Abstract

This paper provides a detailed description of the cost-sorted distance (CSD) method for visually and computationally identifying objective function minima within clustered population-based optimization results. CSD requires sorting the design vector population by cost and computing Euclidean distances between each pair of designs. It may be applied in conjunction with any population-based optimization method (e.g., particle swarm, genetic algorithm, simulated annealing, ant colony, firefly), but it is naturally compatible with the firefly algorithm (FA) because FA also requires the distances between each pair of design vectors and benefits from cost-sorting the population (the computational work required for CSD is a byproduct of FA). A modified FA is presented that uses CSD to more thoroughly search near potential minima and a systematic method for tuning the algorithm to reliably identify multiple minima is documented. The tuned algorithm's efficacy is demonstrated using a class of benchmark problems and a “real world” electromechanical design problem, where the identification of attractive design alternatives can be challenging.

References

References
1.
Theodoridis
,
S.
, and
Koutroumbas
,
K.
,
2008
,
Pattern Recognition
, 4th ed.,
Academic Press
,
Amsterdam
.
2.
Ryan
,
T. P.
,
2000
,
Statistical Methods for Quality Improvement
,
Wiley
,
New York
.
3.
Lotov
,
A. V.
, and
Miettinen
,
K.
,
1998
,
Multiobjective Optimization
,
J.
Branke
,
K.
Deb
,
K.
Miettinen
, and
R.
Słowiński
, eds.,
Springer
,
Berlin
, pp.
213
243
.
4.
Vathy-Fogarassy
,
A.
, and
Abonyi
,
J.
,
2013
,
Graph-Based Clustering and Data Visualization Algorithms
,
Springer
,
London
.
5.
Mattson
,
C.
, and
Messac
,
A.
,
2005
, “
Pareto Frontier Based Concept Selection Under Uncertainty, With Visualization
,”
Optim. Eng.
,
6
(
1
), pp.
85
115
. 10.1023/B:OPTE.0000048538.35456.45
6.
Stump
,
G. M.
,
Lego
,
S.
,
Yukish
,
M.
,
Simpson
,
T. W.
, and
Donndelinger
,
J. A.
, “
Visual Steering Commands for Trade Space Exploration: User-Guided Sampling With Example
,”
ASME J. Comput. Inf. Sci. Eng.
,
9
(
4
), p.
044501
. 10.1115/1.3243633
7.
Daskilewicz
,
M. J.
, and
German
,
B. J.
,
2011
, “
Rave: A Computational Framework to Facilitate Research in Design Decision Support
,”
ASME J. Comput. Inf. Sci. Eng.
,
12
(
2
), p.
021005
. 10.1115/1.4006464
8.
Elliott
,
C. M.
, and
Buckner
,
G. D.
,
2018
, “
Design Optimization of a Novel Elastomeric Baffle Magnetorheological Fluid Device
,”
J. Intell. Mater. Syst. Struct.
,
29
(
19
), pp.
3774
3791
. 10.1177/1045389X18799211
9.
Yang
,
X.-S.
,
2009
, “
Firefly Algorithms for Multimodal Optimization
,”
Stoch. Algorit. Found. Appl.
,
5792
, pp.
169
178
. 10.1007/978-3-642-04944-6_14
10.
Lukasik
,
S.
, and
Zak
,
S.
,
2009
,
Computational Collective Intelligence: Semantic Web, Social Networks and Multiagent Systems
,
N.
Nguyen
,
R.
Kowalczyk
, and
S.
Chen
, eds.,
Springer
,
Wroclaw, Poland
.
11.
Yang
,
X.-S.
,
2010
,
Research and Development in Intelligent Systems XXVI
,
M.
Bramer
,
R.
Ellis
, and
M.
Petridis
, eds.,
Springer
,
London
, pp.
209
218
.
12.
Yang
,
X.-S.
,
2014
,
Nature-Inspired Optimization Algorithms
,
Elsevier
,
Amsterdam, Boston
.
13.
Fister
,
I.
,
Fister Jr
,
I.
,
Yang
,
X.-S.
, and
Brest
,
J.
,
2013
, “
A Comprehensive Review of Firefly Algorithms
,”
SwarmEvol. Comput.
,
13
, pp.
34
46
. 10.1016/j.swevo.2013.06.001
14.
Simon
,
D.
,
2013
,
Evolutionary Optimization Algorithms, Biologically Inspired and Population-Based Approaches to Computer Intelligence
,
John Wiley & Sons
,
Hoboken, NJ
.
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