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Fig. 10 Algorithm Convergence for Generalize Rastrigin 2.6 ( f5)
Table IV presents the mean fitness for minimization result
on the functions. The performance of R-PSO outperform the
PSO for functions f2 – f5. For function f1, it is the simplesphere model and the mean fitness result is the same.
However, the convergence of PSO is faster than R-PSO due to
a single lbest but R-PSO still tries different lbest which is
already a gbest as shown in Fig.6.
For function f2, the R-PSO is very close to the solution,
while the PSO is divergent without having close the the
solution as a result of the best local optimum (or gbest) as
shown in Fig .7. The PSO is trapped in the lbest while R-PSOcan escape and find the new lbest using the agent particle. The
R-PSO can practically prevent the premature convergence and
notably increase the convergence in the evolution procedure.
For function f3, a saddle point contains serval lbest,
therefore, it is hardly to find the optimum solution. PSO
eventually diverges while the R-PSO still can demonstrates a
better result and convergence precision as shown in fig.8.
Function f4 and f5 are multimodal functions where the local
optimum increases exponentially depending on the dimension
size. It is the complex problem and very hard to find the
solution. PSO can be trapped in a local optimum on its route to
the global optimum, while R-PSO eventually can still find a
solution as shown in Fig.9 and Fig.10. It has been shown that
our R-PSO is the better optimization method than the PSO for
such complex problems in term of both convergence and
speed. Thus, the proposed lbest circle topology using radius-
neighborhood search is very effective for most test functions.
V. CONCLUSION
We propose the R-PSO by regrouping the particles within a
given radius and determine the agent particle which is the best
particle of the group for each local optimum. The R-PSO is
able to maintain appropriate swarm diversity, jump out thelocal optimum using the agent particle to achieve the global
optimum. We prove the performance of the R-PSO using well-
known complex problems. The result shows that our proposedmethod can solve the complex problems more effectively and
efficiently than the traditional PSO.
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2013 International Computer Science and Engineering Conference (ICSEC): ICSEC 2013 English Track Full Papers