Research Papers: Design Automation

A New Hybrid Algorithm for Multi-Objective Robust Optimization With Interval Uncertainty

[+] Author and Article Information
Shuo Cheng, Jianhua Zhou

University of Michigan-Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China

Mian Li

University of Michigan-Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mianli@sjtu.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 2, 2014; final manuscript received October 27, 2014; published online November 26, 2014. Assoc. Editor: Christopher Mattson.

J. Mech. Des 137(2), 021401 (Feb 01, 2015) (9 pages) Paper No: MD-14-1100; doi: 10.1115/1.4029026 History: Received February 02, 2014; Revised October 27, 2014; Online November 26, 2014

Uncertainty is a very critical but inevitable issue in design optimization. Compared to single-objective optimization problems, the situation becomes more difficult for multi-objective engineering optimization problems under uncertainty. Multi-objective robust optimization (MORO) approaches have been developed to find Pareto robust solutions. While the literature reports on many techniques in MORO, few papers focus on using multi-objective differential evolution (MODE) for robust optimization (RO) and performance improvement of its solutions. In this article, MODE is first modified and developed for RO problems with interval uncertainty, formulating a new MODE-RO algorithm. To improve the solutions’ quality of MODE-RO, a new hybrid (MODE-sequential quadratic programming (SQP)-RO) algorithm is proposed further, where SQP is incorporated into the procedure to enhance the local search. The proposed hybrid approach takes the advantage of MODE for its capability of handling not-well behaved robust constraint functions and SQP for its fast local convergence. Two numerical and one engineering examples, with two or three objective functions, are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving MORO problems while, on the average, MODE-SQP-RO improves the quality of robust solutions obtained by MODE-RO with comparable numbers of function evaluations.

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Grahic Jump Location
Fig. 3

Flowchart of MODE-RO

Grahic Jump Location
Fig. 4

Flowchart of MODE-SQP-RO

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Fig. 5

Average hyper area (AHA)

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Fig. 10

Robust optimal solutions for three-objective example

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Fig. 11

Robust optimal solutions for vibrating platform

Grahic Jump Location
Fig. 12

(a) Objective robustness and (b) constraint robustness verification for R1

Grahic Jump Location
Fig. 6

Robust optimal solutions for OSY

Grahic Jump Location
Fig. 13

(a) Objective robustness and (b) constraint robustness verification for R2

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Fig. 7

(a) Objective robustness and (b) constraint robustness verification for R1

Grahic Jump Location
Fig. 8

(a) Objective robustness and (b) constraint robustness verification for R2

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Fig. 9

Overall spread (OS)



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