in the present paper are somewhat weaker than the famous ambrosetti rabinowitz type superquadratic condition here we assume that the primitive of the nonlinearity g is either asymptotically quadratic or superquadratic as u

predicting the output from a complex computer code when fast approximations are available s we consider prediction and uncertainty analysis for complex computer codes which can be run at different levels of sophistication in particular we wish to improve efficiency by combining expensive runs of the most complex versions of the code with relatively cheap runs from one or more simpler approximations a bayesian approach is described in which prior beliefs about the codes are represented in terms of gaussian processes an example is presented using two versions of an oil reservoir simulator 1 c complex mathematical models implemented in large computer codes have been used to study real systems in many areas of scientific research sacks et al 1989 usually because physical experimentation is too costly and sometimes impossible as in the case of large environmental systems a computer experiment involves running the code with various input values for the purpose of learning something about the real system often a simulator can be run at different levels of complexity with versions ranging from the most sophisticated high level code to the most basic for example in 4 we consider two codes which simulate oil pressure at a well of a hydrocarbon reservoir both codes use finite element analysis in which the rocks comprising the reservoir are represented by small interacting grid blocks the flow of oil within the reservoir can be simulated by considering the interaction between the blocks the two codes differ in the resolution of the grid so that we have a very accurate slow version using many small blocks and a crude approximation using large blocks which runs much faster alternatively a mathematical model could be expanded to include more of the scientific laws underlying the physical processes simple fast versions of the code may well include the most important features and are useful for preliminary investigations in real time applications the number of runs from a high level simulator may be limited by expense then there is a need to trade off the complexity of the expensive code with the availability of the simpler approximations the purpose of the current paper is to explore ways in which runs from several levels of a code can be used to make inference about the output from the most complex code we may also have uncertainty about values for the input parameters which apply in any given application uncertainty analysis of computer codes describes how this uncertainty on the inputs affects our uncertainty about the output

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

tabu search method with random moves for globally optimal design optimum engineering design problems are usually formulated as non convex optimization problems of continuous variables because of the absence of convexity structure they can have multiple minima and global optimization becomes difficult traditional methods of optimization such as penalty methods can often be trapped at a local optimum the tabu search method with random moves to solve approximately these problems is introduced its reliability and efficiency are examined with the help of standard test functions by the analysis of the implementations it is seen that this method is easy to use and no derivative information is necessary it outperforms the random search method and composite genetic algorithm in particular it is applied to minimum weight design examples of a three bar truss coil springs a z section and a channel section for the channel section the optimal design using the tabu search method with random moves saved 26 14 per cent over the weight of the sumt method

a test for symmetries of multivariate probability distributions a monte carlo test for multivariate symmetries is proposed the monte carlo simulations are performed conditionally on a minimal sufficient statistic for the class of distributions with symmetric density additionally a general purpose test statistic based on a distance measure between the probability density function and its symmetrised version is introduced the monte carlo tests for spherical symmetry and multivariate reflection symmetry are studied numerically for this statistic and the results indicate that the tests perform well compared to other tests the method is illustrated with an analysis of a real dataset

multiplicity results and qualitative properties for neumann semilinear elliptic problems abstract in this paper we establish the existence of multiple ordered classical solutions for neumann semilinear elliptic problems and provide qualitative information about them no symmetry assumptions are required neither on the nonlinearity nor on the domain for some results the growth of the nonlinearity at infinity is arbitrary we also consider the cases when the nonlinearity is either superlinear or asymptotically linear with strong resonances extensive use is made of the mountain pass theorem and leray schauder topological degree

nonparametric monte carlo tests for multivariate distributions summary in this paper nonparametric monte carlo test procedures are proposed for composite hypotheses in which the multivariate distribution belongs to a nonparametric family when a random variable is in distribution equal to a product of two independent variables monte carlo simulations can be performed conditionally on one of the variables they can be applied to testing several commonly used distributions including elliptically symmetric reflectively symmetric liouville dirichlet and symmetric scale mixture distributions the tests are exactly valid when the hypothetical distributions are without nuisance location parameters finite sample simulations show that the monte carlo tests outperform bootstrap tests the method is illustrated with analysis of a real dataset

permutation genetic algorithm for stacking sequence design of composite laminates abstract stacking sequence design of a composite laminate with a given set of plies is a combinatorial problem of seeking an optimal permutation permutation genetic algorithms optimizing the stacking sequence of a composite laminate for maximum buckling load are studied a new permutation ga named gene rank ga is developed and compared with an existing partially mapped permutation ga originally developed for solving the travelling salesman problem the two permutation gas are also compared with a standard non permutation ga it is demonstrated through examples that the permutation gas are more efficient for stacking sequence optimization than a standard ga repair strategies for standard ga and the two permutation gas for dealing with constraints are also developed it is shown that using repair can significantly reduce computation cost for both standard ga and permutation ga

testing for spherical symmetry of a multivariate distribution rotationally invariant tests based on test statistics of the von mises type are proposed under the hypothesis of spherical symmetry of a multivariate distribution the tests are distribution free when the hypothesis of spherical symmetry is true the asymptotic distribution of the test statistics are derived under the null hypothesis and under any fixed alternative a simple criterion for consistency is given the results are illustrated by numerous examples of test statistics which give rise to tests being consistent against all alternatives

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

stochastic simulations conditioned on sufficient statistics summary a general method for doing monte carlo simulations conditioned on sufficient statistics is presented the basic idea is to adjust the parameter values in the corresponding unconditional simulation so that the actual value of the sufficient statistic is obtained in the case of multiple solutions to this problem the method has to be modified even if the corresponding value of the simulated variable is unique for each simulation the methods are illustrated for some simple models in which the conditional distributions are well known as a more complicated example an exact analysis of variance test in the gamma model is performed other examples are a modification of the kolmogorov goodness of fit test into an exact test and minimum variance unbiased estimation of cumulative distributions

multiplicity of solutions for resonant neumann problems with an indefinite and unbounded potential we examine semilinear neumann problems driven by the laplacian plus an unbounded and indefinite potential the reaction is a caratheodory function which exhibits linear growth near we allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue and we prove several multiplicity results our approach uses critical point theory morse theory and the reduction method the lyapunov schmidt method

sign changing solutions for resonant neumann problems we consider semilinear neumann problems at resonance we are concerned with two distinct cases in the first one the potential function is unbounded and indefinite in the second case the potential function is bounded and the reaction exhibits a concave parametric term near the origin we prove two existence theorems producing sign changing solutions the first main result is a complement of the results obtained by papageorgiou and r dulescu 2015 22 the second theorem gives an answer to the open question raised by candito et al 2016 4 our approach uses variational methods together with flow invariance arguments

multifidelity quasi newton method for design optimization multifidelity approaches are frequently used in design when high fidelity models are too expensive to use directly and lower fidelity models of reasonable accuracy exist in optimization corrected

an approximation concepts approach to shape optimal design abstract in the past much of the work done in structural optimization consisted in resizing the members of fixed configuration models in that case a powerful design procedure has now emerged which is based on the coordinate use of explicit high quality approximations of the behavior constraints and dual methods of mathematical programming there is however a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself the main objectives of this paper are to recall briefly a convenient geometric representation in which the boundaries of the structure are represented by bezier or b spline curves and then to discuss the choice of optimization algorithm it is shown that cost efficient methods for structural sizing may be advantageously extended to shape optimal design problems different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods many large scale applications are treated to demonstrate the generality and the efficiency of the new formulation finally considerations are given about an integrated approach including cad computer codes and finite element optimization software

parametric domain decomposition for accurate reduced order models applications of mp lrom methodology abstract the multivariate predictions of local reduced order models mp lrom methodology recently proposed by the authors moosavi et al 0000 uses machine learning based regression methods to predict the errors of reduced order models this study considers two applications of mp lrom first the error model is used in conjunction with a greedy sampling algorithm to generate decompositions of one dimensional parametric domains with overlapping regions such that the associated local reduced order models meet the prescribed accuracy requirements once a parametric domain decomposition is constructed any parametric configuration belongs to at least one of the partitions the local reduced order model associated with that partition approximates the full order model at the given parameters within an accuracy level that is estimated a priori the parameter domain decomposition creates a database of the available local bases local reduced order and high fidelity models and identifies the most accurate solutions for an arbitrary parametric configuration next this database is used to enhance the accuracy of the reduced order models using 1 lagrange interpolation of reduced bases in the matrix space 2 lagrange interpolation of reduced bases in the tangent space of the grassmann manifold 3 concatenation of reduced bases followed by a gram schmidt orthogonalization process and 4 lagrange interpolation of high fidelity model solutions numerical results with a viscous burgers model illustrate the potential of the mp lrom methodology to improve the design of parametric reduced order models

hybrid optimization strategy beyond local optima in aerospace panel designs convergence to local optima rather than the global optimum is a common shortcoming of directed seareh gradient based optimization techniques successive convergence on better local optima is an efficient way of finding the global optimum and is achieved by the proposed hybrid global optimization strategy which combines ideas from the improving hit and run and the tunneling global optimization methods the searching technique of improving hit and run is adapted to find suitable starting points to converge on other better local optima the suitability of candidate starting points is confirmed by the concept of the tunneling method the strategy presented has unique features due to the underlying structural theory being exact in the sense of differential equations being solved for the member or element stiffnesses so that they are transcendental functions of the load factor hence the buckling eigenproblem for the entire structure is a transcendental one instead of the linear one associated with the more usual finite element method formulations constrained minimum mass aerospace panel stability design problems are used to demonstrate the efficiency and robustness of the hybrid global optimization strategy

a genetic algorithm approach to single and multiobjective structural optimization with discrete continuous variables a search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems this procedure known as a genetic algorithm ga utilizes a blending of the principles of natural genetics and natural selection a lack of dependence on the gradient information makes gas less susceptible to pitfalls of convergence to a local optimum to model the multiple objective functions in the problem formulation a co operative game theoretic approach is proposed examples dealing with single and multiobjective geometrical design of structures with discrete continuous design variables and using artificial genetic search are presented simulation results indicate that gas converge to optimum solutions by searching only a small fraction of the solution space the optimum solutions obtained using gas compare favourably with optimum solutions obtained using gradient based search techniques the results indicate that the efficiency and power of gas can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency