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.

Feature selection (FS) is a classic and challenging optimization task in the field of machine learning and data mining. An equilibrium optimizer (EO) is a novel physics-based optimization algorithm; it was inspired by controlled volume mass balance models for estimating dynamic and equilibrium states. This article presents two binary equilibrium optimizer algorithm and for selecting the optimal feature subset for classification problems. The first algorithm maps the continuous EO into a discrete type using S-shaped and V-shaped transfer functions (BEO-S and BEO-V). The second algorithm is based on the position of the current optimal solution (target) and position vector (BEO-T). To verify the performance of the proposed algorithm, 19 well-known UCI datasets are tested and compared with other advanced FS methods. The experimental results show that among the proposed binary EO algorithms, BEO-V2 has the best comprehensive performance and has better performance than other state-of-the-art metaheuristic algorithms in terms of the performance measures.

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy flights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy “DE/best/2” in differential algorithm. Lévy flights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space.