A hybrid algorithm based on PBIL algorithm and zooming algorithm and its convergence proof

Abstract

A hybrid algorithm (HA) based on population based incremental learning (PBIL) algorithm and zooming algorithm (ZA) is proposed, and its convergence is proved in this paper. In the hybrid algorithm, PBIL algorithm is employed for the evolutionary process as it can accelerate the convergence speed by a reduced time complexity, zooming algorithm is used to improve the PBIL algorithm as it can reduce search space on a large scale, and develop the convergence speed and the precision of solution obviously. The convergent analysis shows that if the population is big, and the parameters are proper, the hybrid algorithm converges to the global optimal solution. © 2013 Springer-Verlag.