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Research Papers

Robust Optimization of Mixed-Integer Problems Using NURBs-Based Metamodels

[+] Author and Article Information
Cameron J. Turner

e-mail: cturner@mines.edu
Colorado School of Mines,
College of Engineering and Computational Sciences,
1500 Illinois Street, Golden, CO 80401

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received October 22, 2012; final manuscript received October 25, 2012; published online December 11, 2012. Assoc. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 12(4), 041010 (Dec 11, 2012) (7 pages) doi:10.1115/1.4007988 History: Received October 22, 2012; Revised October 25, 2012

The optimization of mixed-integer problems is a classic problem with many industrial and design applications. A number of algorithms exist for the numerical optimization of these problems, but the robust optimization of mixed-integer problems has been explored to a far lesser extent. We present here a general methodology for the robust optimization of mixed-integer problems using nonuniform rational B-spline (NURBs) based metamodels and graph theory concepts. The use of these techniques allows for a new and powerful definition of robustness along integer variables. In this work, we define robustness as an invariance in problem structure, as opposed to insensitivity in the dependent variables. The application of this approach is demonstrated on two test problems. We conclude with a performance analysis of our new approach, comparisons to existing approaches, and our views on the future development of this technique.

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Figures

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Fig. 1

A sample NURBs curve. Note the spline curve, control mesh, and control points

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Fig. 2

Overview of the graph-based robust optimization process for NURBs-based metamodels

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Fig. 3

Demonstration of Definition 1

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Fig. 4

The sinusoidal test function of one continuous and one integer variable (top). The NURBs-based metamodel, with the local optima discovered (bottom).

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Fig. 5

Results from the first test problem. Note the reduced MST graphs (below captions) the MQR matrices, the MQR scale guide, and the isomorphism matrix.

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Fig. 6

Robot schematic. Two of the four possible solutions to grasping a particular tool location point.

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Fig. 7

Metamodel of the robot problem

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Fig. 8

Results from the robot test problem. Note the reduced MST graphs (below captions) the MQR matrices, the MQR scale guide, and the isomorphism matrix.

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