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Research Papers: Design Automation

On Global Convergence in Design Optimization Using the Particle Swarm Optimization Technique

[+] Author and Article Information
Forrest W. Flocker

Department of Engineering
and Technology,
University of Texas of the Permian Basin,
4901 East University Boulevard,
Odessa, TX 79762
e-mail: flocker_f@utpb.edu

Ramiro H. Bravo

Department of Engineering
and Technology,
University of Texas of the Permian Basin,
4901 East University Boulevard,
Odessa, TX 79762
e-mail: bravo_r@utpb.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 3, 2016; final manuscript received May 19, 2016; published online June 20, 2016. Assoc. Editor: Christopher Mattson.

J. Mech. Des 138(8), 081402 (Jun 20, 2016) (8 pages) Paper No: MD-16-1001; doi: 10.1115/1.4033727 History: Received January 03, 2016; Revised May 19, 2016

The particle swarm optimization (PSO) method is becoming a popular optimizer within the mechanical design community because of its simplicity and ability to handle a wide variety of objective functions that characterize a proposed design. Typical examples arising in mechanical design are nonlinear objective functions with many constraints, which typically arise from the various design specifications. The method is particularly attractive to mechanical design because it can handle discontinuous functions that occur when the designer must choose from a discrete set of standard sizes. However, as in other optimizers, the method is susceptible to converging to a local rather than global minimum. In this paper, convergence criteria for the PSO method are investigated and an algorithm is proposed that gives the user a high degree of confidence in finding the global minimum. The proposed algorithm is tested against five benchmark optimization problems, and the results are used to develop specific guidelines for implementation.

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References

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Figures

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Fig. 1

Basic PSO algorithm

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Fig. 2

Basic SDR algorithm

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Fig. 3

Iterated PSO algorithm

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Fig. 4

Iterated SDR algorithm

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Fig. 5

Iterated SDR for the case where the global minimum is very small

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Fig. 6

Convergence behavior of the basic PSO algorithm for the 30-dimensional Griewank problem

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Fig. 7

Problem 1, a two-dimensional problem with many local minima

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Fig. 8

Success rate of the iterated SDR algorithm for problem1

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Fig. 9

Two-dimensional tripod function

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Fig. 10

Success rate of the iterated SDR algorithm for problem 2—2D tripod

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Fig. 11

Two-dimensional version of the ten-dimensional alpine problem

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Fig. 12

Success rate of the iterated SDR algorithm for problem 3—10D alpine

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Fig. 13

Two-dimensional version of the Griewank problem shown on an abbreviated domain

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Fig. 14

Success rate of the iterated SDR algorithm for problem 4—30D Griewank

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Fig. 15

Two-dimensional version of the 30D Ackley problem

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Fig. 16

Success rate of the iterated SDR algorithm for problem 5—30D Ackley

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