Lévy Flight Trajectory-Based Whale Optimization Algorithm for Global Optimization

The whale optimization algorithm (WOA) has been shown to be powerful in searching for an optimal solution. This paper proposes an improvement to the whale optimization algorithm that is based on a Lévy flight trajectory and called the Lévy flight trajectory-based whale optimization algorithm (LWOA). The LWOA makes the WOA faster and more robust and avoids premature convergence. The Lévy flight trajectory is helpful for increasing the diversity of the population against premature convergence and enhancing the capability of jumping out of local optimal optima. This method helps obtaining a better tradeoff between the exploration and exploitation of the WOA. The proposed algorithm is characterized by quick convergence and high precision, and it can effectively get rid of a local optimum. The LWOA is further compared with other well-known nature-inspired algorithms on 23 benchmarks and solving infinite impulse response model identification. The statistical results on the benchmark functions show that the LWOA can significantly outperform others on a majority of the benchmark functions, especially in solving an optimization problem that has high dimensionality. Additionally, the superior identification capability of the proposed algorithm is evident from the results obtained through the simulation study compared with other algorithms. All the results prove the superiority of the LWOA.