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Article

The Great Wall Construction Algorithm Incorporating Marginal Benefit Assessment for Numerical Optimization and Real-World Applications

1
School of Management, Northwestern Polytechnical University, Xi’an 710072, China
2
Adam Smith businesses School, The University of Glasgow, Glasgow G1 1XQ, UK
3
School of Foreign Languages, Sun Yat-Sen University, Guangzhou 510275, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2026, 18(6), 945; https://doi.org/10.3390/sym18060945 (registering DOI)
Submission received: 23 April 2026 / Revised: 12 May 2026 / Accepted: 20 May 2026 / Published: 31 May 2026
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)

Abstract

Complex global optimization problems are widely encountered in wireless sensor network deployment, engineering design, energy scheduling, structural optimization, and intelligent parameter optimization. Due to their gradient-free search mechanism, strong global exploration capability, simple implementation, and adaptability to nonlinear and multimodal optimization problems, swarm intelligence algorithms have become effective tools for solving complex optimization tasks. In this study, an enhanced Great Wall Construction Algorithm based on a Marginal Benefit Assessment mechanism, termed GWCA-MBA, is proposed for numerical optimization and engineering applications. The proposed method incorporates three cooperative enhancement strategies into the original GWCA framework, including a quasi-oppositional chaotic initialization strategy, a Marginal Benefit Assessment-based adaptive role scheduling mechanism, and an elite differential-Lévy refinement strategy. These mechanisms jointly improve population diversity, adaptive search capability, and local exploitation precision. To evaluate its effectiveness, GWCA-MBA is comprehensively tested on the CEC2017, CEC2020, and CEC2022 benchmark suites and compared with several representative metaheuristic algorithms. Experimental results demonstrate that GWCA-MBA achieves the best Friedman mean ranks of 2.70, 3.50, and 2.33 on the CEC2017, CEC2020, and CEC2022 benchmark suites, respectively, indicating superior overall optimization performance and robustness. In addition, the proposed algorithm exhibits highly stable convergence behavior with significantly lower standard deviation values than the compared algorithms on most benchmark functions. To further verify its engineering applicability, GWCA-MBA is applied to a three-dimensional wireless sensor network coverage optimization problem and two constrained engineering design problems. In the wireless sensor network deployment problem, GWCA-MBA achieves a coverage rate of 75.90%, outperforming the compared algorithms and demonstrating strong spatial optimization capability and practical applicability. Moreover, GWCA-MBA also achieves the first Friedman ranking in the engineering application experiments, further demonstrating its strong practical optimization capability and generalization performance in real-world optimization problems. Overall, GWCA-MBA effectively balances exploration and exploitation and provides a competitive optimization framework for complex numerical optimization and practical engineering applications.
Keywords: metaheuristic algorithms; swarm intelligence algorithm; great wall construction algorithm; numerical optimization; wireless sensor networks; engineering applications metaheuristic algorithms; swarm intelligence algorithm; great wall construction algorithm; numerical optimization; wireless sensor networks; engineering applications

Share and Cite

MDPI and ACS Style

Zhang, C.; Li, C.; Ling, L. The Great Wall Construction Algorithm Incorporating Marginal Benefit Assessment for Numerical Optimization and Real-World Applications. Symmetry 2026, 18, 945. https://doi.org/10.3390/sym18060945

AMA Style

Zhang C, Li C, Ling L. The Great Wall Construction Algorithm Incorporating Marginal Benefit Assessment for Numerical Optimization and Real-World Applications. Symmetry. 2026; 18(6):945. https://doi.org/10.3390/sym18060945

Chicago/Turabian Style

Zhang, Chi, Chenfei Li, and Luqi Ling. 2026. "The Great Wall Construction Algorithm Incorporating Marginal Benefit Assessment for Numerical Optimization and Real-World Applications" Symmetry 18, no. 6: 945. https://doi.org/10.3390/sym18060945

APA Style

Zhang, C., Li, C., & Ling, L. (2026). The Great Wall Construction Algorithm Incorporating Marginal Benefit Assessment for Numerical Optimization and Real-World Applications. Symmetry, 18(6), 945. https://doi.org/10.3390/sym18060945

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