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Research Papers

Practical Robust Design Optimization Using Evolutionary Algorithms

[+] Author and Article Information
Amit Saha

Multidisciplinary Design Optimization Group,  University of New South Wales (UNSW@ADFA), Canberra ACT 2600, AustraliaAmit.Saha@student.adfa.edu.au

Tapabrata Ray

Multidisciplinary Design Optimization Group,  University of New South Wales (UNSW@ADFA), Canberra ACT 2600, AustraliaT.Ray@adfa.edu.au

J. Mech. Des 133(10), 101012 (Oct 25, 2011) (19 pages) doi:10.1115/1.4004807 History: Received January 14, 2011; Revised July 28, 2011; Accepted July 29, 2011; Published October 25, 2011; Online October 25, 2011

Robust design optimization (RDO) seeks to find optimal designs which are less sensitive to the uncontrollable variations that are often inherent to the design process. Studies using Evolutionary Algorithms (EAs) for RDO are not too many. In this work, we propose enhancements to an EA based robust optimization procedure with explicit function evaluation saving strategies. The proposed algorithm, IDEAR, takes into account a specified expected uncertainty in the design variables and then imposes the desired robustness criteria during the optimization process to converge to robust optimal solution(s). We pick up a number of Bi-objective engineering design problems from the standard literature and study them in the proposed robust optimization framework to demonstrate the enhanced performance. A cross-validation study is performed to analyze whether the solutions obtained are truly robust and also make some observations on how robust optimal solutions differ from the performance maximizing solutions in the design space. We perform a rigorous analysis of the key features of IDEAR to illustrate its functioning. The proposed function evaluation saving strategies are generic and their applications are worth exploring in other areas of computational design optimization.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Percentage of infeasible solutions in a neighborhood of performance maximizing optimal solutions: The X-axis represents a solution and the corresponding value on the Y-axis represents the percentage of solutions in its neighborhood violating boundary constraints and design constraints. (Population size used is 40)

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Figure 2

Robust optimal solutions of the welded beam problem as compared to the performance maximizing solutions

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Figure 3

Comparative performance of IDEAR and DGR for the welded beam problem with 10,000 function evaluations

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Figure 4

Comparative performance of IDEAR and DGR for the welded beam problem with 5000 function evaluations

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Figure 5

Comparative performance of IDEAR and DGR for the welded beam problem with 2000 function evaluations

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Figure 6

Percentage of infeasible solutions in the neighborhood of the robust optimal solutions

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Figure 7

Effect of robustness criteria on the design variables of the welded beam design problem

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Figure 8

Robust optimal solutions of the car side impact problem as compared to the performance maximizing solutions

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Figure 9

Comparative performance of IDEAR and DGR for the car side impact problem with 10,000 function evaluations

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Figure 10

Comparative performance of IDEAR and DGR for the car side impact problem with 5000 function evaluations

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Figure 11

Comparative performance of IDEAR and DGR for the car side impact problem with 2000 function evaluations

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Figure 12

Design variables of the performance maximizing solutions and the robust solutions for the car side impact problem (Only the first seven design variables are shown, as the last four were fixed as per the problem definition)

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Figure 13

Robust optimal solutions of the speed reducer design problem as compared to the performance maximizing solutions

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Figure 14

Comparative performance of IDEAR and DGR for the speed reducer design problem with 10,000 function evaluations

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Figure 15

Comparative performance of IDEAR and DGR for the speed reducer design problem with 5000 function evaluations. It is to be noted that DGR failed to obtain a single feasible solution in this case.

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Figure 16

Robust optimal solutions of the I-Beam design problem as compared to the performance maximizing solutions

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Figure 17

Comparative performance of IDEAR and DGR for the I-Beam design problem with 10,000 function evaluations

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Figure 18

Comparative performance of IDEAR and DGR for the I-Beam design problem with 5000 function evaluations

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Figure 19

Comparative performance of IDEAR and DGR for the I-Beam design problem with 2000 function evaluations

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Figure 20

Constraint values of the I-Beam problem

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Figure 21

Percentage of infeasible solutions in the neighborhood for the welded beam design problem

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Figure 22

Percentage of infeasible solutions in the neighborhood for the car side impact problem

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Figure 23

Percentage of infeasible solutions in the neighborhood for the speed reducer design problem

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Figure 24

Percentage of infeasible solutions in the neighborhood for the I-Beam design problem

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Figure 25

Demonstration of the function evaluation saving strategies: The function evaluation requirement of the inner loop is nullified and function evaluation expenditure of the outer loop (N 40) is observed

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Figure 26

Variation of the robust front with different values of H for the welded beam design problem

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Figure 27

Variation of the robust front with different values of H for the car side impact design problem

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Figure 28

Even though the solutions with H = 10 appear to be better converged than with H = 20, they are not robust as the higher percentage of infeasible neighbors show

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Figure 29

For every solution, a reference set of solutions is obtained using LHS and then the points in the solution archive, closest to these points are chosen for the robustness evaluation of this solution

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