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  • optimization  (34)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 41 (2000), S. 149-171 
    ISSN: 1573-1634
    Keywords: hydrodynamic isolation ; plume ; remediation ; genetic algorithms ; optimization ; aquifer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Produced water constitutes a large amount of waste fluids during the production operation of an oil field. Underground injection for disposing the wastewater from hydrocarbon production is an engineering problem due to the possibility of leakage of injected pollutant material from receiving medium to a drinking water source. This paper describes a method for optimization of polluted aquifer remediation design using one of the artificial intelligence optimization methods, namely Genetic Algorithms (GAs). As a case study, the contaminated area was created by using a groundwater transport simulator, which is based on Method of Characteristics (MOC). Then, the developed computer program was run to find the optimum solution for remediation, and the solution yielded from the program was verified by using a groundwater simulator. The plume was captured and the concentration level of chloride ion within the aquifer was diminished by using extraction wells. The analytical model approach provided different alternatives for appropriate isolation of plume. GAs were used as an optimization technique for making a decision among the alternatives, by considering operation time, number of wells, pumping rate and drawdown as decision variables and constraints.
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  • 2
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    Springer
    Annals of biomedical engineering 21 (1993), S. 489-499 
    ISSN: 1573-9686
    Keywords: Work of breathing ; Inspiratory pressure-time integral ; Respiratory modeling ; Dogs ; Humans
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract We hypothesized that the viscoelastic properties of the respiratory system should have significant implications for the energetically optimal frequency of breathing, in view of the fact that these properties cause marked dependencies of overall system resistance and elastance on frequency. To test our hypothesis we simulated two models of canine and human respiratory system mechanics during sinusoidal breathing and calculated the inspiratory work ( $$\dot W$$ ) and pressure-time integral (PTI) per minute under both resting and exercise conditions. The two models were a two-compartment viscoelastic model and a single-compartment model. Requiring minute alveolar ventilation to be fixed, we found that both models predicted almost identical optimum breathing frequencies. The calculated PTI was very insensitive to increases in breathing frequency above the optimal frequencies, while $$\dot W$$ was found to increase slowly with frequency above its optimum. In contrast, both $$\dot W$$ and PTI increased sharply as frequency decreased below their respective optima. A sensitivity analysis showed that the model predictions were very insensitive to the elastance and resistance values chosen to characterize tissue viscoelasticity. We conclude that the $$\dot W$$ criterion for choosing the frequency of breathing is compatible with observations in nature, whereas the optimal frequency predictions of the PTI are rather too high. Both criteria allow for a fairly wide margin of choice in frequency above the optimum values without incurring excessive additional energy expenditure. Furthermore, contrary to our expectations, the viscoelastic properties of the respiratory system tissues do not pose a noticeable problem to the respiratory controller in terms of energy expenditure.
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  • 3
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    Springer
    Optimization and engineering 1 (2000), S. 67-86 
    ISSN: 1573-2924
    Keywords: vibration absorbers ; optimization ; noise reduction ; sound power
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract This paper presents a design methodology for reducing radiated noise from enclosures using multiple optimized tuned absorbers. The methodology starts from the sound power spectrum of the enclosed noise source and ends with optimally sized/located absorbers on a surrounding thin shell enclosure. The design approach combines a finite element method vibration prediction code, a boundary element method sound power prediction code and a combined stochastic/gradient-based optimization algorithm. A design example has been optimized for a thin shell covering a motor/gearbox. The addition of a small amount of weight (130 g or 1.6% of the weight of the shell) produced substantial reductions in radiated sound power (13 dB in the targeted 1/3 octave band centered at 125 Hz). The design has been validated by experiment.
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  • 4
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    Springer
    Journal of engineering mathematics 37 (2000), S. 27-43 
    ISSN: 1573-2703
    Keywords: anisotropic elasticity ; Kelvin modes ; optimization ; strain energy.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Pointwise optimization of the material symmetry of an anisotropic elastic material with respect to fixed and specified stress (or strain) states is accomplished. The conceptual variables in this problem are the type of material symmetry and the orientation of the canonical symmetry axis for the material at a point in the material. The actual variables are the coefficients of the elasticity (or compliance) matrix. The results are presented in the form of the elasticity (or compliance) matrices that minimize the strain energy with respect to specified, but arbitrary, stress (or strain) states.
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  • 5
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 4123-4155 
    ISSN: 0029-5981
    Keywords: Petrov-Galerkin methods ; weighting parameters ; optimization ; spectral averaged phase errors ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Fourier analysis of the linear and quadratic N + 1 and N + 2 Petrov-Galerkin finite element methods applied to the one-dimensional transient convective-diffusion equation is performed. The results show that a priori optimization of the N + 1 method is not possible because dissipative errors are introduced as dispersive errors are reduced (any optimization is subjective). However, a priori optimization of the N + 2 Petrov-Galerkin method is possible because the reduction of dispersion errors can be accomplished without the addition of artificial dissipation.The Spectrally Weighted Average Phase Error Method (SWAPEM) for the optimization of the N + 2 Petrov-Galerkin method is introduced, in which the N + 2 weighting parameter is chosen at each time step to minimize the integral over wave number of the phase error of Fourier modes, weighted by the frequency content of the global solution at the previous time step (obtained via FFT). The method is dynamic, and general in that the dependence of the weighting parameter on the solution waveform is accounted for. Optimal values predicted by the method are in excellent agreement with those suggested by the numerical experimentation of others. Simulations of the pure convective transport of a Gaussian plume and a triangle wave are discussed to illustrate the effectiveness of the method.
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  • 6
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 977-986 
    ISSN: 1069-8299
    Keywords: sequential function approximation ; interpolation functions ; optimization ; parallel direct search ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational method for the solution of differential equations is proposed. With this method an accurate approximation is built by incremental additions of optimal local basis functions. The parallel direct search software package (PDS), that supports parallel objective function evaluations, is used to solve the associated optimization problem efficiently. The advantage of the method is that, although it resembles adaptive methods in computational mechanics, an a priori grid is not necessary. Moreover, the traditional matrix construction and evaluations are avoided. Computational cost is reduced while efficiency is enhanced by the low-dimensional parallel-executed optimization and parallel function evaluations. In addition, the method should be applicable to a broad class of interpolation functions. Results and global convergence rates obtained for one- and two-dimensional boundary value problems are satisfactorily compared to those obtained by the conventional Galerkin finite element method. © 1997 John Wiley & Sons, Ltd.
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  • 7
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 999-1008 
    ISSN: 1069-8299
    Keywords: optimization ; sensitivity analysis ; constraint approximation ; non-linear analysis ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the finite element non-linear analysis of engineering problems combined with an optimization method, two techniques - a semi-analytical sensitivity method and bi-point constraint approximation - have been proposed. To validate the proposed methods, a raft foundation on a soil medium has been analysed and the results have been compared. From the numerical results, it has been found that, for non-linear analysis, the semi-analytical sensitivity method is more efficient than the finite difference method and the bi-point approximation gives results which compare favourably with the finite element results. © 1997 John Wiley & Sons, Ltd.
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  • 8
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 777-796 
    ISSN: 0029-5981
    Keywords: finite element method ; force method ; reanalysis ; eigenvalue ; structural variation ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a force-based finite element method that involves eigen-space transformation of element stiffness matrices in the first analysis. In each subsequent analysis (‘reanalysis’) associated with structural variations, the solution obtained previously is modified making use of intrinsic properties of eigen solutions and avoiding the time-consuming task of solving a large system of equations. The structural variations may involve changes in material properties, birth or death of elements, or change in boundary conditions. Numerical examples are presented to compare the accuracy and computational efficiency of the proposed method with the displacement-based finite element method. © 1997 by John Wiley & Sons, Ltd.
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  • 9
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    International Journal for Numerical Methods in Engineering 41 (1998), S. 1463-1484 
    ISSN: 0029-5981
    Keywords: optimization ; shape design ; heuristics ; evolutionary optimization ; splines ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of finding the optimal shape of a continuous structure is addressed using, alternatively, heuristic, evolutionary and mixed evolutionary and heuristic optimization strategies. Boundaries are represented by B-splines. Two heuristics for minimizing the weight of a structure subject to limits on von Mises stresses and geometrical constraints are implemented: ‘generalized biological growth’ and ‘penalized biological growth’. Penalized biological growth adds to generalized biological growth a control for shape changes. This control is based on the overall state of constraints satisfaction in the structure. The two heuristics are very efficient at improving the designs, but they do not yield globally optimal shapes. Therefore, they are interfaced with an evolutionary optimizer. Different strategies for mixing evolutionary search and biological growth are compared. Results are obtained for fan disk shape problems. They show that mixing evolutionary search with biological growth improves the efficiency of the optimization. The method offers to the designer new paths for a better component determination. © 1998 John Wiley & Sons, Ltd.
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  • 10
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 293-328 
    ISSN: 0029-5981
    Keywords: structural synthesis ; optimization ; topology optimization ; discrete variable optimization ; Mixed-Integer Non-linear Programming ; MINLP ; the Modified OA/ER algorithm ; MINLP strategy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Part II describes the Mixed-Integer Non-linear Programming (MINLP) approach to structural synthesis where standard dimensions are added to simultaneous topology and parameter optimization. For this purpose, the mechanical superstructure has been enhanced and a special MINLP-MS model formulation for mechanical superstructures from Part I adapted to standard dimension alternatives, which give rise to complex MINLP problems that are difficult to solve. A Linked Two-Phase MINLP Strategy has been developed to efficiently accelerate the solutions of highly combinatorial MINLP problems, performed by the Modified OA/ER algorithm. In the first phase, the strategy uses only continuous dimensions making it easier to find an optimal topology. Based on the obtained global linear approximation of the superstructure, the proposed strategy in the second phase continues to perform an overall simultaneous optimization, where standard dimensions are added as additional discrete optimization alternatives. Thus, simultaneous topology, parameter and standard dimension optimization is now performed in the second phase. The synthesis of a multiple cantilever beam, introduced in Part I, was performed in accordance with the steps proposed by the MINLP optimization approach. This approach enables the obtaining of additional savings when compared to the one in Part I. © 1998 John Wiley & Sons, Ltd.
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  • 11
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 655-687 
    ISSN: 0029-5981
    Keywords: crashworthiness ; multibody dynamics ; flexible structures ; simulation ; design ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Different formulations based on multibody dynamics are shown to be suitable for the development of a methodology for the impact simulation and crashworthiness design of railway vehicles. The proposed design methodology comprises different computer-aided tools of increasing complexity and accuracy which can be used with greater advantage and efficiency in the different design stages of railway stock. In general, the crashworthiness design methods and associated multibody dynamic tools which are presented in this paper require information to be obtained from numerical or experimental crush tests of specific structural components, subassemblies and critical energy absorption devices normally located in car extremities. This hybrid feature lends to the present design process various efficiency gains as a result of a better understanding of the crash and different collapse mechanisms and ease of use. To access the merits of the present methodologies some new designs are discussed and the application of the proposed numerical tools is illustrated for different structural configurations of car extremities. A formulation for the sensitivity analysis and optimization of planar constrained mechanical systems is also presented. An example of crashworthiness design of an end underframe model of a railway car is solved to demonstrate the use of the methodology. © 1997 by John Wiley & Sons, Ltd.
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  • 12
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1109-1126 
    ISSN: 0029-5981
    Keywords: three-dimensional conduction heat transfer ; special boundary integral formulation ; Design Sensitivity Analysis (DSA) ; Direct Differentiation Approach (DDA) ; optimization ; CONMIN algorithm ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In some steady heat conduction problems in special geometries which consist of a closely spaced surface and circular holes in an infinite domain, thermal system designers may want to optimize the configuration of circular holes in terms of their radii and locations to achieve the goal of uniform temperature distribution over a closely spaced surface. In this paper, an efficient optimization procedure for this kind of problem is proposed utilizing (i) the special boundary element analysis, (ii) the corresponding design sensitivity analysis and (iii) the CONMIN algorithm. Three sample problems were solved to demonstrate the efficiency and the usefulness of the proposed optimization procedure. Some industrial engineering examples of such problems can be found in the injection molding process, the compression molding process, and so on. © 1998 John Wiley & Sons, Ltd.
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  • 13
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 971-1003 
    ISSN: 0029-5981
    Keywords: computer-simulation surrogates ; optimization ; Pareto optimality ; non-parametric statistical validation ; predictability ; quasi-convex analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the surrogate approach to simulation-based optimization, the large-scale simulation is evoked only to construct and validate a simplified input-output model; this simplified input-output model then serves as a simulation surrogate in subsequent engineering optimization studies. We present here ‘basic’ and Pareto surrogate formulations through an illustrative application from fluid dynamics.The critical ingredient of both formulations is a non-parametric statistical validation and error estimation procedure which, based on verifiable hypotheses, precisely quantifies the effect of surrogate-for-simulation substitution on system predictability, stability, and optimality. The Pareto formulation improves upon the basic approach by operating only in the vicinity of the efficient frontier of the output achievable set A for problems with many inputs and few outputs, this considerably reduces the dimensionality of the problem, and correspondingly improves the surrogate error estimates. © 1998 John Wiley & Sons, Ltd.
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  • 14
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 1-21 
    ISSN: 0029-5981
    Keywords: response surface approximations ; transient thermoelastic analysis ; optimization ; thermal design ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Response surface methodology is used to construct approximations to temperature and stress in transient thermoelastic analysis of non-linear systems. The analysis forms the core component of a heating/cooling rate maximization problem in which the ordinates of the ambient temperature at equally spaced time intervals are chosen as the design variables. Polynomials or cubic splines are fitted through the ordinates to describe the ambient temperature profile required for the convective heat transfer analysis. An experimental design method based on D-optimality and a genetic algorithm was used to select the design points used to create the approximations. Linear response surfaces were found to be sufficiently accurate, thereby minimizing the number of finite element analyses. Two examples of which one is a thick-walled pressure vessel are used to illustrate the methodology. © 1998 John Wiley & Sons, Ltd.
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  • 15
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 433-450 
    ISSN: 0029-5981
    Keywords: mesh partitioning ; finite elements ; parallel computing ; optimization ; heuristics ; frontal method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We address the problem of automatic partitioning of unstructured finite element meshes in the context of parallel numerical algorithms based on domain decomposition. A two-step approach is proposed, which combines a direct partitioning scheme with a non-deterministic procedure of combinatorial optimization. In contrast with previously published experiments with non-deterministic heuristics, the optimization step is shown to produce high-quality decompositions at a reasonable compute cost. We also show that the optimization approach can accommodate complex topological constraints and minimization objectives. This is illustrated by considering the particular case of topologically one-dimensional partitions, as well as load balancing of frontal subdomain solvers. Finally, the optimization procedure produces, in most cases, decompositions endowed with geometrically smooth interfaces. This contrasts with available partitioning schemes, and is crucial to some modern numerical techniques based on domain decomposition and a Lagrange multiplier treatment of the interface conditions.
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  • 16
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1021-1030 
    ISSN: 0029-5981
    Keywords: optimization ; finite element ; magnetostatic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we present an improvement of the optimization technique of the moving asymptotes applied to a class of magnetostatic design problem. Our approach includes, among other aspects, an active set strategy which turns possible to find feasible points during the iterative process. We present some numerical results obtained on real-life case studies where the functions are computed by a complex finite-element routine.
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  • 17
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1721-1738 
    ISSN: 0029-5981
    Keywords: probabilistic analysis ; optimization ; safety index ; structural reliability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of this paper is to conduct reliability-based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate examples.
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  • 18
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1659-1680 
    ISSN: 0029-5981
    Keywords: elasticity ; stress singularity ; finite elements ; optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A semianalytical singular element is proposed to model the stress fields in plane and axisymmetric elastic bodies in the vicinity of singular points. The element generation is performed taking into account the structure of analytical solution in the vicinity of such points. This renders the element well suited for any type of singular points. Introduction of specially generated shape functions in the approximating expressions for displacements enables one to ensure the displacement compatibility with the standard elements. A detailed consideration is given to the convergence of the finite-element procedure. The extensive possibilities of the proposed singular element are exemplified by solving particular elastic problems. The applicability of the elaborated singular element is discussed with respect to optimization of geometry and material properties in the vicinity of singular points. Two optimization problems are presented to illustrate a search for the body geometry providing the optimal stress distribution.
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  • 19
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1761-1774 
    ISSN: 0029-5981
    Keywords: optimization ; algorithms ; structural ; design ; comparative ; evaluation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 1951-1965 
    ISSN: 0029-5981
    Keywords: optimization ; thermoelasticity ; topology ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2-D linear-elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analysed.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 361-382 
    ISSN: 0029-5981
    Keywords: optimization ; genetic ; algorithms ; trusses ; real-world ; multicriteria ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Genetic algorithms, a search technique which combines Darwinian ‘survival-of-the-fittest’ with randomized well structured information, is applied to the problems of real-world truss optimization. In this work a population of binary strings or ‘chromosomes’, which represent the coded truss design variables, a ‘fitness’ as a ranking measure of the adaptability to the environment, selection criteria and mechanical natural operators such as crossover and mutation are used to improve the population, so that over the generations the genetic algorithm gets better and better and at the end of the convergence, a ‘rebirth’ of the population is used to improve the usual process.An overview of the genetic algorithm will be described, continuing the rebirth effect; then, the chromosome representation of trusses is exposed. Afterwards, the objective scalar function is defined taking into account that it seems reasonable in real world to optimize trusses in minimum weight trying, at the same time, to use the minimum number of cross-section types obtained from the market. It also seems reasonable to have the possibility to change the shape of the conceptual design, moving some joints. To simulate nearly real conditions, several load cases, constraints in the elastic joint displacements, ultimate tensile and elastic and plastic buckling in the bars have been taken into account. A hyperstatic 10 bars truss is subjected to a deep analysis in different situations in order to evaluate with other authors when possible as truss optimization with two criteria and buckling effect has not been found in specialized literature. A 160-bar transmission tower is also optimized.
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  • 22
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2055-2071 
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; optimization ; smoothing ; finite elements ; finite volume methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1985-2003 
    ISSN: 0029-5981
    Keywords: shape design ; optimization ; boundary integral equation ; design sensitivity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A design optimization procedure is developed using the boundary integral equation (BIE) method for linear elastostatic two-dimensional domains. Optimal shape design problems are treated where design variables are geometric parameters such as the positions and sizing dimensions of entire features on a component or structure. A fully analytical approach is adopted for the design sensitivity analysis where the BIE is implicitly differentiated. The ability to evaluate response sensitivity derivatives with respect to design variables such as feature positions is achieved through the definition of appropriate design velocity fields for these variables. How the advantages of the BIE method are amplified when extended to sensitivity analysis for this category of shape design problems is also highlighted. A mathematical programming approach with the penalty function method is used for solving the overall optimization problem. The procedure is applied to three example problems to demonstrate the optimum positioning of holes and optimization of radial dimensions of circular arcs on structures.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3305-3325 
    ISSN: 0029-5981
    Keywords: global ; optimization ; algorithms ; nonlinear ; engineering ; design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: After a brief overview of the methods from the literature, two new algorithms (zooming and domain elimination) for global optimization of general NLP problems are introduced. Operations analysis and stopping criteria for the methods are discussed. Numerical evaluation of the methods is carried out using a set of mathematical programming test problems. Performance of the methods is compared with the Controlled Random Search (CRS) and the Simulated Annealing (SA) methods. The methods are superior to SA for the test problems, as they are more robust, efficient and accurate. The CRS is more efficient than the new methods; however, it is applicable to unconstrained problems only. Therefore, it is concluded that the new methods are useful for engineering optimization applications.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 399-419 
    ISSN: 0029-5981
    Keywords: flaw identification ; boundary element method ; inverse analysis ; crack problems ; optimization ; sensitivity analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two-dimensional structures. An introduction to inverse analysis is given, with special reference to methods of flaw identification, along with a brief review of the optimization methods employed. Both the standard boundary element and the dual boundary element method are presented, with the dual boundary element method proposed as the basis for the new formulation. The flaw identification method is presented, along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries. Examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1933-1953 
    ISSN: 0029-5981
    Keywords: structures ; optimization ; large scale ; structural design ; sequential quadratic programming ; self-scaling ; numerical algorithms ; algorithm evaluation ; test problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic idea of an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems - small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1213-1230 
    ISSN: 0029-5981
    Keywords: metal forming ; preform design ; forging ; sensitivity analysis ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An optimization algorithm for preform die shape design in metal-forming processes is developed in this paper. The preform die shapes are represented by cubic B-spline curves. The control points of the B-spline are used as the design variables. The optimization objective is to reduce the difference between the realized and desired final forging shapes. The sensitivities of the objective function with respect to the design variables are developed in detail. The numerical examples show that the optimization method and the sensitivity analysis developed in this paper are very useful and the design results are satisfactory. Importantly, the preform die shapes designed by this method are easily manufacturable and can be implemented in practical metal-forming operations. This optimization method and the sensitivity analysis can also be applied in the preform design of complex industrial metal-forming problems. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1505-1524 
    ISSN: 0029-5981
    Keywords: linkages ; synthesis ; position problems ; optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper describes a procedure for the optimal dimensional synthesis of mechanisms which is based on the solution of non-linear position problems. Planar mechanisms are modelled very easily by means of finite elements of bi-hinged rod type. The judicious choice of constraint conditions makes possible the solution of classical position problems: initial, finite-displacement, deformed and static-equilibrium problems, as well as the main types of dimensional synthesis: path generation, functions, rigid body guidance, mixed, and multiple. A single synthesis error function applies to all these types, and moreover is general since it is valid for mechanisms of any configuration. This function is based on the idea that the best mechanism for the given synthesis conditions is the one that least needs to be deformed when it is obliged to satisfy them exactly, to which end the elastic deformation of the elements is permitted. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 165-188 
    ISSN: 0029-5981
    Keywords: engineering design ; optimization ; discrete variables ; numerical methods ; test problems ; evaluation of methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Continuous-discrete variable non-linear optimization problems are defined and categorized into six different types. These include a full range of problems from continuous to purely discrete and non-differentiable. Methods for solution of these problems are studied and their characteristics are catalogued. The branch and bound, simulated annealing and genetic algorithms are found to be the most general methods for solving discrete problems. After some enhancements, these and two other methods are implemented into a program for certain applications. Several example problems are solved to study performance of the methods. It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational effort compared to the continuous variable optimization problems. In addition, there is no guarantee that the best solution has been obtained; however, good practical solutions are usually obtained. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 40 (1997), S. 1525-1550 
    ISSN: 0029-5981
    Keywords: adjoint problem ; discrete curvature ; finite element method ; free surface flow ; optimization ; quasi-Newton method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the finite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four different finite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important effects of gravity and surface tension forces. © 1997 by John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 787-803 
    ISSN: 0029-5981
    Keywords: multi-point approximations ; multivariate Hermite ; optimization ; design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approximation based on multiple function and gradient information is developed using Hermite interpolation concepts. The goal is to build a high-quality approximation for complex and multidisciplinary design optimization problems employing analysis such as aeroservoelasticity, structural control, probability, etc. The proposed multidimensional approximation utilizes exact analyses data generated during the course of iterative optimization. The approximation possesses the property of reproducing the function and gradient information of known data points. The accuracy of the new approach is compared with linear, reciprocal and other standard approximations. Because the proposed algorithm uses more data points, its efficiency has to be compared in the context of iterative optimization.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 263-292 
    ISSN: 0029-5981
    Keywords: structural synthesis ; optimization ; topology optimization ; mixed-integer nonlinear programming ; MINLP ; Modified OA/ER algorithm ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the Mixed-Integer Non-linear Programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved by means of simultaneous topology, parameter and standard dimension optimization.Part I of this three-part series of papers contains a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The MINLP optimization approach is performed through three steps. The first one includes the generation of a mechanical superstructure of different topology alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the formulated MINLP problem. Some MINLP methods are also presented. A Modified OA/ER algorithm is applied to solve the MINLP problem and a simple example of a multiple cantilever beam is given to demonstrate the steps of the proposed MINLP optimization approach.As simultaneous optimization, extended to include also standard dimensions, requires additional effort, the development of suitable strategies to carry out the optimization is further discussed in Part II. The modelling of MINLP superstructures and the topology and parameter optimization of roller and sliding hydraulic steel gate structures are shown in Part III of the paper. An example of the synthesis of an already erected roller gate, i.e. the Intake Gate of Aswan II in Egypt, is presented as a comparative design research work. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 329-364 
    ISSN: 0029-5981
    Keywords: structural synthesis ; optimization ; topology optimization ; discrete variable optimization ; Mixed-Integer Non-linear Programming ; MINLP ; the Modified OA/ER algorithm ; MINLP strategy ; hydraulic gate ; sliding gate ; roller gate ; Aswan ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Part III of this three-part series of papers describes the synthesis of roller and sliding hydraulic steel gate structures performed by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP approach enables the determination of the optimal number of gate structural elements (girders, plates), optimal gate geometry, optimal intermediate distances between structural elements and all continuous and standard crossectional sizes. For this purpose, special logical constraints for topology alterations and interconnection relations between the alternative and fixed structural elements are formulated. They have been embedded into a mathematical optimization model for roller and sliding steel gate structures GATOP. GATOP has been developed according to a special MINLP model formulation for mechanical superstructures (MINLP-MS), introduced in Parts I and II. The model contains an economic objective function of self-manufacturing and transportation costs of the gate. As the GATOP model is non-convex and highly non-linear, it is solved by means of the Modified OA/ER algorithm accompanied by the Linked Two-Phase MINLP Strategy, both implemented in the TOP computer code. An example of the synthesis is presented as a comparative design research work of the already erected roller gate, the so-called Intake Gate in Aswan II in Egypt. The optimal result yields 29·4 per cent of net savings when compared to the actual costs of the erected gate. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 42 (1998), S. 517-534 
    ISSN: 0029-5981
    Keywords: structural optimization ; optimization ; function approximation ; response surface methodology ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to find the region of interest containing the optimal design, and techniques for finding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the ‘best’ regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-effective. In a further attempt to improve efficiency, different regression models were investigated. The results indicate that the use of the two methods investigated does not significantly improve the results. Finding an accurate global approximation is challenging, and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Engineering 38 (1995), S. 3087-3120 
    ISSN: 0029-5981
    Keywords: structures ; structural design ; optimization ; Lagrangian ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.
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