Research Papers

Consistency Constraint Allocation in Augmented Lagrangian Coordination

[+] Author and Article Information
James T. Allison1

 The Mathworks, Inc., Natick, MA 01760james.allison@mathworks.com

Panos Y. Papalambros

Department of Mechanical Engineering, University of Michigan, G.G. Brown Building, Ann Arbor, MI 48109pyp@umich.edu


Corresponding author.

J. Mech. Des 132(7), 071007 (Jun 17, 2010) (8 pages) doi:10.1115/1.4001525 History: Received September 03, 2008; Revised February 24, 2010; Published June 17, 2010; Online June 17, 2010

Many engineering systems are too complex to design as a single entity. Decomposition-based design optimization methods partition a system design problem into subproblems, and coordinate subproblem solutions toward an optimal system design. Recent work has addressed formal methods for determining an ideal system partition and coordination strategy, but coordination decisions have been limited to subproblem sequencing. An additional element in a coordination strategy is the linking structure of the partitioned problem, i.e., the allocation of constraints that guarantee that the linking variables among subproblems are consistent. There may exist many alternative linking structures for a decomposition-based strategy that can be selected for a given partition, and this selection should be part of an optimal simultaneous partitioning and coordination scheme. This article develops a linking structure theory for a particular class of decomposition-based optimization algorithms, augmented Lagrangian coordination (ALC). A new formulation and coordination technique for parallel ALC implementations is introduced along with a specific linking structure theory, yielding a partitioning and coordination selection method for ALC that includes consistency constraint allocation. This method is demonstrated using an electric water pump design problem.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Input and output relationships for a system of analysis functions

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Figure 2

Analysis function digraph for example system

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Figure 3

Subproblem graph

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Figure 4

Condensed subproblem graph

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Figure 6

Graph representation of consistency constraint options for x1

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Figure 7

ALC P/C results for electric water pump problem

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Figure 8

Consistency constraint allocation option for point 3



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