Article presented at CEC 2013 by Fernandes, Merelo, Laredo, Cotta and Rosa.

1. A Study on Time-varying PartiallyA Study on Time-varying Partially
ConnectedConnected
Topologies for the Particle SwarmTopologies for the Particle Swarm
Fernandes, Merelo, Laredo, Cotta, Rosa
UGR+UMA+UNILU+IST

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Particle Swarm optimizationParticle Swarm optimization

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No formula here, get a move onNo formula here, get a move on
● Movement combines inertia term with following
the best.
● The best is a term that depends on population
topology.
● You only follow the best if you know about it.
● Different population structures are defined.

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Act local, think globalAct local, think global
LBest
GBest

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A bit ofA bit of
this andthis and
thatthat
Von Neumann

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A dynamic, partially connected,A dynamic, partially connected,
population structurepopulation structure
● Nodes move every timestep to one of the
nodes in their Moore Neighborhood, if there's
one available.

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Testing the new populatonTesting the new populaton
structurestructure
● Using the usual Sphere, Rosenbrock, Rastrigin,
Griewank and Schaffer functions.
● Best fitness at the origin.
● Multimodal.
●
Usually difficult for gbest

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Comparison with static vN: best fitnessComparison with static vN: best fitness

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Comparison with static vN: iterationsComparison with static vN: iterations

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Comparison with l/gbestComparison with l/gbest

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Comparison with l/gbest:Comparison with l/gbest:
iterationsiterations

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Iterations to solution inIterations to solution in
successful runssuccessful runs
VN faster than lbest, some
times also faster than gbest

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vN vNR lB gB
0
10
20
30
40
50
success
Rank by success rateRank by success rate

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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
vNR
vN
lB
gB
rank
Rank by overall performanceRank by overall performance

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1 2 3 4 5
0
4
8
12
16
20
7x7 8x8
9x9 10x10
Connectivity histogram.

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1
59
117
175
233
291
349
407
465
523
581
639
697
755
813
871
929
987
0
5
10
15
20
25
30
35
k=1 k=2 k=3 k=4 k=5
iterations, t
numberofparticles
Evolution of connectivity

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ConclusionsConclusions
● Dynamic and partially connected structures
offer the best of both worlds.
● Size of the grid is not critical, but as a rule of
thumb: 2 x number of particles.
● Dynamic structures are better than static.

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That's allThat's all
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