A novel particle swarm optimization algorithm with Levy flight

• This paper proposes a new approach for solving continuous optimization problems.
• The proposed approach is a combination of particle swarm optimization (PSO) and Levy flight (LFPSO).
• The performance and accuracy of the LFPSO are examined on numerical benchmark functions especially multimodal functions.
• The results obtained by LFPSO show that the LFPSO is more effective than state-of-the-art PSO (SPSO).
• In addition, to evaluate achievement of the proposed method, the LFPSO algorithm is compared the other PSO variants and other methods. The LFPSO outperforms the PSO variants and other algorithms and it is closely successful with the ABC algorithm.

Particle swarm optimization (PSO) is one of the well-known population-based techniques used in global optimization and many engineering problems. Despite its simplicity and efficiency, the PSO has problems as being trapped in local minima due to premature convergence and weakness of global search capability. To overcome these disadvantages, the PSO is combined with Levy flight in this study. Levy flight is a random walk determining stepsize using Levy distribution. Being used Levy flight, a more efficient search takes place in the search space thanks to the long jumps to be made by the particles. In the proposed method, a limit value is defined for each particle, and if the particles could not improve self-solutions at the end of current iteration, this limit is increased. If the limit value determined is exceeded by a particle, the particle is redistributed in the search space with Levy flight method. To get rid of local minima and improve global search capability are ensured via this distribution in the basic PSO. The performance and accuracy of the proposed method called as Levy flight particle swarm optimization (LFPSO) are examined on well-known unimodal and multimodal benchmark functions. Experimental results show that the LFPSO is clearly seen to be more successful than one of the state-of-the-art PSO (SPSO) and the other PSO variants in terms of solution quality and robustness. The results are also statistically compared, and a significant difference is observed between the SPSO and the LFPSO methods. Furthermore, the results of proposed method are also compared with the results of well-known and recent population-based optimization methods.

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