PERFORMANCE AND SCALABILITY OF PARTICLE SWARMS WITH WITH
DYNAMIC AND PARTIALLY CONNECTED GRID TOPOLOGIES
Carlos M. Fernandes1,2
J.L.J. Laredo3
J.J. Merelo2
Carlos Cotta4
Agostinho C. Rosa1
1LaSEEB-ISR-IST, University of Lisbon (IST), Portugal2 Departamento de Arquitectura y Tecnología de Computadores, University of Granada, Spain
3 Faculty of Sciences, Technology and Communications, University of Luxembourg, Luxembourg
4 Departamento de Lenguages y Ciencias de la Computación, University of Malaga, Spain
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Motivation
Particle Swarm and Population Structure
ECTA 2013, Vilamoura, Portugal
Speed (exploitation)
Robustness (exploration)
Information flow
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Particle Swarm Optimization (PSO)
Cultural and social interaction: cognitive, social and random factors.
ECTA 2013, Vilamoura, Portugal
Bio-inspired: bird flock and fish school.
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PSO – equations and parameters
X i(t) =
X i – position of particle i (vector)V i – velocity of particle i (vector)
Vi(t) =
ω Vi(t-1)+c1 r1(pi-xi(t-1))+c2
r2(pg-xi(t-1))
Xi(t-1)+Vi(t)
Social factor
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Topologies
ECTA 2013, Vilamoura, Portugal
k=2k=n
k=5
k=9
lbest
gbest
von Neumann
Moore
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Our proposal: a partially connected grid topology
ECTA 2013, Vilamoura, Portugal
Rule: The particles move randomly to adjacent nodes (defined by Moore neighborhood).
PSO topology: pg is updated according to the local neighborhood.
grid with size XxY
a. Maintain local interactions
b. Room for improvements
c. Easily model other topologies
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o Objective: evaluate performance of partially connected grid topologies with von Neumann and Moore neighborhood.
o 5 functions (d = 30; except f5, with d = 2)
o von Neumann, Moore, lbest and gbest topologies.
o Population size: n = 40; c1=c2=1.494; ω= 0.729
o Grids with different size (7x7, 8x8, 9x9, 10x10)
o Three performance metrics:
best fitness
iterations to a solution
success rate
Test Set
ECTA 2013, Vilamoura, Portugal
8ECTA 2013, Vilamoura, Portugal
Results – von Neumann
Fitness values: the proposed structure is able to improve lbest in f1, f2, f3 and f5; in f1 and f3 the differences are statistically significant.Iterations to a solution: improves lbest in every function, with statistical differences between the results.
lbest
Fitness values: is able to improve gbest in f1, f3, f4 and f5; the differences are statistically significant.Iterations to a solution: in general, gbest is faster, but it fails to meet the criteria in more than 50% of the runs.
gbest
standard von Neumann
Fitness values: 9x9 structure improves significantly in f1; equivalent in the remaining.Iterations to a solution: 9x9 structure improves significantly in f1, f3, f4 and f5.
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Results – von Neumann
Rank by success rates Rank by overall performance
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Results – Moore
lbest and gbest: similar conclusions.
Standard Moore configuration: a 7x7 structure is able to clearly improve the standard configuration in f1, f2 and f3 (is worst in f5); however, the 9x9 structure does not improve the performance in any function (and it is worst in f1 and f5).
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Scalability
o Tested f1, f2, f3 and f4 with d=15, d=30 and d=60
o von Neumann configurations.
o the proposed partially connected topology scales better than the standard von Neumann topology in f3 and f4; similar in f1 and f2.
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o The proposed structure with von Neumann neighborhood performs consistently throughout the test set.
o Improves the performance of other topologies in the majority of the scenarios and under different evaluation criteria.
o A sparse connectivity degrades Moore neighborhood performance.
o The structure is robust to the ratio between the grid size and the swarm size. A fixed size with ratio 1:2 performs well on every function.
o The proposed topology scales similarly to the standard von Neumann topology in two functions, and better in the other two functions.
Conclusions
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o Increase the test set size.
o Non-random movement strategies.
o Information flow.
o Islands, multi-swarms.
Future Research
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Questions?
ECTA 2013, Vilamoura, Portugal
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