Numerical difficulties associated with using equality constraints toachieve multi-level decomposition in structural optimization

Thareja, Rajiv R.; Haftka, Raphael T.

doi:10.2514/6.1986-854

Cited by 22 publications

(9 citation statements)

References 16 publications

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“…Both CO 1 and CO 2 can lead to system problems that have more equalityconstraintsthan optimizationvariables, with CO 1 typically leading to more constraints than does CO 2 . Example (9) illustrates this: the system problem has a single variable but two equality constraints.…”

Section: Overdetermined System-level Constraintsmentioning

confidence: 97%

“…However, as we discuss, dif culties necessarily arise in solving the resulting computational optimization problems in theory and in practice. Dif culties in solving problems with CO and related methods have been observed by a number of researchers, including Thareja and Haftka, 9 Cormier et al, 10 Giesing and Barthelemy, 11 and Kodiyalam. 12 We point out that they derive from the intrinsic mathematical properties of CO. Our line of inquiry is constructive because it clari es practical computational issues in MDO.…”

Section: Introductionmentioning

confidence: 97%

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Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design

2002

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Analytical features of multidisciplinary optimization (MDO) problem formulations have signi cant practical consequences for the abilityof nonlinear programmingalgorithmsto solve the resulting computationaloptimization problems reliably and ef ciently. We explore this important but frequently overlooked fact using the notion of disciplinary autonomy. Disciplinary autonomy is a desirable goal in formulating and solving MDO problems; however, the resulting system optimization problems are frequently dif cult to solve. We illustrate the implications of MDO problem formulation for the tractability of the resulting design optimization problem by examining a representative class of MDO problem formulations known as collaborative optimization. We also discuss an alternative problem formulation, distributed analysis optimization, that yields a more tractable computational optimization problem. Nomenclature= system objective function g i = design constraints for D i l i = design variables local to D i min = minimize s = design variables shared by disciplines s.t. = subject to

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Section: Overdetermined System-level Constraintsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design

2002

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“…Collaborative optimization (CO) [Schmit and Ramanathan 1978;Thareja and Haftka 1986;Braun and Kroo 1997;Sobieski and Kroo 2000] is a bilevel MDO approach designed to provide discipline autonomy while maintaining interdisciplinary compatibility. The optimization problem is decomposed into a number of independent optimization subproblems, each corresponding to one discipline.…”

Section: Collaborative Optimizationmentioning

confidence: 99%

pyMDO

Martins

Marriage

Tedford

2009

ACM Trans. Math. Softw.

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We present pyMDO, an object-oriented framework that facilitates the usage and development of algorithms for multidisciplinary optimization (MDO). The resulting implementation of the MDO methods is efficient and portable. The main advantage of the proposed framework is that it is flexible, with a strong emphasis on object-oriented classes and operator overloading, and it is therefore useful for the rapid development and evaluation of new MDO methods. The top layer interface is programmed in Python and it allows for the layers below the interface to be programmed in C, C++, Fortran, and other languages. We describe an implementation of pyMDO and demonstrate that we can take advantage of object-oriented programming to obtain intuitive, easy-to-read, and easy-to-develop codes that are at the same time efficient. This allows developers to focus on the new algorithms they are developing and testing, rather than on implementation details. Examples demonstrate the user interface and the corresponding results show that the various MDO methods yield the correct solutions.

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“…Several modifications to multilevel approach are suggested and the interested readers are referred to Refs. [5][6][7]. Schmit and Mehrinfar [8] extended the multilevel approach to design of composite structures.…”

Section: Introductionmentioning

confidence: 99%