The hippopotamus optimization algorithm (HO) is a novel metaheuristic algorithm that solves optimization problems by simulating the behavior of hippopotamuses. However, the traditional HO algorithm may encounter performance degradation and fall into local optima when dealing with complex global optimization and engineering design problems. In order to solve these problems, this paper proposes a modified hippopotamus optimization algorithm (MHO) to enhance the convergence speed and solution accuracy of the HO algorithm by introducing a sine chaotic map to initialize the population, changing the convergence factor in the growth mechanism, and incorporating the small-hole imaging reverse learning strategy. The MHO algorithm is tested on 23 benchmark functions and successfully solves three engineering design problems. According to the experimental data, the MHO algorithm obtains optimal performance on 13 of these functions and three design problems, exits the local optimum faster, and has better ordering and stability than the other nine metaheuristics. This study proposes the MHO algorithm, which offers fresh insights into practical engineering problems and parameter optimization.

Aiming at the problem that the honey badger algorithm easily falls into local convergence, insufficient global search ability, and low convergence speed, this paper proposes a global optimization honey badger algorithm (Global Optimization HBA) (GOHBA), which improves the search ability of the population, with better ability to jump out of the local optimum, faster convergence speed, and better stability. The introduction of Tent chaotic mapping initialization enhances the population diversity and initializes the population quality of the HBA. Replacing the density factor enhances the search range of the algorithm in the entire solution space and avoids premature convergence to a local optimum. The addition of the golden sine strategy enhances the global search capability of the HBA and accelerates the convergence speed. Compared with seven algorithms, the GOHBA achieves the optimal mean value on 14 of the 23 tested functions. On two real-world engineering design problems, the GOHBA was optimal. On three path planning problems, the GOHBA had higher accuracy and faster convergence. The above experimental results show that the performance of the GOHBA is indeed excellent.

The grey wolf optimizer is a widely used parametric optimization algorithm. It is affected by the structure and rank of grey wolves and is prone to falling into the local optimum. In this study, we propose a grey wolf optimizer for fusion cell-like P systems. Cell-like P systems can parallelize computation and communicate from cell membrane to cell membrane, which can help the grey wolf optimizer jump out of the local optimum. Design new convergence factors and use different convergence factors in other cell membranes to balance the overall exploration and utilization capabilities of the algorithm. At the same time, dynamic weights are introduced to accelerate the convergence speed of the algorithm. Experiments are performed on 24 test functions to verify their global optimization performance. Meanwhile, a support vector machine model optimized by the grey wolf optimizer for fusion cell-like P systems has been developed and tested on six benchmark datasets. Finally, the optimizing ability of grey wolf optimizer for fusion cell-like P systems on constrained optimization problems is verified on three real engineering design problems. Compared with other algorithms, grey wolf optimizer for fusion cell-like P systems obtains higher accuracy and faster convergence speed on the test function, and at the same time, it can find a better parameter set stably for the optimization of support vector machine parameters, in addition to being more competitive on constrained engineering design problems. The results show that grey wolf optimizer for fusion cell-like P systems improves the searching ability of the population, has a better ability to jump out of the local optimum, has a faster convergence speed, and has better stability.

A multi-strategy improved honey badger algorithm (MIHBA) is proposed to address the problem that the honey badger algorithm may fall into local optimum and premature convergence when dealing with complex optimization problems. By introducing Halton sequences to initialize the population, the diversity of the population is enhanced, and premature convergence is effectively avoided. The dynamic density factor of water waves is added to improve the search efficiency of the algorithm in the solution space. Lens opposition learning based on the principle of lens imaging is also introduced to enhance the ability of the algorithm to get rid of local optimums. MIHBA achieves the best ranking in 23 test functions and 4 engineering design problems. The improvement of this paper improves the convergence speed and accuracy of the algorithm, enhances the adaptability and solving ability of the algorithm to complex functions, and provides new ideas for solving complex engineering design problems.