Abstract: For the traditional particle swarm optimization(PSO) algorithm converges slowly and it is easy to fall into local minimum point,an improved PSO algorithm was proposed．The new algorithm combines memory character of fractional differential,reflects the historical information of particles’ movement and therefore improves the optimization process．Using Alpha-stable distribution instead of uniform distribution to generate random value can make the particle to escape from local minima in a certain probability and therefore there is more effective global search capability in new algorithm．Simulation results show that there is not only faster convergence speed and more effective global search capability under the single function in new algorithm,but also more satisfactory results under a complex and deceptive function．It is confirmed that the Alpha-stable distribution and fractional calculus can improve the performance of the PSO algorithm.

Key words: Particle swarm,Optimization algorithm,Fractional calculus,Alpha-stable distribution