With a hypothesis that the social hierarchy of the grey wolves would be also followed in their searching positions, an improved grey wolf optimization (GWO) algorithm with variable weights (VW-GWO) is proposed. And to reduce the probability of being trapped in local optima, a new governing equation of the controlling parameter is also proposed. Simulation experiments are carried out, and comparisons are made. Results show that the proposed VW-GWO algorithm works better than the standard GWO, the ant lion optimization (ALO), the particle swarm optimization (PSO) algorithm, and the bat algorithm (BA). The novel VW-GWO algorithm is also verified in high-dimensional problems.

Many new algorithms have been proposed to solve the mathematical equations formulated to describe the real-world problems. But there still does not exist one algorithm that could solve the problems all. And most of the proposed algorithms have defects in some aspects, they need to be improved in application. In order to find a more efficient optimization algorithm and inspired by the better performance of the Arithmetic Optimization algorithm (AOA) and Aquila Optimizer (AO), we proposed a hybridization algorithm of them and abbreviated AOAAO in this paper. Considering the better performance of the Harris Hawk optimization (HHO) algorithm, an energy parameter E was also introduced to balance the exploration and exploitation procedures of individuals in AOAAO swarms, and furthermore, piecewise linear map was introduced to decrease the randomness of the energy parameter. Pseudo code of the proposed AOAAO algorithm was presented, Simulation experiments were carried out on the benchmark functions and three classical engineering problems were also involved in optimization. Nine popular well demonstrated algorithms were included for comparison. Results confirmed the AOAAO would be more efficient in optimization with faster convergence rate, and higher convergence accuracy.

Considering the complicated multimodality, separability, scalability, symmetry characteristics of real-world engineering problems, we are still under the way to find more capable algorithms to solve them. The Aquila optimization (AO) algorithm was just proposed recently, however, the original version of this algorithm had some defects in the exploitation procedure, and resulted in incapability to exploit more information. Therefore, a simplified improved AO (IAO) algorithm was proposed and the equation controlling the exploitation procedure was removed, the former two strategies were kept and the latter two were dropped. To confirm the capability of the proposed IAO, simulation experiments on unimodal, multimodal benchmark functions and the CEC21 basic functions were carried out. Simulation experiments on three famous real-world engineering problems were also carried out. Comparison were made with the original AO algorithm, and some other newly proposed nature-inspired algorithms. Results on benchmark functions and the CEC14 basic functions verified the better performance, however, results on the real-world engineering problems demonstrated an incapable conclusion. Detailed future work is needed to tell the reason.

The mayfly optimization (MO) algorithm was proposed with a better hybridization of the particle swarm optimization (PSO) and the differential evolution (DE) algorithms. The velocity would be relevant to the Cartesian distance among the relevant individuals. In this paper, a reasonable revision for the velocity updating equations was proposed based on the idea of moving towards each other as capable as they can. Simulation results proved that the improved MO algorithm would perform better than the original one.