Three Strategies Enhance the Bionic Coati Optimization Algorithm for Global Optimization and Feature Selection Problems
Abstract
1. Introduction
- An adaptive search strategy is proposed, which integrates individual learning capabilities and the learnability of disparities, effectively enhancing the algorithm’s global exploration capabilities.
- A balancing factor is introduced, incorporating phase-based and dynamically adjustable characteristics, to achieve a well-balanced interplay between the exploration and exploitation phases.
- A centroid guidance strategy is devised, which combines the concept of centroid guidance with the utilization of fractional-order historical memory, thereby improving the algorithm’s exploitation capabilities.
- By integrating the aforementioned three strategies, the bionic ABCCOA algorithm is formulated. Experimental results on 27 FS problems demonstrate its superiority in terms of classification accuracy, stability, and runtime. This confirms that bionic ABCCOA is a promising bionic FS method.
2. Mathematical Model of Coati Optimization Algorithm
2.1. Population Initialization Phase
2.2. Global Exploration Phase
2.3. Local Exploitation Phase
2.4. Execution Framework of COA Algorithm
Algorithm 1: Pseudo code of COA algorithm |
Input: Population size (N), Dimension (D), Upper bound (ub) and lower bound (lb), Maximum of iterations (T). |
Output: Global best solution (Xbest). |
1. Initialize population based on Equation (1) and calculate the individual fitness function values of the population. 2. for t = 1:T 3. Calculate positions of iguanas using the globally best individual. 4. Phase 1: The attack behavior of coatis (Global Exploration Phase) 5. for 6. for j = 1:D 7. Calculate the jth dimensional new state of the ith individual based on Equation (4). 8. end for 9. end for 10. for 11. for j = 1:D 12. Calculate the jth dimensional new state of the ith individual based on Equation (5). 13. end for 14. end for 15. Use Equation (7) to preserve the new state of individual . 16. Phase 2: The escape behavior of coatis (Local Exploitation Phase) 17. for i = 1:N 18. for j = 1:D 19. Calculate the jth dimensional new state of the ith individual based on Equation (8). 20. end for 21. end for 22. Use Equation (10) to preserve the new state of individual . 23. Save the global best solution Xbest. 24. end for 25. Output the global best solution Xbest obtained by solving the optimization problem using the COA algorithm. |
3. The Proposal of ABCCOA Algorithm
3.1. Adaptive Search Strategy
3.2. Balancing Factor
3.3. Centroid Guidance Strategy
3.4. Execution Framework of ABCCOA Algorithm
Algorithm 2: Pseudo code of ABCCOA algorithm |
Input: Population size (), Dimension (), Upper bound () and lower bound (), Maximum of iterations (). |
Output: Global best solution (). |
1. Initialize population based on Equation (1) and calculate the individual fitness function values of the population. 2. for 3. Calculate positions of iguanas using the globally best individual. 4. Calculate Balancing Factor based on Equation (18). 5. if 6. Phase 1: The attack behavior of coatis (Global Exploration Phase) 7. if 8. for 9. for 10. Calculate the dimensional new state of the individual based on Equation (4). 11. end for 12. end for 13. for 14. for 15. Calculate the dimensional new state of the individual based on Equation (5). 16. end for 17. end for 18. else 19. for 20. Calculate the new state of the individual based on Equation (15). 21. end for 22. end if 23. Use Equation (7) to preserve the new state of individual . 24. else 25. Phase 2: The escape behavior of coatis (Local Exploitation Phase) 26. if 27. for 28. for 29. Calculate the dimensional new state of the individual based on Equation (8). 30. end for 31. end for 32. else 33. for 34. Calculate the new state of the individual based on Equation (20). 35. end for 36. end if 37. end if 38. Use Equation (10) to preserve the new state of individual . 39. Save the global best solution . 40. end for 41. Output the global best solution obtained by solving the optimization problem using the COA algorithm. |
4. Experimental Results and Discussion on CEC2020 and Real Problems
4.1. Strategies and Parameter Analysis
4.2. Population Diversity Analysis
4.3. Exploration/Exploitation Balance Analysis
4.4. Fitness Function Values Analysis on CEC2020
4.5. Nonparametric Test Analysis on CEC2020
4.6. Convergence Analysis on CEC2020
4.7. Fitness Function Values Analysis on Real Problems
5. Experimental Results and Discussion on FS Problems
5.1. FS Problems Model
- Step 1: Using Equation (23), we convert real-valued individual in the ABCCOA algorithm into a binary individual .
- Step 2: The binary individual is utilized to select a feature subset combination from the original dataset. Here, indicates that the jth feature in the original dataset is selected in the ith feature subset combination, whereas indicates that the jth feature is not selected.
- Step 3: The classification accuracy of the selected feature subset combinations is computed using a K-Nearest Neighbors (KNN) classifier, where K is set to 5.
- Step 4: The objective function value for the feature subset combination is computed using Equation (22) with the information output by the KNN classifier.
5.2. Fitness Function Values Analysis of FS Problems
5.3. Classification Accuracy and Feature Subset Size Analysis of FS Problems
5.4. Runtime Analysis of FS Problems
5.5. Comprehensive Analysis of FS Problems
6. Conclusions and Future Works
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Problems | Metrics | COA | GGO | IPOA | PRO | QAGO | QHDBO | HEOA | STOA | IMODE | ABCCOA |
---|---|---|---|---|---|---|---|---|---|---|---|
CEC2020_F1 | Mean | 3.1909 × 103 | 2.8022 × 105 | 2.3920 × 103 | 4.0006 × 103 | 3.7112 × 103 | 1.4334 × 103 | 9.2230 × 105 | 1.7426 × 103 | 1.0000 × 102 | 1.0000 × 102 |
Std | 3.3719 × 103 | 1.2304 × 106 | 2.4564 × 103 | 3.0737 × 103 | 3.5303 × 103 | 1.5126 × 103 | 6.8025 × 105 | 2.1007 × 103 | 0.0000 × 100 | 1.0556 × 10−14 | |
CEC2020_F2 | Mean | 1.9082 × 103 | 1.8364 × 103 | 1.4853 × 103 | 1.4333 × 103 | 1.9506 × 103 | 1.6920 × 103 | 1.2850 × 103 | 1.8119 × 103 | 1.3453 × 103 | 1.2784 × 103 |
Std | 3.3197 × 102 | 3.3372 × 102 | 2.1359 × 102 | 1.8320 × 102 | 2.6218 × 102 | 1.6673 × 102 | 1.0412 × 102 | 2.6013 × 102 | 2.1524 × 102 | 1.1347 × 102 | |
CEC2020_F3 | Mean | 7.6108 × 102 | 7.3357 × 102 | 7.2055 × 102 | 7.2118 × 102 | 7.4366 × 102 | 7.2806 × 102 | 7.2263 × 102 | 7.2482 × 102 | 7.1801 × 102 | 7.1718 × 102 |
Std | 1.5046 × 101 | 1.2631 × 101 | 6.1067 × 100 | 4.3600 × 100 | 1.8048 × 101 | 6.4219 × 100 | 4.5734 × 100 | 6.8581 × 100 | 3.8629 × 100 | 3.5531 × 100 | |
CEC2020_F4 | Mean | 1.9045 × 103 | 1.9033 × 103 | 1.9011 × 103 | 1.9017 × 103 | 1.9017 × 103 | 1.9011 × 103 | 1.9022 × 103 | 1.9016 × 103 | 1.9009 × 103 | 1.9007 × 103 |
Std | 2.9976 × 100 | 1.5294 × 100 | 3.1868 × 10−1 | 8.0634 × 10−1 | 6.9471 × 10−1 | 5.5801 × 10−1 | 5.4287 × 10−1 | 8.4758 × 10−1 | 3.4417 × 10−1 | 2.1239 × 10−1 | |
CEC2020_F5 | Mean | 1.0452 × 104 | 1.3219 × 104 | 4.7648 × 103 | 1.9134 × 105 | 2.2577 × 103 | 3.6506 × 103 | 3.8663 × 104 | 3.1948 × 103 | 1.8119 × 103 | 1.7500 × 103 |
Std | 1.0876 × 104 | 1.5027 × 104 | 2.6024 × 103 | 2.7411 × 105 | 2.5618 × 102 | 9.3224 × 102 | 3.6543 × 104 | 6.6865 × 102 | 6.4939 × 101 | 5.4569 × 101 | |
CEC2020_F6 | Mean | 1.7598 × 103 | 1.8005 × 103 | 1.6973 × 103 | 1.7170 × 103 | 1.7293 × 103 | 1.6193 × 103 | 1.6773 × 103 | 1.6311 × 103 | 1.6249 × 103 | 1.6113 × 103 |
Std | 1.0650 × 102 | 1.1254 × 102 | 6.9794 × 101 | 7.4794 × 101 | 1.0833 × 102 | 3.1798 × 101 | 7.9426 × 101 | 4.9920 × 101 | 4.7920 × 101 | 2.9837 × 101 | |
CEC2020_F7 | Mean | 9.1304 × 103 | 5.0144 × 103 | 2.4814 × 103 | 1.4209 × 104 | 2.4609 × 103 | 2.8087 × 103 | 1.1044 × 104 | 2.4544 × 103 | 2.1410 × 103 | 2.1062 × 103 |
Std | 7.1463 × 103 | 7.4174 × 103 | 1.7018 × 102 | 2.5252 × 104 | 2.3036 × 102 | 2.8361 × 102 | 1.0598 × 104 | 1.1367 × 102 | 8.0007 × 101 | 2.1880 × 101 | |
CEC2020_F8 | Mean | 2.3080 × 103 | 2.3057 × 103 | 2.3100 × 103 | 2.3100 × 103 | 2.3072 × 103 | 2.3077 × 103 | 2.3030 × 103 | 2.3068 × 103 | 2.3069 × 103 | 2.3100 × 103 |
Std | 1.0866 × 101 | 1.8825 × 101 | 1.0581 × 10−12 | 2.3739 × 10−3 | 1.5463 × 101 | 1.2572 × 101 | 2.3518 × 101 | 1.7244 × 101 | 1.7146 × 101 | 4.5475 × 10−13 | |
CEC2020_F9 | Mean | 2.7744 × 103 | 2.7070 × 103 | 2.7354 × 103 | 2.7440 × 103 | 2.7310 × 103 | 2.6821 × 103 | 2.7374 × 103 | 2.7055 × 103 | 2.7344 × 103 | 2.6550 × 103 |
Std | 1.9217 × 101 | 1.0097 × 102 | 4.4992 × 101 | 4.7359 × 101 | 7.9166 × 101 | 9.2976 × 101 | 5.8952 × 101 | 7.8665 × 101 | 4.4548 × 101 | 1.1648 × 102 | |
CEC2020_F10 | Mean | 2.9306 × 103 | 2.9390 × 103 | 2.9337 × 103 | 2.9304 × 103 | 2.9309 × 103 | 2.9197 × 103 | 2.9220 × 103 | 2.9315 × 103 | 2.9212 × 103 | 2.9026 × 103 |
Std | 4.7628 × 101 | 2.6650 × 101 | 2.1468 × 101 | 2.4738 × 101 | 2.1773 × 101 | 2.2733 × 101 | 2.0299 × 101 | 2.1700 × 101 | 2.3416 × 101 | 1.3847 × 101 | |
Mean Rank | 8.20 | 7.50 | 5.70 | 7.10 | 6.40 | 4.20 | 6.10 | 4.70 | 2.80 | 1.70 | |
Final Rank | 10 | 9 | 5 | 8 | 7 | 3 | 6 | 4 | 2 | 1 |
Problems | COA | GGO | IPOA | PRO | QAGO | QHDBO | HEOA | STOA | IMODE |
---|---|---|---|---|---|---|---|---|---|
CEC2020_F1 | − | − | − | − | − | − | − | − | = |
CEC2020_F2 | − | − | − | − | − | − | = | − | − |
CEC2020_F3 | − | − | − | − | − | − | − | − | − |
CEC2020_F4 | − | − | − | − | − | − | − | − | − |
CEC2020_F5 | − | − | − | − | − | − | − | − | − |
CEC2020_F6 | − | − | − | − | − | − | − | − | = |
CEC2020_F7 | − | − | − | − | − | − | − | − | − |
CEC2020_F8 | + | + | − | − | + | + | + | + | = |
CEC2020_F9 | − | − | − | − | − | = | − | = | − |
CEC2020_F10 | − | − | − | − | − | − | − | − | − |
+/−/= | 1/9/0 | 1/9/0 | 0/10/0 | 0/10/0 | 1/9/0 | 1/8/1 | 1/8/1 | 1/8/1 | 0/7/3 |
Problems | Metrics | COA | GGO | IPOA | PRO | QAGO | QHDBO | HEOA | STOA | IMODE | ABCCOA |
---|---|---|---|---|---|---|---|---|---|---|---|
RP1 | Mean | 5.261 × 102 | 5.347 × 102 | 5.257 × 102 | 5.599 × 102 | 5.262 × 102 | 5.247 × 102 | 5.249 × 102 | 5.360 × 102 | 5.246 × 102 | 5.245 × 102 |
Std | 1.981 × 100 | 8.537 × 100 | 1.596 × 100 | 1.022 × 101 | 2.812 × 100 | 1.118 × 100 | 1.179 × 100 | 6.981 × 100 | 6.270 × 10−02 | 1.919 × 10−2 | |
RP2 | Mean | −3.067 × 104 | −3.067 × 104 | −3.067 × 104 | −3.005 × 104 | −3.067 × 104 | −3.067 × 104 | −3.067 × 104 | −3.067 × 104 | −3.067 × 104 | −3.067 × 104 |
Std | 7.768 × 10−7 | 3.223 × 10−4 | 3.374 × 10−11 | 2.249 × 102 | 1.100 × 10−11 | 1.110 × 10−11 | 1.110 × 10−11 | 3.598 × 10−2 | 1.042 × 10−6 | 1.392 × 10−6 | |
RP3 | Mean | 1.280 × 10−2 | 1.274 × 10−2 | 1.267 × 10−2 | 2.226 × 10−2 | 1.268 × 10−2 | 1.267 × 10−2 | 1.267 × 10−2 | 1.314 × 10−2 | 1.267 × 10−2 | 1.267 × 10−2 |
Std | 1.402 × 10−4 | 1.021 × 10−4 | 5.570 × 10−6 | 8.296 × 10−3 | 2.380 × 10−5 | 5.254 × 10−6 | 5.682 × 10−8 | 4.130 × 10−4 | 1.170 × 10−7 | 4.378 × 10−13 | |
RP4 | Mean | 2.691 × 100 | 2.916 × 100 | 2.664 × 100 | 3.429 × 100 | 2.660 × 100 | 2.673 × 100 | 2.668 × 100 | 2.735 × 100 | 2.660 × 100 | 2.659 × 100 |
Std | 5.083 × 10−2 | 3.480 × 10−1 | 1.415 × 10−2 | 4.178 × 10−1 | 7.474 × 10−3 | 5.196 × 10−2 | 1.761 × 10−2 | 9.737 × 10−2 | 7.470 × 10−3 | 1.712 × 10−6 | |
RP5 | Mean | 1.670 × 100 | 1.685 × 100 | 1.670 × 100 | 1.974 × 100 | 1.670 × 100 | 1.670 × 100 | 1.670 × 100 | 1.737 × 100 | 1.670 × 100 | 1.670 × 100 |
Std | 2.497 × 10−4 | 6.173 × 10−2 | 1.187 × 10−8 | 1.204 × 10−1 | 5.800 × 10−10 | 2.258 × 10−16 | 2.182 × 10−16 | 4.694 × 10−2 | 1.950 × 10−7 | 1.934 × 10−16 | |
Mean Rank | 5.80 | 6.60 | 3.20 | 10.00 | 3.40 | 3.00 | 2.40 | 7.20 | 1.60 | 1.00 | |
Final Rank | 7 | 8 | 5 | 10 | 6 | 4 | 3 | 9 | 2 | 1 |
Datasets | Metrics | COA | FATA | HOA | MCOA | MSAACO | SBOA | PLO | ABCCOA |
---|---|---|---|---|---|---|---|---|---|
Aggregation | MIN | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.106 | 0.106 | 0.100 |
AVG | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.106 | 0.106 | 0.100 | |
MAX | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.106 | 0.106 | 0.100 | |
Banana | MIN | 0.211 | 0.196 | 0.192 | 0.199 | 0.212 | 0.195 | 0.197 | 0.188 |
AVG | 0.211 | 0.196 | 0.192 | 0.199 | 0.212 | 0.195 | 0.197 | 0.188 | |
MAX | 0.211 | 0.196 | 0.192 | 0.199 | 0.212 | 0.195 | 0.197 | 0.188 | |
Iris | MIN | 0.025 | 0.080 | 0.025 | 0.050 | 0.050 | 0.075 | 0.115 | 0.025 |
AVG | 0.025 | 0.088 | 0.025 | 0.050 | 0.051 | 0.075 | 0.115 | 0.025 | |
MAX | 0.025 | 0.110 | 0.025 | 0.050 | 0.055 | 0.075 | 0.115 | 0.025 | |
Bupa | MIN | 0.285 | 0.285 | 0.333 | 0.333 | 0.307 | 0.350 | 0.311 | 0.285 |
AVG | 0.296 | 0.292 | 0.334 | 0.333 | 0.313 | 0.350 | 0.311 | 0.285 | |
MAX | 0.344 | 0.311 | 0.337 | 0.333 | 0.337 | 0.350 | 0.311 | 0.285 | |
Glass | MIN | 0.312 | 0.290 | 0.269 | 0.259 | 0.259 | 0.312 | 0.248 | 0.226 |
AVG | 0.314 | 0.308 | 0.269 | 0.265 | 0.260 | 0.323 | 0.255 | 0.250 | |
MAX | 0.333 | 0.356 | 0.269 | 0.280 | 0.270 | 0.344 | 0.312 | 0.270 | |
Breastcancer | MIN | 0.059 | 0.059 | 0.053 | 0.053 | 0.055 | 0.053 | 0.053 | 0.048 |
AVG | 0.060 | 0.060 | 0.063 | 0.053 | 0.055 | 0.053 | 0.053 | 0.050 | |
MAX | 0.066 | 0.066 | 0.068 | 0.053 | 0.055 | 0.053 | 0.055 | 0.059 | |
Lipid | MIN | 0.245 | 0.247 | 0.253 | 0.229 | 0.245 | 0.237 | 0.258 | 0.222 |
AVG | 0.247 | 0.263 | 0.253 | 0.240 | 0.249 | 0.252 | 0.262 | 0.222 | |
MAX | 0.251 | 0.268 | 0.257 | 0.261 | 0.265 | 0.263 | 0.268 | 0.222 | |
HeartEW | MIN | 0.090 | 0.140 | 0.190 | 0.147 | 0.138 | 0.113 | 0.122 | 0.105 |
AVG | 0.110 | 0.165 | 0.248 | 0.164 | 0.142 | 0.123 | 0.129 | 0.107 | |
MAX | 0.147 | 0.190 | 0.281 | 0.188 | 0.147 | 0.154 | 0.156 | 0.122 | |
Zoo | MIN | 0.089 | 0.070 | 0.038 | 0.070 | 0.076 | 0.038 | 0.044 | 0.031 |
AVG | 0.121 | 0.095 | 0.041 | 0.073 | 0.114 | 0.071 | 0.065 | 0.035 | |
MAX | 0.134 | 0.109 | 0.050 | 0.076 | 0.134 | 0.083 | 0.115 | 0.044 | |
Vote | MIN | 0.029 | 0.029 | 0.031 | 0.035 | 0.046 | 0.048 | 0.050 | 0.027 |
AVG | 0.042 | 0.049 | 0.035 | 0.045 | 0.050 | 0.061 | 0.054 | 0.027 | |
MAX | 0.048 | 0.060 | 0.050 | 0.070 | 0.058 | 0.098 | 0.062 | 0.027 | |
Congress | MIN | 0.017 | 0.039 | 0.037 | 0.027 | 0.060 | 0.048 | 0.042 | 0.017 |
AVG | 0.017 | 0.052 | 0.038 | 0.027 | 0.065 | 0.048 | 0.048 | 0.025 | |
MAX | 0.017 | 0.062 | 0.042 | 0.027 | 0.068 | 0.048 | 0.056 | 0.035 | |
Lymphography | MIN | 0.064 | 0.110 | 0.059 | 0.084 | 0.107 | 0.090 | 0.084 | 0.059 |
AVG | 0.086 | 0.132 | 0.076 | 0.090 | 0.139 | 0.113 | 0.103 | 0.067 | |
MAX | 0.110 | 0.163 | 0.107 | 0.095 | 0.172 | 0.132 | 0.126 | 0.084 | |
Vehicle | MIN | 0.257 | 0.262 | 0.241 | 0.267 | 0.257 | 0.236 | 0.247 | 0.236 |
AVG | 0.275 | 0.285 | 0.266 | 0.279 | 0.273 | 0.251 | 0.257 | 0.251 | |
MAX | 0.288 | 0.300 | 0.289 | 0.294 | 0.295 | 0.263 | 0.267 | 0.263 | |
WDBC | MIN | 0.061 | 0.037 | 0.069 | 0.066 | 0.046 | 0.068 | 0.056 | 0.037 |
AVG | 0.066 | 0.053 | 0.086 | 0.067 | 0.049 | 0.089 | 0.070 | 0.046 | |
MAX | 0.075 | 0.064 | 0.102 | 0.070 | 0.058 | 0.103 | 0.081 | 0.055 | |
BreastEW | MIN | 0.039 | 0.036 | 0.037 | 0.035 | 0.039 | 0.041 | 0.039 | 0.021 |
AVG | 0.058 | 0.045 | 0.043 | 0.039 | 0.047 | 0.050 | 0.054 | 0.038 | |
MAX | 0.067 | 0.051 | 0.055 | 0.056 | 0.057 | 0.061 | 0.064 | 0.059 | |
SonarEW | MIN | 0.054 | 0.125 | 0.057 | 0.049 | 0.034 | 0.035 | 0.044 | 0.015 |
AVG | 0.073 | 0.152 | 0.074 | 0.077 | 0.053 | 0.050 | 0.073 | 0.038 | |
MAX | 0.093 | 0.189 | 0.089 | 0.091 | 0.081 | 0.062 | 0.099 | 0.050 | |
Libras | MIN | 0.153 | 0.138 | 0.238 | 0.204 | 0.178 | 0.271 | 0.164 | 0.092 |
AVG | 0.170 | 0.158 | 0.245 | 0.228 | 0.200 | 0.296 | 0.192 | 0.129 | |
MAX | 0.194 | 0.178 | 0.259 | 0.262 | 0.218 | 0.328 | 0.224 | 0.144 | |
Hillvalley | MIN | 0.341 | 0.313 | 0.376 | 0.261 | 0.318 | 0.294 | 0.374 | 0.266 |
AVG | 0.360 | 0.323 | 0.391 | 0.281 | 0.331 | 0.310 | 0.396 | 0.298 | |
MAX | 0.374 | 0.337 | 0.404 | 0.304 | 0.345 | 0.322 | 0.416 | 0.323 | |
Musk | MIN | 0.063 | 0.109 | 0.076 | 0.020 | 0.018 | 0.088 | 0.070 | 0.064 |
AVG | 0.093 | 0.133 | 0.098 | 0.033 | 0.028 | 0.109 | 0.090 | 0.080 | |
MAX | 0.112 | 0.145 | 0.112 | 0.040 | 0.045 | 0.127 | 0.109 | 0.088 | |
Clean | MIN | 0.067 | 0.073 | 0.084 | 0.075 | 0.020 | 0.047 | 0.075 | 0.017 |
AVG | 0.089 | 0.091 | 0.094 | 0.103 | 0.044 | 0.078 | 0.083 | 0.027 | |
MAX | 0.126 | 0.105 | 0.100 | 0.128 | 0.066 | 0.102 | 0.094 | 0.034 | |
Semeion | MIN | 0.114 | 0.106 | 0.131 | 0.070 | 0.119 | 0.089 | 0.080 | 0.063 |
AVG | 0.123 | 0.115 | 0.139 | 0.082 | 0.128 | 0.097 | 0.088 | 0.080 | |
MAX | 0.133 | 0.123 | 0.145 | 0.096 | 0.135 | 0.110 | 0.093 | 0.106 | |
Madelon | MIN | 0.244 | 0.230 | 0.237 | 0.158 | 0.107 | 0.190 | 0.183 | 0.091 |
AVG | 0.268 | 0.262 | 0.251 | 0.201 | 0.121 | 0.209 | 0.204 | 0.109 | |
MAX | 0.287 | 0.281 | 0.259 | 0.259 | 0.136 | 0.225 | 0.243 | 0.125 | |
Isolet | MIN | 0.161 | 0.151 | 0.178 | 0.164 | 0.065 | 0.136 | 0.134 | 0.060 |
AVG | 0.172 | 0.162 | 0.184 | 0.176 | 0.086 | 0.147 | 0.153 | 0.075 | |
MAX | 0.184 | 0.177 | 0.189 | 0.184 | 0.110 | 0.157 | 0.178 | 0.097 | |
Lung | MIN | 0.072 | 0.051 | 0.051 | 0.115 | 0.087 | 0.047 | 0.038 | 0.021 |
AVG | 0.093 | 0.072 | 0.081 | 0.122 | 0.095 | 0.082 | 0.071 | 0.042 | |
MAX | 0.124 | 0.093 | 0.098 | 0.135 | 0.113 | 0.120 | 0.113 | 0.063 | |
MLL | MIN | 0.081 | 0.071 | 0.082 | 0.072 | 0.101 | 0.123 | 0.053 | 0.041 |
AVG | 0.090 | 0.100 | 0.101 | 0.096 | 0.125 | 0.147 | 0.074 | 0.061 | |
MAX | 0.101 | 0.117 | 0.125 | 0.123 | 0.145 | 0.160 | 0.092 | 0.082 | |
Ovarian | MIN | 0.110 | 0.061 | 0.101 | 0.071 | 0.062 | 0.041 | 0.051 | 0.012 |
AVG | 0.123 | 0.093 | 0.118 | 0.095 | 0.083 | 0.072 | 0.079 | 0.020 | |
MAX | 0.180 | 0.118 | 0.123 | 0.114 | 0.098 | 0.081 | 0.100 | 0.034 | |
CNS | MIN | 0.118 | 0.084 | 0.071 | 0.088 | 0.080 | 0.117 | 0.101 | 0.061 |
AVG | 0.133 | 0.108 | 0.099 | 0.115 | 0.109 | 0.136 | 0.119 | 0.086 | |
MAX | 0.153 | 0.126 | 0.119 | 0.142 | 0.137 | 0.150 | 0.125 | 0.091 | |
Mean Rank | MIN | 4.70 | 4.70 | 5.04 | 4.44 | 4.63 | 5.00 | 4.63 | 1.19 |
AVG | 4.85 | 5.26 | 5.04 | 4.44 | 4.67 | 5.15 | 4.70 | 1.15 | |
MAX | 5.07 | 5.11 | 4.44 | 4.33 | 4.37 | 5.07 | 4.85 | 1.63 | |
Final Rank | MIN | 5 | 5 | 8 | 2 | 3 | 7 | 3 | 1 |
AVG | 5 | 8 | 6 | 2 | 3 | 7 | 4 | 1 | |
MAX | 6 | 8 | 4 | 2 | 3 | 6 | 5 | 1 |
Datasets | COA | FATA | HOA | MCOA | MSAACO | SBOA | PLO | ABCCOA |
---|---|---|---|---|---|---|---|---|
Aggregation | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 99.36 | 99.36 | 100.00 |
Banana | 87.64 | 89.34 | 89.81 | 88.96 | 87.55 | 89.43 | 89.25 | 90.19 |
Iris | 100.00 | 96.33 | 100.00 | 100.00 | 99.67 | 100.00 | 90.00 | 100.00 |
Bupa | 73.04 | 72.90 | 66.81 | 66.67 | 69.28 | 66.67 | 71.01 | 73.04 |
Glass | 69.05 | 69.52 | 73.81 | 75.00 | 76.19 | 68.57 | 75.00 | 76.19 |
Breastcancer | 97.12 | 96.76 | 96.40 | 97.84 | 96.40 | 97.84 | 97.55 | 97.12 |
Lipid | 74.31 | 73.62 | 74.31 | 75.52 | 75.00 | 74.66 | 72.84 | 77.59 |
HeartEW | 90.56 | 85.37 | 74.63 | 85.19 | 87.41 | 90.37 | 88.89 | 92.41 |
Zoo | 90.50 | 93.50 | 100.00 | 95.00 | 91.00 | 95.50 | 97.00 | 100.00 |
Vote | 96.67 | 97.36 | 99.08 | 96.55 | 96.78 | 96.67 | 96.32 | 97.70 |
Congress | 98.85 | 96.78 | 97.13 | 97.70 | 94.02 | 95.40 | 98.05 | 98.85 |
Lymphography | 94.14 | 88.97 | 95.52 | 93.10 | 87.93 | 91.38 | 91.72 | 95.86 |
Vehicle | 73.49 | 71.95 | 74.32 | 72.49 | 73.49 | 76.45 | 75.56 | 75.98 |
WDBC | 94.07 | 96.55 | 92.48 | 93.63 | 95.75 | 92.21 | 93.54 | 96.64 |
BreastEW | 96.37 | 98.23 | 99.29 | 98.05 | 96.99 | 97.96 | 96.99 | 99.20 |
SonarEW | 95.61 | 85.37 | 98.29 | 93.90 | 96.10 | 98.54 | 95.12 | 98.05 |
Libras | 83.75 | 84.72 | 79.31 | 76.53 | 79.58 | 71.39 | 82.64 | 87.78 |
Hillvalley | 61.82 | 65.37 | 62.73 | 70.50 | 65.37 | 70.33 | 60.50 | 67.85 |
Musk | 92.11 | 87.79 | 93.47 | 98.32 | 99.16 | 92.74 | 94.95 | 98.32 |
Clean | 91.05 | 93.47 | 96.42 | 91.05 | 97.68 | 95.79 | 95.47 | 99.26 |
Semeion | 91.42 | 91.60 | 91.70 | 94.56 | 90.53 | 94.34 | 95.31 | 94.65 |
Madelon | 74.29 | 74.52 | 79.37 | 80.38 | 88.85 | 82.25 | 82.54 | 89.29 |
Isolet | 84.34 | 85.02 | 86.98 | 83.22 | 92.99 | 89.16 | 88.26 | 93.99 |
Lung | 89.80 | 92.12 | 91.20 | 86.80 | 89.50 | 91.09 | 92.21 | 95.38 |
MLL | 90.01 | 89.11 | 88.93 | 89.38 | 86.23 | 83.70 | 91.80 | 93.25 |
Ovarian | 86.38 | 89.71 | 86.98 | 89.56 | 90.81 | 92.01 | 91.23 | 97.79 |
CNS | 85.38 | 88.13 | 89.12 | 87.30 | 88.03 | 84.98 | 86.89 | 90.50 |
Mean Rank | 5.07 | 5.11 | 4.26 | 4.70 | 4.70 | 4.63 | 4.59 | 1.44 |
Final Rank | 7 | 8 | 2 | 5 | 5 | 4 | 3 | 1 |
Datasets | COA | FATA | HOA | MCOA | MSAACO | SBOA | PLO | ABCCOA |
---|---|---|---|---|---|---|---|---|
Aggregation | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 |
Banana | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 |
Iris | 1.00 | 2.20 | 1.00 | 2.00 | 1.90 | 3.00 | 1.00 | 1.00 |
Bupa | 3.20 | 2.90 | 2.10 | 2.00 | 2.20 | 3.00 | 3.00 | 3.00 |
Glass | 3.20 | 3.00 | 3.00 | 3.60 | 4.10 | 3.60 | 2.70 | 3.20 |
Breastcancer | 3.10 | 2.80 | 2.80 | 3.00 | 2.00 | 3.00 | 2.80 | 2.20 |
Lipid | 1.60 | 2.60 | 2.20 | 2.00 | 2.40 | 2.40 | 1.80 | 2.00 |
HeartEW | 3.20 | 4.30 | 2.60 | 4.00 | 3.70 | 4.70 | 3.80 | 5.00 |
Zoo | 5.60 | 5.90 | 6.50 | 4.50 | 5.30 | 4.80 | 6.00 | 5.60 |
Vote | 1.90 | 4.10 | 4.30 | 2.30 | 3.30 | 5.00 | 3.30 | 1.00 |
Congress | 1.00 | 3.70 | 2.00 | 1.00 | 1.80 | 1.00 | 4.90 | 2.30 |
Lymphography | 5.90 | 5.80 | 6.50 | 5.00 | 5.40 | 6.30 | 5.10 | 5.40 |
Vehicle | 6.50 | 5.90 | 6.30 | 5.70 | 6.20 | 7.10 | 6.60 | 6.30 |
WDBC | 3.80 | 6.60 | 5.40 | 2.80 | 3.10 | 5.60 | 3.70 | 4.70 |
BreastEW | 7.60 | 8.60 | 11.10 | 6.40 | 6.10 | 9.40 | 8.00 | 9.20 |
SonarEW | 19.90 | 12.30 | 34.90 | 13.30 | 10.80 | 21.90 | 17.60 | 12.20 |
Libras | 21.70 | 18.30 | 52.60 | 14.90 | 14.80 | 34.80 | 32.10 | 16.90 |
Hillvalley | 16.60 | 11.00 | 55.30 | 15.20 | 19.20 | 43.40 | 40.80 | 8.80 |
Musk | 36.20 | 38.70 | 64.80 | 29.70 | 34.40 | 72.30 | 73.10 | 108.00 |
Clean | 13.40 | 54.10 | 103.20 | 38.00 | 38.60 | 67.80 | 70.00 | 34.50 |
Semeion | 116.60 | 100.20 | 163.80 | 83.50 | 109.70 | 118.00 | 116.80 | 80.80 |
Madelon | 183.60 | 161.50 | 326.10 | 123.40 | 104.20 | 247.30 | 234.60 | 61.80 |
Isolet | 194.10 | 167.20 | 412.10 | 152.20 | 138.70 | 302.20 | 289.80 | 131.70 |
Lung | 138.2 | 98.3 | 187.6 | 387.8 | 30.9 | 210.6 | 56.8 | 19.43 |
MLL | 73.4 | 198.2 | 137.8 | 102.5 | 88.4 | 49.8 | 56.3 | 30.8 |
Ovarian | 98.2 | 70.38 | 89.8 | 83.2 | 76.4 | 87.6 | 33.5 | 17.8 |
CNS | 93.2 | 74.8 | 101.5 | 81.2 | 94.2 | 78.2 | 59.3 | 26.5 |
Mean Rnak | 4.04 | 4.37 | 5.59 | 3.11 | 3.22 | 5.67 | 4.15 | 2.85 |
Final Rank | 4 | 6 | 7 | 2 | 3 | 8 | 5 | 1 |
Datasets | COA | FATA | HOA | MCOA | MSAACO | SBOA | PLO | ABCCOA |
---|---|---|---|---|---|---|---|---|
Aggregation | 9.62 | 6.01 | 7.01 | 8.45 | 9.78 | 8.20 | 10.02 | 5.66 |
Banana | 11.09 | 8.84 | 9.92 | 15.21 | 18.29 | 22.26 | 21.92 | 8.12 |
Iris | 5.49 | 6.97 | 6.48 | 8.74 | 8.75 | 9.22 | 8.97 | 4.95 |
Bupa | 6.19 | 7.95 | 8.70 | 9.36 | 8.61 | 9.40 | 9.81 | 5.78 |
Glass | 5.97 | 8.61 | 10.26 | 9.12 | 9.11 | 9.43 | 9.53 | 5.74 |
Breastcancer | 6.57 | 9.23 | 7.36 | 10.30 | 9.47 | 10.30 | 10.63 | 6.94 |
Lipid | 6.88 | 9.49 | 10.68 | 9.79 | 9.02 | 10.19 | 10.12 | 6.28 |
HeartEW | 8.58 | 9.45 | 7.06 | 9.83 | 9.88 | 9.75 | 9.72 | 6.46 |
Zoo | 8.65 | 9.26 | 9.82 | 9.63 | 9.49 | 9.48 | 9.33 | 6.41 |
Vote | 8.10 | 9.47 | 8.60 | 10.14 | 10.07 | 10.20 | 9.88 | 6.28 |
Congress | 7.46 | 9.55 | 9.78 | 9.81 | 9.98 | 9.94 | 10.06 | 6.03 |
Lymphography | 8.24 | 9.19 | 9.94 | 9.35 | 9.63 | 9.87 | 9.46 | 6.48 |
Vehicle | 10.62 | 10.96 | 8.23 | 11.52 | 11.90 | 11.79 | 11.81 | 7.81 |
WDBC | 9.46 | 9.68 | 7.40 | 10.34 | 13.04 | 10.01 | 10.86 | 6.39 |
BreastEW | 10.15 | 9.43 | 9.40 | 10.99 | 10.85 | 11.01 | 10.93 | 7.06 |
SonarEW | 8.78 | 8.43 | 9.28 | 9.41 | 9.01 | 9.76 | 9.53 | 6.59 |
Libras | 9.71 | 8.72 | 9.49 | 10.00 | 10.17 | 8.99 | 11.50 | 6.93 |
Hillvalley | 9.87 | 9.27 | 9.69 | 10.59 | 10.81 | 11.50 | 12.19 | 6.42 |
Musk | 11.68 | 10.34 | 10.33 | 10.90 | 11.20 | 12.20 | 12.96 | 6.55 |
Clean | 10.19 | 9.72 | 9.87 | 11.11 | 10.17 | 11.94 | 12.01 | 6.59 |
Semeion | 25.24 | 21.99 | 22.09 | 25.53 | 24.20 | 27.37 | 27.87 | 18.77 |
Madelon | 42.40 | 57.20 | 63.49 | 42.30 | 43.07 | 66.32 | 64.94 | 38.34 |
Isolet | 26.61 | 34.41 | 33.64 | 31.50 | 31.37 | 44.53 | 41.53 | 26.89 |
Lung | 159.01 | 116.91 | 119.00 | 105.60 | 101.40 | 90.30 | 89.50 | 79.29 |
MLL | 198.02 | 210.98 | 198.23 | 141.45 | 138.12 | 158.10 | 110.98 | 90.18 |
Ovarian | 181.24 | 178.91 | 198.22 | 138.91 | 145.98 | 156.32 | 129.98 | 101.30 |
CNS | 78.27 | 86.44 | 87.68 | 93.21 | 101.20 | 93.03 | 87.88 | 69.00 |
Mean Rnak | 3.52 | 3.59 | 4.48 | 5.33 | 5.37 | 6.33 | 6.30 | 1.07 |
Final Rank | 2 | 3 | 4 | 5 | 6 | 8 | 7 | 1 |
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Functions | Type | Name | Values |
---|---|---|---|
CEC2020_F1 | Unimodal | Shifted and Rotated Bent Cigar Function | 100 |
CEC2020_F2 | Multi-modal | Shifted and Rotated Schwefel’s Function | 1100 |
CEC2020_F3 | Shifted and Rotated unacek bi-Rastrigin Function | 700 | |
CEC2020_F4 | Expanded Rosenbrock’s plus Griewangk’s Function | 1900 | |
CEC2020_F5 | Hybrid | Hybrid Function 1 (N = 3) | 1700 |
CEC2020_F6 | Hybrid Function 2 (N = 4) | 1600 | |
CEC2020_F7 | Hybrid Function 3 (N = 5) | 2100 | |
CEC2020_F8 | Composition | Composition Function 1 (N = 3) | 2200 |
CEC2020_F9 | Composition Function 2 (N = 4) | 2400 | |
CEC2020_F10 | Composition Function 3 (N = 5) | 2500 |
Algorithms | Time | Parameters Setting |
---|---|---|
COA [63] | 2023 | No Parameters |
GGO [65] | 2024 | |
HEOA [66] | 2024 | |
IPOA [67] | 2024 | |
PRO [68] | 2024 | |
QAGO [69] | 2024 | |
QHDBO [70] | 2024 | |
STOA [71] | 2019 | |
IMODE [72] | 2020 |
Type | Name | Feature Number | Classification Number | Instance Size |
---|---|---|---|---|
Low | Aggregation | 2 | 7 | 788 |
Banana | 2 | 2 | 5300 | |
Iris | 4 | 3 | 150 | |
Bupa | 6 | 2 | 345 | |
Glass | 9 | 7 | 214 | |
Breastcancer | 9 | 2 | 699 | |
Lipid | 10 | 2 | 583 | |
HeartEW | 13 | 2 | 270 | |
Medium | Zoo | 16 | 7 | 101 |
Vote | 16 | 2 | 435 | |
Congress | 16 | 2 | 435 | |
Lymphography | 18 | 4 | 148 | |
Vehicle | 18 | 4 | 846 | |
WDBC | 30 | 2 | 569 | |
BreastEW | 30 | 2 | 569 | |
SonarEW | 60 | 2 | 208 | |
High | Libras | 90 | 15 | 360 |
Hillvalley | 100 | 2 | 606 | |
Musk | 166 | 2 | 476 | |
Clean | 167 | 2 | 476 | |
Semeion | 256 | 10 | 1593 | |
Madelon | 500 | 2 | 2600 | |
Isolet | 617 | 26 | 1559 | |
Lung | 12,533 | 5 | 203 | |
MLL | 12,582 | 3 | 72 | |
Ovarian | 15154 | 2 | 253 | |
CNS | 7129 | 2 | 60 |
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Cao, Q.; Yuan, S.; Fang, Y. Three Strategies Enhance the Bionic Coati Optimization Algorithm for Global Optimization and Feature Selection Problems. Biomimetics 2025, 10, 380. https://doi.org/10.3390/biomimetics10060380
Cao Q, Yuan S, Fang Y. Three Strategies Enhance the Bionic Coati Optimization Algorithm for Global Optimization and Feature Selection Problems. Biomimetics. 2025; 10(6):380. https://doi.org/10.3390/biomimetics10060380
Chicago/Turabian StyleCao, Qingzheng, Shuqi Yuan, and Yi Fang. 2025. "Three Strategies Enhance the Bionic Coati Optimization Algorithm for Global Optimization and Feature Selection Problems" Biomimetics 10, no. 6: 380. https://doi.org/10.3390/biomimetics10060380
APA StyleCao, Q., Yuan, S., & Fang, Y. (2025). Three Strategies Enhance the Bionic Coati Optimization Algorithm for Global Optimization and Feature Selection Problems. Biomimetics, 10(6), 380. https://doi.org/10.3390/biomimetics10060380