Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum behaved particle swarm optimization was proposed as a variant of PSO with better global search capability. This paper proposes a novel method for enhancing the global search capability of PSO and guiding its search with fractional calculus concepts. With the commonly used definitions of fractional differential known as Grünwald Letnikov(GL), the authors introduce its discrete expression into the position update in QPSO to improve its convergence speed and accuracy. Some empirical studies on popular benchmark functions are performed in order to make a full evaluation on performance and comparison between standard QPSO and QPSO with different fractional order. The new algorithm, named fractional order Quantum particle swarm optimization, shows to perform well in finding optimal solutions with much higher convergence accuracy in many optimization problems.
