construction of a probabilistic model for impedance matrices impedance matrices allow for the coupling of domains with very different properties and possibly modeled with different methods this paper presents the construction of a probabilistic model for such matrices using a nonparametric method that allows for the consideration of data errors as well as model errors to enable the application of this method in the case of a domain for which no finite element model is available the identification of a hidden state variables model from the knowledge of the impedance matrix at a discrete set of frequencies is also described finally the construction of the probabilistic model of the impedance of a pile foundation on a layered unbounded soil illustrates the capabilities of the method

required relationship between objective function and pareto frontier orders practical implications it is well known that the weighted sum aggregate objective function fails to capture pareto points that are located on a concave region of the pareto frontier conditions are established for a general aggregate objective function to capture points on a concave pareto frontier region specifically these conditions are developed in terms of the relative orders of the pareto frontier and aggregate objective function these critical conditions can be used in practice to allow an aggregate objective function to capture any potentially desirable pareto point conversely failure to satisfy these critical conditions can represent a pivotal failure point of the general application of design optimization because we may fail to obtain the design we seek

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

nonparametric probabilistic approach of uncertainties for elliptic boundary value problem the paper is devoted to elliptic boundary value problems with uncertainties such a problem has already been analyzed in the context of the parametric probabilistic approach of system parameters uncertainties or for random media model uncertainties are induced by the mathematical physical process which allows the boundary value problem to be constructed from the design system if experiments are not available the bayesian approach cannot be used to take into account model uncertainties recently a nonparametric probabilistic approach of both the model uncertainties and system parameters uncertainties has been proposed by the author to analyze uncertain linear and non linear dynamical systems nevertheless the use of this concept that has to be developed for dynamical systems cannot directly be applied for elliptic boundary value problem for instance for a linear elastostatic problem relative to an elastic bounded domain we then propose an extension of the nonparametric probabilistic approach in order to take into account model uncertainties for strictly elliptic boundary value problems the theory and its validation are presented

generalizations of orthogonal polynomials we give a survey of recent generalizations of orthogonal polynomials that includes multidimensional matrix and vector orthogonal polynomials and multivariate versions multipole orthogonal rational functions variants and extensions of the orthogonality conditions multiple orthogonality most of these generalizations are inspired by the applications in which they are applied we also give a glimpse of these applications which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role moment problems numerical quadrature rational approximation linear algebra recurrence relations and random matrices

a nonparametric probabilistic approach for quantifying uncertainties in low dimensional and high dimensional nonlinear models summary a nonparametric probabilistic approach for modeling uncertainties in projection based nonlinear reduced order models is presented when experimental data are available this approach can also quantify uncertainties in the associated high dimensional models the main underlying idea is twofold first to substitute the deterministic reduced order basis rob with a stochastic counterpart second to construct the probability measure of the stochastic reduced order basis srob on a subset of a compact stiefel manifold in order to preserve some important properties of a rob the stochastic modeling is performed so that the probability distribution of the constructed srob depends on a small number of hyperparameters these are determined by solving a reduced order statistical inverse problem the mathematical properties of this novel approach for quantifying model uncertainties are analyzed through theoretical developments and numerical simulations its potential is demonstrated through several example problems from computational structural dynamics copyright 2016 john wiley sons ltd

integral grothendieck riemann roch theorem we show that in characteristic zero the obvious integral version of the grothendieck riemann roch formula obtained by clearing the denominators of the todd and chern characters is true without having to divide the chow groups by their torsion subgroups the proof introduces an alternative to grothendieck s strategy we use resolution of singularities and the weak factorization theorem for birational maps

maximum entropy approach for modeling random uncertainties in transient elastodynamics a new approach is presented for analyzing random uncertainties in dynamical systems this approach consists of modeling random uncertainties by a nonparametric model allowing transient responses of mechanical systems submitted to impulsive loads to be predicted in the context of linear structural dynamics the information used does not require the description of the local parameters of the mechanical model the probability model is deduced from the use of the entropy optimization principle whose available information is constituted of the algebraic properties related to the generalized mass damping and stiffness matrices which have to be positive definite symmetric matrices and the knowledge of these matrices for the mean reduced matrix model an explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to monte carlo numerical simulation in order to compute the transient responses of structures submitted to impulsive loads the fundamental properties related to the convergence of the stochastic solution with respect to the dimension of the random reduced matrix model are analyzed finally an example is presented

richardson extrapolation based sensitivity analysis in the multi objective optimization of analog circuits the feasible solutions provided by a multi objective evolutionary algorithm moea in the optimal sizing of analog integrated circuits ics can be very sensitive to process variations therefore to select the optimal sizes of metal oxide semiconductor field effect transistors mosfets but with low sensitivities we propose to perform multi parameter sensitivity analysis however since moeas generate feasible solutions without an explicit equation then we show the application of richardson extrapolation to approximate the partial derivatives associated to the sensitivities of the performances of an amplifier with respect to the sizes of every mosfet the proposed multi parameter sensitivity analysis is verified through the optimization of a recycled folded cascode rfc operational transconductance amplifier ota we show the behavior of the multi parameter sensitivity approach versus generations the final results show that the optimal sizes selected after executing the sensitivity approach guarantee the lowest sensitivities values while improving the performances of the rfc ota

approximating pareto frontier using a hybrid line search approach the aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach but it is well known that this technique sometimes fail in different aspects for determining the pareto frontier this paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point once the first pareto solution is obtained a simplified version of the former one is used in the context of pareto dominance to obtain a set of efficient points which will assure a thorough distribution of solutions on the pareto frontier in the current form the proposed technique is well suitable for problems having multiple objectives it is not limited to bi objective problems and require the functions to be continuous twice differentiable in order to assess the effectiveness of this approach some experiments were performed and compared with two recent well known population based metaheuristics namely parego and nsga ii when compared to parego and nsga ii the proposed approach not only assures a better convergence to the pareto frontier but also illustrates a good distribution of solutions from a computational point of view both stages of the line search converge within a short time average about 150ms for the first stage and about 20ms for the second stage apart from this the proposed technique is very simple easy to implement and use to solve multiobjective problems

orthogonal basis functions in discrete least squares rational approximation we consider a problem that arises in the field of frequency domain system identification if a discrete time system has an input output relation y z g z u z with transter function g then the problem is to find a rational approximation n for g the data given are measurements of input and output spectra in the frequency points zk u zk y zk nk 1 together with some weight the approximation criterion is to minimize the weighted discrete least squares norm of the vector obtained by evaluating g n in the measurement points if the poles of the system are fixed then the problem reduces to a linear least squares problem in two possible ways by multiplying out the denominators and hide these in the weight which leads to the construction of orthogonal vector polynomials or the problem can be solved directly using an orthogonal basis of rational functions the orthogonality of the basis is important because if the transfer function n is represented with respect to a nonorthogonal basis then this least squares problem can be very ill conditioned even if an orthogonal basis is used but with respect to the wrong inner product e g the lebesgue measure on the unit circle numerical instability can be fatal in practice we show that both approaches lead to an inverse eigenvalue problem which forms the common framework in which fast and numerically stable algorithms can be designed for the computation of the orthonormal basis

discrete representation of non dominated sets in multi objective linear programming abstract in this paper we address the problem of representing the continuous but non convex set of non dominated points of a multi objective linear programme by a finite subset of such points we prove that a related decision problem is np complete moreover we illustrate the drawbacks of the known global shooting normal boundary intersection and normal constraint methods concerning the coverage error and uniformity level of the representation by examples we propose a method which combines the global shooting and normal boundary intersection methods by doing so we overcome their limitations but preserve their advantages we prove that our method computes a set of evenly distributed non dominated points for which the coverage error and the uniformity level can be guaranteed we apply this method to an optimisation problem in radiation therapy and present illustrative results for some clinical cases finally we present numerical results on randomly generated examples

calibration of the damping dispersion parameter in a non parametric probabilistic approach abstract response predictions in structural dynamics are in general very sensitive to random uncertainties associated with the underlying predictive mathematical model one way to capture parametric and model uncertainties consists in the construction of a non parametric probabilistic model in which the reduced structural matrices are replaced by random matrices the uncertainties are introduced at a global level and controlled through one dispersion parameter each for the mass damping and stiffness matrix in the present paper the role of the damping dispersion parameter is investigated for the case in which the adopted non parametric model is calibrated with respect to an existing parametric model it is shown that in the non parametric model the influence of the damping dispersion on the scatter in the frequency response is relatively small if a calibration criterion based on matrix norms is used a novel method for calibrating this non parametric model is proposed which enforces the same scatter of the frequency response function frf at the first resonance frequency in the parametric and the non parametric model a case study involving a satellite fe model shows that with this approach the frf scatter of the non parametric model reaches a level similar to that of the parametric model used for its calibration

structural model updating and prediction variability using pareto optimal models a multi objective identification method for structural model updating based on modal residuals is presented the method results in multiple pareto optimal structural models that are consistent with the experimentally measured modal data and the modal residuals used to measure the discrepancies between the measured and model predicted modal characteristics these pareto optimal models are due to uncertainties arising from model and measurement errors the relation between the multi objective identification method and the conventional single objective weighted modal residuals method for model updating is investigated using this relation an optimally weighted modal residuals method is also proposed to rationally select the most preferred model among the alternative multiple pareto optimal models for further use in structural model prediction studies computational issues related to the reliable solution of the resulting multi objective and single optimization problems are addressed the model updating methods are compared and their effectiveness is demonstrated using experimental results obtained from a three story laboratory structure tested at a reference and a mass modified configuration the variability of the pareto optimal models and their associated response prediction variability are explored using two structural model classes a simple 3 dof model class and a higher fidelity 546 dof finite element model class it is demonstrated that the pareto optimal structural models and the corresponding response and reliability predictions may vary considerably depending on the fidelity of the model class and the size of measurement errors

unramified cohomology of degree 3 and noether s problem let g be a finite group and w be a faithful representation of g over c the group g acts on the field of rational functions c w the question whether the field of invariant functions c w g is purely transcendental over c goes back to emmy noether using the unramified cohomology group of degree 2 of this field as an invariant saltman gave the first examples for which c w g is not rational over c around 1986 bogomolov gave a formula which expresses this cohomology group in terms of the cohomology of the group g

on the pareto optimum sensitivity analysis in multicriteria optimization to analyse the trade off relations among the set of criteria in multicriteria optimization pareto optimum sensitivity analysis is systematically studied in this paper original contributions cover two parts theoretical demonstrations are firstly made to validate the gradient projection method in pareto optimum sensitivity analysis it is shown that the projected gradient direction evaluated at a given pareto optimum in the design variable space rigorously corresponds to the tangent direction of the pareto curve surface at that point in the objective space this statement holds even for the change of the set of active constraints in the perturbed problem secondly a new active constraint updating strategy is proposed which permits the identification of the active constraint set change to determine the influence of this change upon the differentiability of the pareto curve and finally to compute directional derivatives in non differentiable cases this work will highlight some basic issues in multicriteria optimization some numerical problems are solved to illustrate these novelties

riemann roch for tensor powers mapping a locally free module on a scheme to its l th tensor power gives rise to a natural map from the grothendieck group of all locally free modules to the grothendieck group of all locally free representations of the l th symmetric group in this paper we prove some formulas of riemann roch type for the behavior of this tensor power operation with respect to the push forward homomorphism associated with a projective morphism between schemes we furthermore establish analogous formulas for higher k groups

classes de stiefel whitney de formes quadratiques et de representations galoisiennes reelles i u n peu de t o p o l o g i e a l g6b r ique 226 1 1 le fonc t eu r 226 1 2 le t rans fe r t mu l t i p l i c a t i f 228 1 3 t rans f e r t et c lasses de s t ie fe l whi tney 233 1 4 le cas d u n g r o u p e d iscre t t r a d u c t i o n s 238

a radial boundary intersection aided interior point method for multi objective optimization abstract we propose a novel multi objective optimization technique combining non convex radial boundary intersection based decomposition with an interior point method which utilizes both line search and trust region steps suitable for non convex nonlinear optimization radial boundary intersection decomposes the multi objective optimization problem into subproblems which are concerned with finding the solutions closest to a reference point along equally spaced lines emanating radially outwards from the latter point the proposed approach is found to be able to generate good approximations of the pareto front including the periphery by generating a sufficiently diverse set of pareto optimal solutions the proposed method is extensively tested on a large number of recent benchmark problems and real world problems and the performance is found to be favorable in comparison to those of some of the cutting edge stochastic evolutionary optimization algorithms that are commonly used to solve non convex multi objective optimization problems

whitney stratified chains and cochains this paper contains the technical constructions necessary for a geometric cycle definition of cohomology and homology in the context of whitney stratifications cup and cap products are interpreted as the transverse intersection of geometric cocycles and cycles

an evolutionary shape optimization for elastic contact problems subject to multiple load cases most structures in the real life are subject to multiple load cases this paper aims at extending the evolutionary structural optimization eso algorithm to optimal contact shape design for elastic bodies under the multiple load cases to evaluate the reference stresses of each contact node in a finite element framework an extreme stress criterion the worst case design and a weighted average criterion pareto design are presented in the extreme stress method the highest nodal contact stress under all load cases is adopted as the reference level in the weighted average method the weighted sum of nodal contact stresses over all the load cases is regarded as the reference it is found that these two criteria can produce different results in this paper the examples are presented to demonstrate some new features of contact shape optimization in the presence of the multiple load cases

a successive approach to compute the bounded pareto front of practical multiobjective optimization problems this work focuses on the generation of the pareto front for practical applications such as analog circuit sizing the pareto front is the solution to a multiobjective optimization problem it shows all possible optimal compromises between conflicting design objectives performances in technical applications the pareto front is usually bounded it is shown in this work that the boundary of the pareto front consists of so called trade off limits if certain criteria are fulfilled these trade off limits can be computed by solving a multiobjective optimization problem for a subset of the performances a novel approach to pareto optimization is presented which is based on the generation of the trade off limits the pareto front for any number of performances is built up systematically in a successive manner pareto optimal solutions on the boundary of a pareto front are generated first in the next step the inner part of the pareto front is populated with pareto optimal solutions this is the first approach which generates a discretized approximation that shows the total extent of a bounded pareto front without requiring to calculate suboptimal solutions it requires that the pareto front exists is bounded and connected with no gaps and that the set of weakly pareto optimal solutions and pareto optimal solutions are equal

stiefel whitney classes of real representations of finite groups abstract we prove the existence and uniqueness of stiefel whitney classes of real representations subject to the hirzebruch axioms within the category of finite groups we also give a method of constructing and computing with these classes using multiplicative transfer and induced representations and apply our formulae in certain simple cases

necessary and sufficient karush kuhn tucker conditions for multiobjective markov chains optimality the solution concepts proposed in this paper follow the karush kuhn tucker kkt conditions for a pareto optimal solution in finite time ergodic and controllable markov chains multi objective programming problems in order to solve the problem we introduce the tikhonov s regularizator for ensuring the objective function is strict convex then we consider the c variable method for introducing equality constraints that guarantee the result belongs to the simplex and satisfies ergodicity constraints lastly we restrict the cost functions allowing points in the pareto front to have a small distance from one another the computed image points give a continuous approximation of the whole pareto surface the constraints imposed by the c variable method make the problem computationally tractable and the restriction imposed by the small distance change ensures the continuation of the pareto front we transform the multi objective nonlinear problem into an equivalent nonlinear programming problem by introducing the lagrange function multipliers as a result we obtain that the objective function is strict convex the inequality constraints are continuously differentiable and the equality constraint is an affine function under these settings the kkt optimality necessary and sufficient conditions are elicited naturally a numerical example is solved for providing the basic techniques to compute the pareto optimal solutions by resorting to kkt conditions

time domain formulation in computational dynamics for linear viscoelastic media with model uncertainties and stochastic excitation the paper is devoted to the computational time domain formulation of linear viscoelastic systems submitted to a nonstationary stochastic excitation and in the presence of model uncertainties which are modeled in the framework of the probability theory the objective is to introduce and to develop an adapted and complete formulation of such a problem in the context of computational mechanics a reduced order model in the time domain with stochastic excitation is derived from the computational model for the reduced order model the stochastic modeling of both computational model parameter uncertainties and modeling errors is carried out using the nonparametric probabilistic approach and the random matrix theory we present a new formulation of model uncertainties to construct the random operators for viscoelastic media we then obtained a linear stochastic integro differential equation side with random operators and with a stochastic nonhomogeneous part stochastic excitation a time discretization of this side is proposed in a first step the side is transformed to a linear ito stochastic differential equation isde with random operators then the isde is discretized using an extension of the stormer verlet scheme which is a particularly well adapted algorithm for long time good behavior of the numerical solution finally for the stochastic solver and statistical estimations of the random responses we propose to use the monte carlo simulation for gaussian and non gaussian excitations

normal constraint method with guarantee of even representation of complete pareto frontier multiobjective optimization is rapidly becoming an invaluable tool in engineering design a particular class of solutions to the multiobjective optimization problem is said to belong to the pareto frontier a pareto solution the set of which comprises the pareto frontier is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other accordingly the pareto frontier plays an important role in engineering design it characterizes the tradeoffs between conflicting design objectives some optimization methods can be used to automatically generate a set of pareto solutions from which a final design is subjectively chosen by the designer for this approach to be successful the generated pareto set must be truly representative of the complete optimal design space pareto frontier in other words the set must not overrepresent one region of the design space or neglect others some commonly used methods comply with this requirement whereas others do not this paper offers a new phase in the development of the normal constraint method which is a simple approach for generating pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives the even distribution of the generated pareto solutions can facilitate the process of developing an analytical expression for the pareto frontier in n dimension an even distribution of pareto solutions also facilitates the task of choosing the most desirable final design from among the set of pareto solutions the normal constraint method bears some similarities to the normal boundary intersection and constraint methods importantly the developments presented in this paper define its critical distinction namely the ability to generate a set of evenly distributed pareto solutions over the complete pareto frontier examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method as well as with the original normal constraint method

stochastic modeling of uncertainties in computational structural dynamics recent theoretical advances this paper deals with a short overview on stochastic modeling of uncertainties we introduce the types of uncertainties the variability of real systems the types of probabilistic approaches the representations for the stochastic models of uncertainties the construction of the stochastic models using the maximum entropy principle the propagation of uncertainties the methods to solve the stochastic dynamical equations the identification of the prior and the posterior stochastic models the robust updating of the computational models and the robust design with uncertain computational models we present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties and for their identification with experimental data we also present the construction of the posterior stochastic model of uncertainties using the bayesian method

a parallel algorithm for discrete least squares rational approximation a new method for discrete least squares linearized rational approximation is presented it generalizes the algorithm of rutishauser gragg harrod reichel for discrete least squares polynomial approximation to the rational case the algorithm is fast in the sense that it requires orderm computation time wherem is the number of data points and is the degree of the approximant we describe how this algorithm can be implemented in parallel

optimizations under uncertainty using gradients hessians and surrogate models in this article a first order moment method and a kriging surrogate model are used for optimizations under uncertainty applied to two bar truss designs and two dimensional lift constrained drag minimizations given uncertainties in statistically independent random normally distributed input variables the two approaches are used to propagate these uncertainties through the mathematical model and to approximate output statistics of interest to assess the validity of the approximations the results are compared with full monte carlo simulations when using first order moment methods for robust optimizations first order sensitivity derivatives appear in the objective function and system constraints therefore second order sensitivity derivatives are needed for gradient based optimization approaches when the kriging surrogate model is used to calculate the objective function value and system constraints it will be shown that a gradient predictor for the kriging model can be successfully used for gradi

multiobjective bilevel optimization in this work nonlinear non convex multiobjective bilevel optimization problems are discussed using an optimistic approach it is shown that the set of feasible points of the upper level function the so called induced set can be expressed as the set of minimal solutions of a multiobjective optimization problem this artificial problem is solved by using a scalarization approach by pascoletti and serafini combined with an adaptive parameter control based on sensitivity results for this problem the bilevel optimization problem is then solved by an iterative process using again sensitivity theorems for exploring the induced set and the whole efficient set is approximated for the case of bicriteria optimization problems on both levels and for a one dimensional upper level variable an algorithm is presented for the first time and applied to two problems a theoretical example and a problem arising in applications

constraint propagation using dominance in interval branch bound for nonlinear biobjective optimization abstract constraint propagation has been widely used in nonlinear single objective optimization inside interval branch bound algorithms as an efficient way to discard infeasible and non optimal regions of the search space on the other hand when considering two objective functions constraint propagation is uncommon it has mostly been applied in combinatorial problems inside particular methods the difficulty is in the exploitation of dominance relations in order to discard the so called non pareto optimal solutions inside a decision domain which complicates the design of complete and efficient constraint propagation methods exploiting dominance relations in this paper we present an interval branch bound algorithm which integrates dominance contractors constraint propagation mechanisms that exploit an upper bound set using dominance relations this method discards from the decision space values yielding solutions dominated by some solutions from the upper bound set the effectiveness of the approach is shown on a sample of benchmark problems

a combined scalarizing method for multiobjective programming problems abstract in this paper a new general scalarization technique for solving multiobjective optimization problems is presented after studying the properties of this formulation two problems as special cases of this general formula are considered it is shown that some well known methods such as the weighted sum method the constraint method the benson method the hybrid method and the elastic constraint method can be subsumed under these two problems then considering approximate solutions some relationships between e weakly properly efficient points of a general without any convexity assumption multiobjective optimization problem and optimal solutions of the introduced scalarized problem are achieved

nondomination level coordinate system for parameterizing and exploring pareto frontiers this paper presents a method for defining a barycentric coordinate system on a k objective pareto frontier that is constructed from nondomination levels calculated over subsets of the objectives taken k 1 at a time unlike past approaches these nondomination level coordinates are not limited by the dimensionality convexity or curvature of the frontier and they have an inherent meaning as relative preferences for the competing objectives this intuitive behavior makes the coordinates particularly useful as the basis for parametric models of the frontier and for conducting sensitivity studies and interactive trade space exploration the method is demonstrated on three mathematical example problems exhibiting different geometric properties and on a conceptual wing sizing problem

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

a method for generating a well distributed pareto set in nonlinear multiobjective optimization a method is presented for generating a well distributed pareto set in nonlinear multiobjective optimization the approach shares conceptual similarity with the physical programming based method the normal boundary intersection and the normal constraint methods in its systematic approach investigating the objective space in order to obtain a well distributed pareto set the proposed approach is based on the generalization of the class functions which allows the orientation of the search domain to be conducted in the objective space it is shown that the proposed modification allows the method to generate an even representation of the entire pareto surface the generation is performed for both convex and nonconvex pareto frontiers a simple algorithm has been proposed to remove local pareto solutions the suggested approach has been verified by several test cases including the generation of both convex and concave pareto frontiers

concept selection using s pareto frontiers we introduce the notion of s pareto optimality and show how it can be used to improve concept selection in engineering design specie c design alternatives are classie ed as s pareto optimal when there are no other alternatives from the same or any other general design concept that exhibit improvement in all design objectives further we say that the set of s pareto design alternatives comprises the s pareto frontier under the proposed approach the s pareto frontier plays a paramount role in the concept selection process as it is used to dee ne and classify concept dominance thes pareto frontier based concept selection method can becharacterized as onethat capitalizes on the benee ts of computational optimization during the conceptual phase of design before a general design concept has been chosen an introduction to s pareto optimality and a method for generating s pareto frontiersaredeveloped anapproachforusing s paretofrontierstoperformconceptselectionisalsopresented the methods proposed can effectively aid in the elimination of dominated design concepts keep competitive concepts and ultimately choose a specie cdesign alternative from theselected design concept a truss design problem is used to illustrate the usefulness of the method nomenclature g vector of inequality constraints h vector of equality constraints j aggregate objective function mi number of points along ni ni ith vector dee ning the utopia plane n number of design objectives nx number of design variables t k relaxation slack variable for concept k x p generic point on the utopia plane x vector of design variables increment by which feasible space is reduced vector of design objectives or design metrics i ith anchor point k optimum design objective value for concept k si s anchor point for the ith objective

comparison of design concepts in multi criteria decision making using level diagrams in this work we address the evaluation of design concepts and the analysis of multiple pareto fronts in multi criteria decision making using level diagrams such analysis is relevant when two or more design concepts with different design alternatives lie in the same objective space but describe different pareto fronts therefore the problem can be stated as a pareto front comparison between two or more design concepts that only differ in their relative complexity implementation issues or the theory applied to solve the problem at hand such analysis will help the decision maker obtain a better insight of a conceptual solution and be able to decide if the use of a complex concept is justified instead of a simple concept the approach is validated in a set of multi criteria decision making benchmark problems

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

a mesh adaptive direct search algorithm for multiobjective optimization abstract this work studies multiobjective optimization mop of nonsmooth functions subject to general constraints we first present definitions and optimality conditions as well as some single objective formulations of mop parameterized with respect to some reference point in the space of objective functions next we propose a new algorithm called m ulti m ads multiobjective mesh adaptive direct search for mop m ulti m ads generates an approximation of the pareto front by solving a series of single objective formulations of mop generated using the nbi natural boundary intersection framework these single objective problems are solved using the m ads mesh adaptive direct search algorithm for constrained nonsmooth optimization the pareto front approximation is shown to satisfy some first order necessary optimality conditions based on the clarke calculus m ulti m ads is then tested on problems from the literature with different pareto front landscapes and on a styrene production process simulation problem from chemical engineering

ability of objective functions to generate points on nonconvex pareto frontiers new ground is broken in our understanding of objective functions ability to capture pareto solutions for multi objective design optimization problems it is explained why widely used objective functions fail to capture pareto solutions when the pareto frontier is not convex in objective space and the means to avoid this limitation when possible is provided these conditions are developed and presented in the general context ofn dimensional objective space and numerical examples are provided an important point is that most objective function structures can be made to generate nonconvex pareto frontier solutions if the curvature of the objective function can be varied by setting one or more parameters because the occurrence of nonconvex efficient frontiers is common in practice the results are of direct practical usefulness

diversity maximization approach for multiobjective optimization one of the most common approaches for multiobjective optimization is to generate the whole or partial efficient frontier and then decide about the preferred solution in a higher level decision making process in this paper a new method for generating the efficient frontier for multiobjective problems is developed called the diversity maximization approach dma this approach is capable of solving mixed integer and combinatorial problems the dma finds pareto optimal solutions by maximizing a proposed diversity measure and guarantees generating the complete set of efficient points given a subset of the efficient frontier dma finds the next pareto optimal solution which combined with the existing ones yields the most diversified subset of efficient points this solution is defined as the most diverse solution in fact it aims to maximize the distance between the new efficient point and the closest point in the given subset of the efficient frontier the proposed approach can be applied to any problem that can be solved for the single objective case we can use the dma by solving directly a modified version of the mixed integer programming mip formulation of the multiobjective problem in this case the pareto optimal solutions are found sequentially in an iterative way consequently as we terminate the procedure before completion a partial efficient frontier is available the diversity measure assures that in every stage of the procedure the partial efficient frontier is well diversified this partial efficient frontier can be perceived as a filtered set of the complete efficient frontier and can be used by the decision maker in case the complete efficient frontier contains too many points an additional way of using dma is by incorporating it in a problem oriented branch and bound algorithm detailed examples of both approaches are given

a new scalarization technique and new algorithms to generate pareto fronts we propose a new scalarization technique for nonconvex multiobjective optimization problems and establish its theoretical properties by combining our new scalarization approach with existing grid

pareto adaptive penalty based boundary intersection method for multi objective optimization abstract penalty based boundary intersection pbi method is a frequently used scalarizing method in decomposition based multi objective evolutionary algorithms moeas it works well when a proper penalty value is provided however the determination of a suitable penalty value depends on the problem itself more precisely the pareto optimal front pf shape as the penalty value increases the pbi method becomes less effective in terms of convergence but is more capable of handling various pf shapes in this study a simple yet effective method called pareto adaptive pbi pap is proposed by which a suitable penalty value can be adaptively identified which therefore can maintain fast convergence speed meanwhile leading to a good approximation of the pf the pap strategy integrated into the state of the art decomposition algorithm moea d denoted as moea d pap is examined on a set of multi objective benchmarks with different pf shapes experimental results show that the pap strategy is more effective than the weighted sum the weighted tchebycheff and the pbi method with representative fixed penalty values in general in addition the moea d pap is examined on a real world problem multi objective optimization of a hybrid renewable energy system whose pf is unknown the outcome of the experiment further confirms its feasibility and superiority

a multiobjective evolutionary algorithm based on decomposition with normal boundary intersection for traffic grooming in optical networks abstract this paper presents a multiobjective optimization algorithm for solving tri objective optimization problems with objectives of very different scales as a version of the multiobjective evolutionary algorithm based on decomposition moea d it adopts the normal boundary intersection nbi based tchebycheff approach to decompose a multiobjective optimization problem into a number of single objective subproblems particular attention has been paid to set the weight vectors of these subproblems for handling disparately scaled objectives we have applied our proposed algorithm to a traffic grooming problem in the telecommunication fields we also propose to use an indirect encoding approach to handle this very complicated problem our experimental studies show that our proposed method is able to produce very promising results for this real world telecommunication problem

many objective particle swarm optimization many objective problems refer to the optimization problems containing more than three conflicting objectives to obtain a representative set of well distributed non dominated solutions close to pareto front in the objective space remains a challenging problem many papers have proposed different multi objective evolutionary algorithms to solve the lack of the convergence and diversity in many objective problems one of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process however this approach was incorporated mainly in multi objective evolutionary algorithms and there are just some few promising adaptations of particle swarm optimization approaches for effectively tackling many objective problems regarding convergence and diversity thus this paper proposes a practical and efficient many objective particle swarm optimization algorithm for solving many objective problems our proposal uses a set of reference points dynamically determined according to the search process allowing the algorithm to converge to the pareto front but maintaining the diversity of the pareto front our experimental results demonstrate superior or similar performance when compared to other state of art algorithms

bilevel programming for generating discrete representations in multiobjective optimization the solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade off information the ultimate goal is to identify a decision maker s most preferred solution without generating the entire set of nondominated solutions we propose a bilevel programming formulation that can be used to this end the bilevel program is capable of delivering an efficient solution that maps into a given set provided that one exits if the decision maker s preferences are known a priori they can be used to specify the given set alternatively we propose a method to obtain a representation of the nondominated set when the decision maker s preferences are not available this requires a thorough search of the outcome space the search can be facilitated by a partitioning scheme similar to the ones used in global optimization since the bilevel programming formulation either finds a nondominated solution in a given partition element or determines that there is none a representation with a specified coverage error level can be found in a finite number of iterations while building a discrete representation the algorithm also generates an approximation of the nondominated set within the specified error factor we illustrate the algorithm on the multiobjective linear programming problem

norm based approximation in multicriteria programming abstract based on new theoretical results on norms heuristic algorithms to approximate the nondominated set of multicriteria programs are proposed by automatically adapting to the problem s structure and scaling the approximation is constructed objectively without interaction with the decision maker as the algorithms extend the results obtained for bicriteria programs difficulties encountered when dealing with more than two criteria are discussed

random matrix theory for modeling uncertainties in computational mechanics this paper deals with data uncertainties and model uncertainties issues in computational mechanics if data uncertainties can be modeled by parametric probabilistic methods for a given mean model a nonparametric probabilistic approach can be used for modeling model uncertainties the first part is devoted to random matrix theory for which we summarize previous published results and for which two new ensembles of random matrices useful for the nonparametric models are introduced in a second part the nonparametric probabilistic approach of random uncertainties is presented for linear dynamical systems and for nonlinear dynamical systems constituted of a linear part with additional localized nonlinearities in a third part a new method is proposed for estimating the parameters of the nonparametric approach from experiments finally examples with experimental comparisons are given

elastic wave propagation in a 3 d unbounded random heterogeneous medium coupled with a bounded medium application to seismic soil structure interaction sssi we present a sub structuring method for the coupling between a large elastic structure and a stratified soil half space exhibiting random heterogeneities over a bounded domain and impinged by incident waves both media are also weakly dissipative the concept of interfaces classically used in sub structuring methods is extended to volume interfaces in the proposed approach the random dimension of the stochastic fields modelling the heterogeneities in the soil is reduced by introducing a karhunen loeve expansion of these stochastic fields the coupled overall problem is solved by monte carlo simulation techniques a realistic example of a large industrial structure interacting with an uncertain stratified soil medium under earthquake is finally presented this case study and others validate the presented methodology and its ability to handle complex mechanical systems copyright 2002 john wiley sons ltd

selection mechanisms based on the maximin fitness function to solve multi objective optimization problems in this paper we study three selection mechanisms based on the maximin fitness function and we propose another one these selection mechanisms give rise to the following moeas mc moea md moea mh moea and mah moea we validated them using standard test functions taken from the specialized literature having from three up to ten objective functions we compare these four moeas among them and also with respect to moea d which is based on decomposition and to sms emoa which is based on the hypervolume indicator our preliminary results indicate that md moea and mah moea are promising alternatives for solving mops with either low or high dimensionality

representing sampled pareto frontiers as parameterized continuous manifolds using self organizing maps this paper describes a method for defining a coordinate system to parameterize a sampled pareto frontier of a continuous multi attribute design problem using a modified self organizing map by defining such a coordinate system the design problem may be reformulated from y f x to y x g where x is a vector of design variables y is a vector of attributes and is a vector of barycentric coordinates exploration of the design problem using as the independent variables has the following desirable properties 1 every vector corresponds to a pareto efficient design and every pareto efficient design has a corresponding 2 the number of coordinates is equal to the number of attributes regardless of the number of design variables 3 each attribute yi has a corresponding coordinate i such that the sign of yi i is positive if the objective is to maximize yi and negative if the objective is to minimize yi i e the attributes improve monotonically as their corresponding coordinates increase

dynamics of structures coupled with elastic media a review of numerical models and methods abstract this paper reviews issues and developments in the field of structure environment interaction problems in which the environment is an elastic body possibly unbounded it covers in particular the fields of soil structure interaction ground borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium the general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled and the domain decomposition technique classically used for its description is put up extensions for the cases of nonlinear structure and uncertain environment are then discussed finally the ongoing research in the fields of unbounded interface moving interface and multiple interfaces are reviewed and summarized

a unified matrix polynomial approach to modal identification abstract one important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single consistent mathematical formulation with a corresponding set of definitions and unifying concepts particularly a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least squares complex exponential lsce the polyreference time domain ptd ibrahim time domain itd eigensystem realization algorithm era rational fraction polynomial rfp polyreference frequency domain pfd and the complex mode indication function cmif methods using this unified matrix polynomial approach umpa allows a discussion of the similarities and differences of the commonly used methods the use of least squares ls total least squares tls double least squares dls and singular value decomposition svd methods is discussed in order to take advantage of redundant measurement data eigenvalue and svd transformation methods are utilized to reduce the effective size of the resulting eigenvalue eigenvector problem as well

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments