Bilevel integrated system synthesis

Sobieszczanski‐Sobieski, Jaroslaw; Agte, Jeremy S.; Sandusky, Robert

doi:10.2514/3.14392

Cited by 23 publications

(30 citation statements)

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“…Under the more strict assumption of convexity, the method of multipliers can be shown to converge to the globally optimal solution of the modified problem. By combining the inner and outer loop results, we are able to show that the solutions generated by the proposed coordination algorithm converge to a KKT point of the modified problem (3).…”

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confidence: 99%

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Augmented Lagrangian coordination for distributed optimal design in MDO

Tosserams

Etman

Rooda

2007

Numerical Meth Engineering

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SUMMARYQuite a number of coordination methods have been proposed for the distributed optimal design of largescale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for which convergence proofs are available have mostly been developed for so-called quasi-separable problems (i.e. problems with individual subsystems coupled only through a set of linking variables, not through constraints and/or objectives). In this paper, we present a new coordination approach for multidisciplinary design optimization problems with linking variables as well as coupling objectives and constraints. Two formulation variants are presented, offering a large degree of freedom in tailoring the coordination algorithm to the design problem at hand. The first, centralized variant introduces a master problem to coordinate coupling of the subsystems. The second, distributed variant coordinates coupling directly between subsystems. Our coordination approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The proposed coordination algorithms can be shown to converge to Karush-Kuhn-Tucker points of the original problem by using the existing convergence results. We illustrate the flexibility of the proposed approach by showing that the analytical target cascading method of Kim et al. (J. Mech. Design-ASME 2003; 125(3):475-480) and the augmented Lagrangian method for quasi-separable problems of Tosserams et al. (Struct. Multidisciplinary Opt. 2007, to appear) are subclasses of the proposed formulations.

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confidence: 99%

“…2 ] T , y 3 = [y [3] 1 , y [3] 3 ] T , and y 4 = [y [4] 1 ], where the top-right index denotes the subproblem of computation. Furthermore, n y 1 = 2, n y 2 = 2, n y 3 = 2, and n y 4 = 1.…”

Section: Linking Variable Sparsitymentioning

confidence: 99%

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Augmented Lagrangian coordination for distributed optimal design in MDO

Tosserams

Etman

Rooda

2007

Numerical Meth Engineering

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“…Bilevel integrated system synthesis (BLISS, Sobieszczanski-Sobieski et al 2000) is another example. Their approach assumes that the linking variables y include a set of analysis input-output variables y io , and a set of global design variables z.…”

Section: Open Design Closed Consistencymentioning

confidence: 99%

A classification of methods for distributed system optimization based on formulation structure

Tosserams

Etman

Rooda

2009

Struct Multidisc Optim

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This paper presents a classification of formulations for distributed system optimization based on formulation structure. Two main classes are identified: nested formulations and alternating formulations. Nested formulations are bilevel programming problems where optimization subproblems are nested in the functions of a coordinating master problem. Alternating formulations iterate between solving a master problem and disciplinary subproblems in a sequential scheme. Methods included in the former class are collaborative optimization and BLISS2000. The latter class includes concurrent subspace optimization, analytical target cascading, and augmented Lagrangian coordination. Although the distinction between nested and alternating formulations has not been made in earlier comparisons, it plays a crucial role in the theoretical and computational properties of distributed optimization methods. The most prominent general characteristics for each class are discussed in more detail, providing valuable insights for the theoretical analysis and further development of distributed optimization methods.

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“…In the MDO literature, several terms are used to describe what we call "architecture": "method" [17,53,54,55,56], "methodology" [57,58,59], "problem formulation" [60,61,62,63], "strategy" [64,65], "procedure" [66,67], and "algorithm" [68,69,70,71] have all been used. Some authors use a variety of terms and occasionally use them interchangeably in the same paper.…”

Section: Introductionmentioning

confidence: 99%

Multidisciplinary Design Optimization: A Survey of Architectures

2013

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Multidisciplinary design optimization (MDO) is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of MDO, various methods (architectures) have been developed and applied to solve MDO problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitates the understanding of the various architectures, and how they relate to each other.A classification of the MDO architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both a theoretical and experimental perspective. For each architecture, several applications to the solution of engineering design problems are cited. The result is a comprehensive but straightforward introduction to MDO for non-specialists, and a reference detailing all current MDO architectures for specialists.

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Bilevel integrated system synthesis

Cited by 23 publications

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Augmented Lagrangian coordination for distributed optimal design in MDO

Augmented Lagrangian coordination for distributed optimal design in MDO

A classification of methods for distributed system optimization based on formulation structure

Multidisciplinary Design Optimization: A Survey of Architectures

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