---

The particle swarm optimizer (PSO) is a population-based metaheuristic optimization method that can be applied to a wide range of problems but it has the drawbacks like it easily falls into local optima and suffers from slow convergence in the later stages. In order to solve these problems, improved PSO (IPSO) variants, have been proposed. To bring about a balance between the exploration and exploitation characteristics of PSO, this paper introduces computationally fast and efficient IPSO algorithms based on a novel class of exponential learning factors (ELF-PSO). This class contains time-varying exponential learning factors (TELF), random exponential learning factors (RELF), self-adjusting exponential learning factors (SELF) and linear-exponential learning factors (LELF) strategies. Experiment is performed and compared with a set of well-known constant, random, time-varying and adaptive learning factors strategies on a suite of nonlinear benchmark functions. The experimental results and statistical analysis prove that ELF-PSO algorithms are able to solve a wide range of difficult nonlinear optimization problems efficiently. Also these results show that the proposed methods outperform other algorithms in most cases.