![](bg8.png)
This behavior may be explained by the fact that in
larger grids the particles are isolated more often and
for longer periods of time. During these periods, the
particles are not using information from the rest of
the swarm. PSO-Bcfe partially overcomes the loss of
communication and information by not evaluating
the particles, thus saving computational resources.
Figure 2 graphically displays the evaluations
required by each version of the algorithm in each
function for different grids. Except for
, PSO-B
number of function evaluations to meet the criteria
increase with the size of the grid, while PSO-Bcfe
scales better, namely in functions
,
and
.
These results show that it is possible to improve
standard PSO’s performance by structuring the
particles on a grid of nodes, let them move
according to simple rules and save computational
resources by letting them follow their current
trajectories without evaluation the new positions.
5 CONCLUSIONS
This paper proposes a general scheme for structuring
dynamic populations for the Particle Swarm
Optimization (PSO) algorithm. The particles are
placed on a grid of nodes where the number of nodes
is larger than the swarm size. The particles move on
the grid according to simple rules and the network of
information is defined by the particle’s position on
the grid and its neighborhood (von Neumann vicinity
is considered here). If isolated (i.e., no neighbors
except itself), a particle is updated but its position is
not evaluated. This strategy results in loss of
information but it decreases the number of
evaluations per generation. The results show that the
payoff in convergence speed overcomes the loss of
information: the number of function evaluations is
reduced in the entire test set, while the accuracy of
the algorithm (i.e., the averaged final fitness) is not
degraded by the conservation of evaluations
strategy.
The proposed algorithm is tested with a Brownian
motion rule and compared to standard static
topologies. Statistical tests and ranking according to
convergence speed and success rates shows that the
dynamic structure with conservation of function
evaluations ranks first and it is significantly better
than the von Neumann, ring and lbest topologies.
Furthermore, the conservation of evaluations
strategy results in a more stable performance when
varying the grid size, while removing this strategy
from the proposed dynamic structure results in a
drop off of the convergence speed when the size of
the grid increases in relation to the swarm size.
The present study is restricted to dynamic structures
based on particles with Brownian motion. However,
a self-organized behavior based on communication
via the grid (stigmergy) can be modeled by the
general framework proposed in this paper. Future
research will be focused on dynamic structures with
stigmergic behavior based on the fitness and position
of the particles.
ACKNOWLEDGEMENTS
The first author wishes to thank FCT, Ministério da
Ciência e Tecnologia, his Research Fellowship
SFRH/ BPD/66876/2009. The work was supported
by FCT PROJECT [PEst-OE/EEI/LA0009/2013],
Spanish Ministry of Science and Innovation projects
TIN2011-28627-C04-02 and TIN2011-28627-C04-
01, Andalusian Regional Government P08-TIC-
03903 and P10-TIC-6083, CEI-BioTIC UGR project
CEI2013-P-14, and UL-EvoPerf project.
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