An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Tosserams, S.; Etman, L.F.P.; Rooda, J.E.

doi:10.1007/s00158-006-0077-z

Cited by 75 publications

(64 citation statements)

References 21 publications

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“…This section presents results for augmented Lagrangian coordination approaches (ALC, Tosserams et al 2006Tosserams et al , 2007Tosserams et al , 2008Tosserams et al , 2009a) that have been used to coordinate the four problem decompositions introduced in the previous section. For each decomposition one appropriate ALC coordination variant is selected.…”

Section: Distributed Optimization Results Using Alcmentioning

confidence: 99%

“…9b, has only linking variables, and was solved with the augmented Lagrangian coordination approach for quasiseparable problems denoted ALC-QS (Tosserams et al 2007). The results of Table 5 again show that the distributed approach is able to find solutions similar to the all-in-one solutions for the first two cases, even though only a local search algorithm is used.…”

Section: Decomposition 2 With Alc-qsmentioning

confidence: 99%

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A micro-accelerometer MDO benchmark problem

Tosserams

Etman

Rooda

2009

Struct Multidisc Optim

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Many optimization and coordination methods for multidisciplinary design optimization (MDO) have been proposed in the last three decades. Suitable MDO benchmark problems for testing and comparing these methods are few however. This article presents a new MDO benchmark problem based on the design optimization of an ADXL150 type lateral capacitive micro-accelerometer. The behavioral models describe structural and dynamic effects, as well as electrostatic and amplification circuit contributions. Models for important performance indicators such as sensitivity, range, noise, and footprint area are presented. Geometric and functional constraints are included in these models to enforce proper functioning of the device. The developed models are analytical, and therefore highly suitable for benchmark and educational purposes. Four different problem decompositions are suggested for four design cases, each of which can be used for testing MDO coordination algorithms. As a reference, results for an all-in-one implementation, and a number of augmented Lagrangian coordination algorithms are given.

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Section: Distributed Optimization Results Using Alcmentioning

confidence: 99%

Section: Decomposition 2 With Alc-qsmentioning

confidence: 99%

A micro-accelerometer MDO benchmark problem

Tosserams

Etman

Rooda

2009

Struct Multidisc Optim

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“…Similar to ATC [29,30] and the augmented Lagrangian approach of Reference [19], we propose a strategy that consists of inner and outer loops. In the outer loops penalty parameters v and w are updated, and in the inner loops the coupled decomposed problem is solved for fixed penalty parameters.…”

Section: Solution Algorithmsmentioning

confidence: 99%

“…To find the solution to the relaxed MDO problem (7) and (19) for fixed weights, we use the iterative BCD algorithm [22]. Instead of solving the relaxed MDO problem as a whole, the BCD method sequentially solves the disciplinary subproblems P 1 , .…”

Section: Inner Loop: Block Coordinate Descentmentioning

confidence: 99%

“…The inner loop BCD algorithm is terminated when the relative change in the objective function value of the relaxed MDO problem for two consecutive inner loop iterations is smaller than some user-defined termination tolerance inner >0. Let F denote the objective of the relaxed problem (7) and (19). Then the inner loop is terminated when…”

Section: Inner Loop: Block Coordinate Descentmentioning

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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