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.

References

References
1.
Eberhart
,
R. C.
, and
Kennedy
,
J.
,
1995
, “
A New Optimizer Using Particle Swarm Theory
,”
6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, Oct. 4–6, Institute of Electrical and Electronics Engineers
, Piscataway, NJ, pp.
39
43
.
2.
Kennedy
,
J.
, and
Eberhart
,
R. C.
,
1995
, “
Particle Swarm Optimization
,”
IEEE International Conference on Neural Networks
, Perth, WA, Nov. 27–Dec. 1, Institute of Electrical and Electronics Engineers, Piscataway, NJ, Vol.
4
, pp.
1942
1948
.
3.
Poli
,
R.
,
2008
, “
Analysis of the Publications on the Applications of Particle Swarm Optimization
,”
J. Artif. Evol. Appl.
,
2008
, p.
685175
.
4.
Poli
,
R.
,
Kennedy
,
J.
, and
Blackwell
,
T.
,
2007
, “
Particle Swarm Optimization: An Overview
,”
Swarm Intell.
,
1
(
1
), pp.
33
57
.
5.
Bravo
,
R. H.
, and
Flocker
,
F. W.
,
2012
, “
Designing HVAC Systems Using Particle Swarm Optimization
,”
HVACR Res.
,
18
(
5
), pp.
845
857
.
6.
Bravo
,
R. H.
, and
Flocker
,
F. W.
,
2011
, “
Optimizing Cam Profiles Using the Particle Swarm Technique
,”
ASME J. Mech. Des.
,
133
(
9
), p.
091003
.
7.
Shi
,
Y.
, and
Eberhart
,
R.
,
1998
, “
Parameter Selection in Particle Swarm Optimization
,”
7th Annual Conference on Evolutionary Programming
, San Diego, CA, Mar. 25–27, pp.
591
600
.
8.
Shi
,
Y.
, and
Eberhart
,
R.
,
1999
, “
Empirical Study of Particle Swarm Optimization
,”
Congress on Evolutionary Computation
, Washington, DC, July 6–9, Vol.
3
, pp.
1945
1950
.
9.
Shi
,
Y.
, and
Eberhart
,
R.
,
1998
, “
A Modified Particle Swarm Optimizer
,”
IEEE International Conference on Evolutionary Computation
, Anchorage, AK, May 4–9, pp.
69
73
.
10.
Clerc
,
M.
, and
Kennedy
,
J.
,
2002
, “
The Particle Swarm—Explosion, Stability, and Convergence in a Multidimensional Complex Space
,”
IEEE Trans. Evol. Comput.
,
6
(
1
), pp.
58
73
.
11.
Van den Bergh
,
F.
,
2002
, “
An Analysis of Particle Swarm Optimizers
,” Ph.D. dissertation, Department of Computer Science, University of Pretoria, Pretoria, South Africa.
12.
Trelea
,
I. C.
,
2003
, “
The Particle Swarm Optimization Algorithm: Convergence Analysis and Parameter Selection
,”
Inf. Process. Lett.
,
85
(
6
), pp.
317
325
.
13.
Zheng
,
Y.-L.
,
Ma
,
L.-H.
,
Zhang
,
L.-Y.
, and
Qian
,
J.-X.
,
2003
, “
On the Convergence Analysis and Parameter Selection in Particle Swarm Optimization
,”
2nd International Conference on Machine Learning and Cybernetics
, Xi'an, China, Nov. 2–5, pp.
1802
1807
.
14.
Jiang
,
M.
,
Luo
,
Y.
, and
Yang
,
S.
,
2007
, “
Stochastics Convergence Analysis and Parameter Selection of the Standard Particle Swarm Optimization Algorithm
,”
Inf. Process. Lett.
,
102
(
1
), pp.
8
16
.
15.
Clerc
,
M.
,
2006
,
Particle Swarm Optimization
,
ISTE
,
London
, Chap. 6.
16.
Venter
,
G.
, and
Sobieszczanski-Sobieski
,
J.
,
2003
, “
Particle Swarm Optimization
,”
AIAA J.
,
41
(
8
), pp.
1583
1589
.
17.
Bathe
,
K.-J.
,
1996
,
Finite Element Procedures
,
Prentice Hall
,
Upper Saddle River, NJ
, Article 4.3.
18.
Clerc
,
M.
,
2006
,
Particle Swarm Optimization
,
ISTE
,
London
, Chap. 4.
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