This document studies time-varying partially connected topologies for particle swarm optimization. It compares different population structures, including local best (lbest), global best (gbest), and a dynamic Von Neumann neighborhood structure. The results show that the dynamic partially connected structure offers the best balance, finding solutions faster and with fewer iterations than the static lbest and gbest models. The optimal grid size is around twice the number of particles. Overall, the dynamic topology performed best in successfully finding solutions.

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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