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Research Papers

Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

[+] Author and Article Information
W. Hu, M. Li

Graduate Research Assistant Department of Mechanical Engineering,  University of Maryland, College Park, MD 20742Assistant Professor  University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China

S. Azarm1

Professor Department of Mechanical Engineering,  University of Maryland, College Park, MD 20742Assistant Professor Department of Chemical Engineering,  The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAE

A. Almansoori

Professor Department of Mechanical Engineering,  University of Maryland, College Park, MD 20742Assistant Professor Department of Chemical Engineering,  The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAE

Offline AA-MORO is essentially an improved MORO with meta-models for objective and constraint functions which are fixed throughout an optimization run.

1

Corresponding author.

J. Mech. Des 133(6), 061002 (Jun 15, 2011) (9 pages) doi:10.1115/1.4003918 History: Received May 11, 2010; Revised March 25, 2011; Published June 15, 2011; Online June 15, 2011

Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

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Figures

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Figure 3

Comparison of Online AA-MORO with two-level and improved MORO approaches: (a)–(d) numerical examples 1–4

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Figure 4

Engineering example: a pin-end column

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Figure 5

Nominal and robust optimal designs for engineering example

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Figure 6

Schematic of reactor-distillation optimization problem

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Figure 7

Optimal results for the reactor-distillation optimization problem

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Figure 1

Feasible domain and optimal design variables for the upper-level problem: (a) iteration 1 and (b) iteration 2

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Figure 2

Comparison between online and offline AA-MORO: (a) ZDT3 and (b) CTP

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