Author details

observations is statistically significantly different from 0 [44]. We can conclude then, that BAM-PSO has a greater performance over a broad set of benchmark functions over all other selected

(Rm) maximum negative

Accepted significance?

(P < 0.05)

ranks

The performance of BAM-PSO can be explained by its senescence mechanism: after particles falls into local minimum, they offer less improvement; then, the senescence mechanism starts acting by producing senescence on the swarm; then, exhausted particles are replaced with random ones through the search space. This favors exploration after premature convergence without completely eliminating exploitation of search space near the local minimum, which in

In this chapter, we introduced a PSO variant algorithm called Particle Swarm Optimization with Bio-inspired Aging Model (BAM-PSO) which was compared with other five popular bioinspired optimizers. This test was performed using popular benchmark functions with low

We observed that the BAM-PSO algorithm has the potential to solve the premature convergence problem of PSO showing good results for both low and high dimensional problems with statistical relevance according to several non-parametric analyses. Furthermore, according to

As shown in results section, BAM-PSO outperforms all other compared swarm-based algorithms with at least a confidence factor as high as P < 0:01. However, the cost of this improved accuracy is found in computation complexity due to the introduction of Eq. (2) and all the lifespan control for the particles; which in turn translates to computing time; this time increase was found to be approximately of at least 9 times the required computation time for the original PSO on the conducted experiments of section 5 and 1.5 times the required computation time for ALC-PSO. However, this increase in time is not fixed, as it depends on how early the premature convergence occurs and how many particles are replaced after senescence.

Finally, these experimental results provide support on the important role of aging mechanisms during the selection process in bio-inspired optimization algorithms, because the population-broad

results shown in Section 4, BAM-PSO performs better than the selected PSO variants.

algorithms with statistical relevance, including ALC-PSO.

Table 5. Non-parametrical Wilcoxon test for benchmark results at D = 30.

5. Conclusions

BAM-PSO

vs ALC-PSO

(R+) positive ranks obtained

20 Particle Swarm Optimization with Applications

and high dimensionality configuration.

the end provides better optimization results than other PSO variants.

(R) negative ranks

vs PSO 156.0 15.0 17 for (P < 0.001) Yes vs SSO 171.0 0.0 17 for (P < 0.001) Yes vs ACS 171.0 0.0 17 for (P < 0.001) Yes

147.0 24.0 27 for (P < 0.01) Yes

obtained

Eduardo Rangel-Carrillo<sup>1</sup> , Esteban A. Hernandez-Vargas<sup>2</sup> , Nancy Arana-Daniel<sup>1</sup> , Carlos Lopez-Franco<sup>1</sup> and Alma Y. Alanis<sup>1</sup> \*

\*Address all correspondence to: almayalanis@gmail.com

