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Research Papers

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

[+] Author and Article Information
Jie Hu

The State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University, Changsha,
Hunan 410082, China
e-mail: hu_jie@hnu.edu.cn

Masoumeh Aminzadeh

Multiscale Systems Engineering Research Group,
George W. Woodruff School of Mechanical
Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Yan Wang

Multiscale Systems Engineering Research Group,
George W. Woodruff School of Mechanical
Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: yan.wang@me.gatech.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 28, 2012; final manuscript received November 6, 2013; published online December 31, 2013. Assoc. Editor: Karthik Ramani.

J. Mech. Des 136(3), 031002 (Dec 31, 2013) (11 pages) Paper No: MD-12-1332; doi: 10.1115/1.4026027 History: Received June 28, 2012; Revised November 06, 2013

In complex systems design, multidisciplinary constraints are imposed by stakeholders. Engineers need to search feasible design space for a given problem before searching for the optimum design solution. Searching feasible design space can be modeled as a constraint satisfaction problem (CSP). By introducing logical quantifiers, CSP is extended to quantified constraint satisfaction problem (QCSP) so that more semantics and design intent can be captured. This paper presents a new approach to formulate searching design problems as QCSPs in a continuous design space based on generalized interval, and to numerically solve them for feasible solution sets, where the lower and upper bounds of design variables are specified. The approach includes two major components. One is a semantic analysis which evaluates the logic relationship of variables in generalized interval constraints based on Kaucher arithmetic, and the other is a branch-and-prune algorithm that takes advantage of the logic interpretation. The new approach is generic and can be applied to the case when variables occur multiple times, which is not available in other QCSP solving methods. A hybrid stratified Monte Carlo method that combines interval arithmetic with Monte Carlo sampling is also developed to verify the correctness of the QCSP solution sets obtained by the branch-and-prune algorithm.

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Figures

Grahic Jump Location
Fig. 1

Variables in QCSP for chassis design

Grahic Jump Location
Fig. 2

Design space (d, D, p) (mm) for suspension system, (a) united solution set and (b) tolerable solution set

Grahic Jump Location
Fig. 3

Design space (Pif, Pir) (Kpa) for tire system (a) united solution set, (b) tolerable solution set, and (c) controllable solution set

Grahic Jump Location
Fig. 4

Verification for the design space of suspension system (a) united solution set and (b) tolerable solution set

Grahic Jump Location
Fig. 5

Verification for the design space of tire system (a) united solution set, (b) tolerable solution set, and (c) controllable solution set

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