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Research Papers

Lagrangian Relaxation Approach for Decentralized Decision Making in Engineering Design

[+] Author and Article Information
Simon Li

Concordia Institute for Information Systems Engineering, Concordia University, Montreal, Quebec H3G !MB, Canadalisimon@ciise.concordia.ca

Complicating variables can also be handled similarly via the duality of the original problem (1).

J. Comput. Inf. Sci. Eng 10(1), 011001 (Feb 12, 2010) (12 pages) doi:10.1115/1.3290763 History: Received October 03, 2008; Revised June 03, 2009; Published February 12, 2010; Online February 12, 2010

To minimize the coordination efforts among design teams and expedite the design process via parallel workflows, a cooperative and decentralized environment is often considered for team-based design. The cooperative environment implies that teams are motivated to achieve the common objective of the design, while the decentralized environment encourages teams to work independently. Due to the nature of the decentralized environment, achieving an optimal solution is not trivial, even though all teams are motivated and willing to do so. In this context, this paper introduces the Lagrangian relaxation approach for solving decentralized design problems. Also, an objective adjustment factor is proposed to improve the convergence of the solution process. Two examples, welded beam design and heat exchanger design, have been used to illustrate and validate the Lagrangian relaxation approach and the objective adjustment factor.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Formulation of a two-team example

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Figure 2

Objective contour of the two-team example

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Figure 7

Plot of the objective values of the welded beam design

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Figure 3

Rectangular matrix representing the constraint-variable relationships

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Figure 4

Lagrangian relaxation formulation of the two-team example

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Figure 5

Illustration of the welded beam design

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Figure 6

Team setup for the welded beam design

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Figure 8

Results of the mathematical problem with various weights on the constraint function

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Figure 9

Illustration of the heat exchanger design

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Figure 10

Square pitch-tube layout (34)

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Figure 11

Team setup for the heat exchanger design

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Figure 12

Plot of the objective values of the heat exchanger design

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