## Journal of Applied Mathematics

### Global Particle Swarm Optimization for High Dimension Numerical Functions Analysis

#### Abstract

The Particle Swarm Optimization (PSO) Algorithm is a popular optimization method that is widely used in various applications, due to its simplicity and capability in obtaining optimal results. However, ordinary PSOs may be trapped in the local optimal point, especially in high dimensional problems. To overcome this problem, an efficient Global Particle Swarm Optimization (GPSO) algorithm is proposed in this paper, based on a new updated strategy of the particle position. This is done through sharing information of particle position between the dimensions (variables) at any iteration. The strategy can enhance the exploration capability of the GPSO algorithm to determine the optimum global solution and avoid traps at the local optimum. The proposed GPSO algorithm is validated on a 12-benchmark mathematical function and compared with three different types of PSO techniques. The performance of this algorithm is measured based on the solutions’ quality, convergence characteristics, and their robustness after 50 trials. The simulation results showed that the new updated strategy in GPSO assists in realizing a better optimum solution with the smallest standard deviation value compared to other techniques. It can be concluded that the proposed GPSO method is a superior technique for solving high dimensional numerical function optimization problems.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 329193, 14 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305559

Digital Object Identifier
doi:10.1155/2014/329193

Mathematical Reviews number (MathSciNet)
MR3176815

Zentralblatt MATH identifier
07010602

#### Citation

Jamian, J. J.; Abdullah, M. N.; Mokhlis, H.; Mustafa, M. W.; Bakar, A. H. A. Global Particle Swarm Optimization for High Dimension Numerical Functions Analysis. J. Appl. Math. 2014 (2014), Article ID 329193, 14 pages. doi:10.1155/2014/329193. https://projecteuclid.org/euclid.jam/1425305559

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