Q-Gaussian swarm quantum particle intelligence on predicting global minimum of potential energy function

Abstract

We present a newly developed q-Gaussian Swarm Quantum-like Particle Optimization (q-GSQPO) algorithm to determine the global minimum of the potential energy function. Swarm Quantum-like Particle Optimization (SQPO) algorithms have already been derived using different attractive potential fields to represent swarm particles moving in a quantum environment. In this paper, we propose a new SQPO algorithm using q-Gaussian probability density function as the attractive potential field (q-GSQPO) rather than the Gaussian one (GSQPO) which corresponds to harmonic potential. The performance of the q-GSQPO algorithm is compared with that of GSQPO algorithm. The results of this study show that the new algorithm outperforms the GSQPO on most of the time in convergence to the global optimum. The most obvious finding of this study is that the new algorithm increases the efficiency of sampling the phase space and avoids the premature convergence to local minima, by increasing the diversity of the swarm. Moreover it was found that generally the computational efforts were comparable for both algorithms. We tested the algorithms by determining the lowest energy positions of the particles moving in the surface landscape of 2, 5, 10, and 50 dimensions.