Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2025 May 29:11:e2901.
doi: 10.7717/peerj-cs.2901. eCollection 2025.

An improved hippopotamus optimization algorithm based on adaptive development and solution diversity enhancement

Shengyu Pei  1   2 , Gang Sun  3 , Lang Tong  4
Affiliations

An improved hippopotamus optimization algorithm based on adaptive development and solution diversity enhancement

Shengyu Pei et al. PeerJ Comput Sci. .

Abstract

This study proposes an improved hippopotamus optimization algorithm to address the limitations of the traditional hippopotamus optimization algorithm in terms of convergence performance and solution diversity in complex high-dimensional problems. Inspired by the natural behavior of hippopotamuses, this article introduces chaotic map initialization, an adaptive exploitation mechanism, and a solution diversity enhancement strategy based on the original algorithm. The chaotic map is employed to optimize the initial population distribution, thereby enhancing the global search capability. The adaptive exploitation mechanism dynamically adjusts the weights between the exploration and exploitation phases to balance global and local searches. The solution diversity enhancement is achieved through the introduction of nonlinear perturbations, which help the algorithm avoid being trapped in local optima. The proposed algorithm is validated on several standard benchmark functions (CEC17, CEC22), and the results demonstrate that the improved algorithm significantly outperforms the original hippopotamus optimization algorithm and other mainstream optimization algorithms in terms of convergence speed, solution accuracy, and global search ability. Moreover, statistical analysis further confirms the superiority of the improved algorithm in balancing exploration and exploitation, particularly when dealing with high-dimensional multimodal functions. This study provides new insights and enhancement strategies for the application of the hippopotamus optimization algorithm in solving complex optimization problems.

Keywords: Adaptive exploitation; Chaotic mapping; Global optimization; Hippopotamus optimization algorithm; Solution diversity.

PubMed Disclaimer

Conflict of interest statement

Gang Sun is an employee of the Hunan Tobacco Workers Training Center.

Figures

Figure 1
Figure 1. Flowchart of IHO.
Figure 2
Figure 2. Convergence curves of five algorithms in each benchmark functions (CEC05, F1–F8).
Figure 3
Figure 3. Convergence curves of five algorithms in each benchmark functions (CEC05, F9–F16).
Figure 4
Figure 4. Convergence curves of five algorithms in each benchmark functions (CEC05, F17–F23).
Figure 5
Figure 5. Boxplot illustrating the performance of the IHO in comparison to other algorithms (CEC05, F1–F8).
Figure 6
Figure 6. Boxplot illustrating the performance of the IHO in comparison to other algorithms (CEC05, F9–F16).
Figure 7
Figure 7. Boxplot illustrating the performance of the IHO in comparison to other algorithms (CEC05, F17–F23).
Figure 8
Figure 8. Convergence curves of five algorithms in each benchmark functions (CEC17 D10).
Figure 9
Figure 9. Convergence curves of five algorithms in each benchmark functions (CEC17, D30).
Figure 10
Figure 10. Convergence curves of three algorithms in each benchmark functions (CEC17, D50).
Figure 11
Figure 11. Convergence curves of five algorithms in each benchmark functions (CEC22, D10).
Figure 12
Figure 12. Convergence curves of five algorithms in each benchmark functions (CEC22, D20).
See this image and copyright information in PMC

Similar articles

See all similar articles

References

    1. Almotairi S, Badr E, Abdul Salam M, Dawood A. Three chaotic strategies for enhancing the self-adaptive harris hawk optimization algorithm for global optimization. Mathematics. 2023;11(19):4181. doi: 10.3390/math11194181. - DOI
    1. Amiri MH, Mehrabi HN, Montazeri M, Mirjalili S, Khodadadi N. Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm. Scientific Reports. 2024;14(1):5032. doi: 10.1038/s41598-024-54910-3. - DOI - PMC - PubMed
    1. Chen Y. Research on 2D-OTSU image segmentation algorithm based on swarm intelligence optimization. Master, Jiangxi University of Science and Technology. 2023.
    1. Chen L, Cao K, Zhang S, Bai H, Han Y, Dai Q. Recent advances in swarm intelligence optimization algorithms. Computer Engineering and Applications. 2024a;60(19):46–67. doi: 10.3778/j.issn.1002-8331.2403-0328. - DOI
    1. Chen Z, Luo L, Zheng L, Ji S, Chen S. Research on ship-machine propeller matching design based on improved moth-flame optimization algorithm. Computer Science. 2024b;51(S1):69–77. doi: 10.11896/jsjkx.230500157. - DOI

LinkOut - more resources