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Research Papers

# Separating Design Optimization Problems Into Decision-Based Design Processes

[+] Author and Article Information
Peyman Karimian

Department of Mechanical Engineering, A. J. Clark School of Engineering, University of Maryland, College Park, MD 20742karimian@umd.edu

Jeffrey W. Herrmann

Department of Mechanical Engineering, A. J. Clark School of Engineering, University of Maryland, College Park, MD 20742jwh2@umd.edu

J. Mech. Des 131(1), 011007 (Dec 15, 2008) (8 pages) doi:10.1115/1.3013443 History: Received May 22, 2008; Revised September 05, 2008; Published December 15, 2008

## Abstract

This paper introduces the technique of separation, which replaces a design optimization problem with a set of subproblems. This separation is similar to decomposition but does not require a second-level coordination. We identify conditions under which this separation yields an exact solution and other conditions under which the error can be bounded. We show that the decision-based design framework, which seeks to find the most profitable design, can be separated into a sequence of subproblems. We also apply separation to a motor design problem and demonstrate how the surrogate constraints and objective functions affect the solution quality. These results indicate a way to apply the principles of decision-based design to design processes.

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## Figures

Figure 3

Decision networks (X=the vector of design variables). (a) The all-at-once formulations (A1 and A2) maximize profit. (b) Separation S1 finds the most profitable attribute values and price and then sets the design variables to satisfy them. (c) Separation S2 finds the best design and then sets the price to maximize profit.

Figure 1

(a) A typical decomposition scheme has multiple first-level subproblems (P1, P2, and P3) that receive inputs from a second-level problem (P∗), which also coordinates their solutions. (b) Separation yields a set of subproblems. Solving one provides the input to the next.

Figure 2

(a) The decision network for the integrated design optimization model and (b) the decision network for the separation

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