0
Research Papers

On the Performance of the PSP Method for Mixed-Variable Multi-Objective Design Optimization

[+] Author and Article Information
Zeeshan Omer Khokhar

MENRVA Research Group, School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canadazok@sfu.ca

Hengameh Vahabzadeh

Product Design and Optimization Laboratory, Mechatronic Systems Engineering, Simon Fraser University, 250-13450 102 Avenue, Surrey, BC V3T0A3, Canadahva1@sfu.ca

Amirreza Ziai

MENRVA Research Group, School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canadaamirreza_ziai@sfu.ca

G. Gary Wang1

Product Design and Optimization Laboratory, Mechatronic Systems Engineering, Simon Fraser University, 250-13450 102 Avenue, Surrey, BC V3T0A3, Canadagary_wang@sfu.ca

Carlo Menon1

MENRVA Research Group, School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canadacmenon@sfu.ca

1

Corresponding authors.

J. Mech. Des 132(7), 071009 (Jul 07, 2010) (11 pages) doi:10.1115/1.4001599 History: Received September 25, 2009; Revised April 06, 2010; Published July 07, 2010; Online July 07, 2010

Practical design optimization problems require use of computationally expensive “black-box” functions. The Pareto set pursuing (PSP) method, for solving multi-objective optimization problems with expensive black-box functions, was originally developed for continuous variables. In this paper, modifications are made to allow solution of problems with mixed continuous-discrete variables. A performance comparison strategy for nongradient-based multi-objective algorithms is discussed based on algorithm efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Results using several methods, along with the modified PSP, are given for a suite of benchmark problems and two engineering design ones. The modified PSP is found to be competitive when the total number of function evaluations is limited, but faces an increased computational challenge when the number of design variables increases.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Flowchart of the C-PSP approach

Grahic Jump Location
Figure 2

(a) Design space with all discrete variables and (b) mixed variables

Grahic Jump Location
Figure 3

Illustration of variables used in calculating spread (26)

Grahic Jump Location
Figure 4

Illustration of Euclidean distance for calculating generational distance and inverted generational distance (26)

Grahic Jump Location
Figure 5

Illustration of calculation of vi(28)

Grahic Jump Location
Figure 6

Pareto frontier of all algorithms on SCH for 50 function evaluations

Grahic Jump Location
Figure 7

Pareto frontier of all algorithms on FON for 200 function evaluations

Grahic Jump Location
Figure 8

Pareto frontier of all algorithms on KUR for 100 function evaluations

Grahic Jump Location
Figure 9

Pareto frontier of all algorithms on ZDT6 for 200 function evaluations

Grahic Jump Location
Figure 10

Pareto frontier of all algorithms on DTLZ1 for 500 function evaluations

Grahic Jump Location
Figure 11

Pareto points obtained for the welded beam design problem

Grahic Jump Location
Figure 12

Pareto points obtained for the spring design problem

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In