Dung Beetle Optimization Algorithm Based on Improved Multi-Strategy Fusion
Abstract
:1. Introduction
- (1)
- To increase the search space of the algorithm, a refractive backward learning method is employed, and an adaptive curve is included to control the size of the dung beetle population.
- (2)
- To enhance and balance local exploitation and global exploration, the algorithm’s convergence is accelerated in the ball-rolling dung beetle phase by using a triangular wandering approach and in the breeding dung beetle phase by using a fused subtractive averaging optimizer.
- (3)
- Late in the iteration, the globally optimal solution is variationally disturbed by an adaptive Gaussian–Cauchy hybrid variational perturbation factor, which improves algorithm efficiency and the impact of finding the ideal solution.
2. Dung Beetle Optimization Algorithm (DBO)
2.1. Rolling Dung Beetle
2.2. Breeding Dung Beetles
2.3. Foraging Dung Beetles
2.4. Stealing Dung Beetles
3. Improving the Dung Beetle Optimization Algorithm
3.1. Refractive Reverse Learning Strategies
3.2. Multi-Strategy Integration Improvement
3.2.1. Adaptive Population Change
3.2.2. Fusion Subtractive Averaging Optimizer
3.2.3. Triangle Wandering Strategy
3.3. Adaptive Gauss–Cauchy Mixed-Variance Perturbation Factor
3.4. MSFDBO Complexity Analysis
3.5. MSFDBO Algorithm Flowchart
4. Experimental Results and Discussion
4.1. CEC2017 Benchmark Function Results and Analysis
4.1.1. Analysis of CEC2017 Statistical Results
4.1.2. Comparative Analysis of CEC2017 Convergence Curves
4.2. Wilcoxon Rank Sum Test
4.3. Friedman Test
5. Engineering Application Design Issues
5.1. Welded Beam Design Issues
5.2. Reducer Design Issues
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Algorithm | Parameters |
---|---|
PSO | ω = 1, c1 = 1.1, c2 = 1.1 |
SCA | a = 2 |
WOA | a = 2 × (1 − t/Tmax), k = 1 |
HHO | B = 1.5, E0 = [−1, 1] |
SFO | A = 4, e = 0.001, SFP = 0.3 |
SCSO | rG = 2~0, =−2rG~rG |
DBO | RDB = 6, EDB = 6, FDB = 7, SDB = 11 |
MSFDBO | R = 1 − t/Tmax |
Test Function | PSO | SFO | WOA | SCA | HHO | SCSO | DBO | MSFDBO |
---|---|---|---|---|---|---|---|---|
CEC2017 50D | 6.0345 | 7.7931 | 5.1379 | 5.8276 | 3.0345 | 3.5862 | 3.2414 | 1.3448 |
CEC2017 100D | 6.0690 | 7.7586 | 4.8966 | 6.0345 | 3.0345 | 3.5172 | 3.3448 | 1.3448 |
Arithmetic | Cost Optimization | ||||
---|---|---|---|---|---|
PSO | 0.1525 | 6.0671 | 9.7399 | 0.2025 | 2.0597 |
SFO | 0.1710 | 4.8328 | 8.2402 | 0.2545 | 2.0189 |
WOA | 0.1580 | 6.4434 | 9.5400 | 0.2034 | 2.0850 |
SCA | 0.2010 | 3.5951 | 9.5716 | 0.2107 | 1.8645 |
HHO | 0.1682 | 4.8085 | 8.9901 | 0.2169 | 1.9105 |
SCSO | 0.2009 | 3.3397 | 9.0395 | 0.2057 | 1.7003 |
DBO | 0.2035 | 3.0899 | 9.5183 | 0.2036 | 1.7331 |
MSFDBO | 0.2057 | 3.2444 | 9.0337 | 0.2059 | 1.6948 |
Algorithms | Optimum Weight | |||||||
---|---|---|---|---|---|---|---|---|
PSO | 3.6000 | 0.7000 | 17.0000 | 8.3000 | 8.3000 | 3.4122 | 5.3642 | 3121.9650 |
SFO | 3.5114 | 0.7000 | 18.2404 | 7.5813 | 7.7169 | 3.5598 | 5.2878 | 3281.4934 |
WOA | 3.5355 | 0.7000 | 17.0000 | 7.8000 | 7.8464 | 3.6251 | 5.3290 | 3126.6302 |
SCA | 3.6000 | 0.7000 | 17.0000 | 7.3000 | 8.1063 | 3.4789 | 5.3751 | 3134.3656 |
HHO | 3.5000 | 0.7000 | 17.0000 | 7.6652 | 7.9002 | 3.5581 | 5.3308 | 3086.9231 |
SCSO | 3.5015 | 0.7000 | 17.0001 | 7.6361 | 7.8095 | 3.3526 | 5.2888 | 3002.0753 |
DBO | 3.6000 | 0.7000 | 17.0000 | 7.3000 | 8.3000 | 3.3502 | 5.2869 | 3046.7137 |
MSFDBO | 3.5000 | 0.7000 | 17.0000 | 7.3000 | 7.7153 | 3.3502 | 5.2867 | 2994.4711 |
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Fang, R.; Zhou, T.; Yu, B.; Li, Z.; Ma, L.; Zhang, Y. Dung Beetle Optimization Algorithm Based on Improved Multi-Strategy Fusion. Electronics 2025, 14, 197. https://doi.org/10.3390/electronics14010197
Fang R, Zhou T, Yu B, Li Z, Ma L, Zhang Y. Dung Beetle Optimization Algorithm Based on Improved Multi-Strategy Fusion. Electronics. 2025; 14(1):197. https://doi.org/10.3390/electronics14010197
Chicago/Turabian StyleFang, Rencheng, Tao Zhou, Baohua Yu, Zhigang Li, Long Ma, and Yongcai Zhang. 2025. "Dung Beetle Optimization Algorithm Based on Improved Multi-Strategy Fusion" Electronics 14, no. 1: 197. https://doi.org/10.3390/electronics14010197
APA StyleFang, R., Zhou, T., Yu, B., Li, Z., Ma, L., & Zhang, Y. (2025). Dung Beetle Optimization Algorithm Based on Improved Multi-Strategy Fusion. Electronics, 14(1), 197. https://doi.org/10.3390/electronics14010197