Multi-Strategy Improved Binary Secretarial Bird Optimization Algorithm for Feature Selection
<p>Hunting behavior simulation of secretary bird.</p> "> Figure 2
<p>Escape behavior simulation of secretary bird.</p> "> Figure 3
<p>Simulation diagram of segmented balance strategy.</p> "> Figure 4
<p>Flowchart of the execution of BSFSBOA.</p> "> Figure 5
<p>Convergence plot of the algorithm for different population sizes.</p> "> Figure 6
<p>Population diversity in SBOA and BSFSBOA runs.</p> "> Figure 7
<p>Exploration/exploitation ratio for BSFSBOA runs.</p> "> Figure 8
<p>Box plots of algorithms for solving low-dimensional UCL FS problems.</p> "> Figure 9
<p>Average ranking in solving low-dimensional UCL FS problems.</p> "> Figure 10
<p>Box plots of algorithms for solving medium-dimensional UCL FS problems.</p> "> Figure 11
<p>Average ranking in solving medium-dimensional UCL FS problems.</p> "> Figure 12
<p>Box plots of algorithms for solving high-dimensional UCL FS problems.</p> "> Figure 13
<p>Average ranking in solving high-dimensional UCL FS problems.</p> "> Figure 14
<p>Average ranking in solving 23 UCL FS problems.</p> "> Figure 15
<p>Convergence curve of algorithms for solving low-dimensional UCL FS problems.</p> "> Figure 16
<p>Convergence curve of algorithms for solving medium-dimensional UCL FS problems.</p> "> Figure 17
<p>Convergence curve of algorithms for solving high-dimensional UCL FS problems.</p> "> Figure 18
<p>Stacked plot of algorithms on classification accuracy and FS subset size on UCL FS problems.</p> "> Figure 19
<p>Average ranking in solving OpenML FS problems.</p> "> Figure 20
<p>Stacked plot of algorithms on classification accuracy and FS subset size on OpenML FS problems.</p> ">
Abstract
:1. Introduction
- The best-rand exploration strategy is proposed to effectively improve the population diversity of the algorithm by utilizing the randomness and optimality of random individuals as well as optimal individuals.
- The segmented balance strategy is proposed to enhance the quality of the FS subset when the algorithm is solved by segmenting the individuals in the population and targeting the individuals of different natures with different levels of exploration and exploitation performance.
- The four-role exploitation strategy is proposed to enhance the effective exploitation of the algorithm and improve the classification accuracy of the FS subset by different degrees of guidance through the four natures of the individuals in the population.
- A FS method based on BSFSBOA is proposed by combining the above three learning strategies, and the proposed FS method is utilized to solve 36 FS problems involving low, medium, and high dimensions, which confirms that it is a robust FS tool with efficient search performance.
2. Mathematical Framework of Secretary Bird Optimization Algorithm
2.1. Mathematical Modelling of Hunting Behavior
2.1.1. Seeking After One’s Prey
2.1.2. Depleting Prey’s Energy
2.1.3. Attacking Prey
2.2. Mathematical Modelling of Escape Behaviour
2.2.1. Escaping by Run or Fly Away
2.2.2. Hiding with the Environment
Algorithm 1: The execution of SBOA |
Input: Initialize parameters: , , , , , . Output: the best candidate solution (). 1: Initialize individuals using Equation (1) and form an initialized population using Equation (2). 2: for 3: Update the best candidate solution (). 4: for 5: Hunting behavior (Exploration phase of SBOA): 6: if 7: Update the position of the secret bird using Equation (4). 8: else if 9: Update the position of the secret bird using Equation (6). 10: else 11: Update the position of the secret bird using Equation (7). 12: end if 13: Use Equation (5) to keep the position of the secret bird . 14: Escape Behavior (Exploitation Phase of SBOA): 15: if 16: Update the position of the secret bird using Equation (11). 17: else 18: Update the position of the secret bird using Equation (14). 19: end if 20: Use Equation (13) to keep the position of the secret bird . 21: end for 22: Save the best candidate solution (). 23: end for 24: Return the best candidate solution (). |
3. Mathematical Modeling of BSFSBOA
3.1. Best-Rand Exploration Strategy
3.2. Segmented Balance Strategy
3.3. Four-Role Exploitation Strategy
3.4. Implementation of the BSFSBOA
Algorithm 2: The execution of BSFSBOA |
Input: Initialize parameters: , , , , , . Output: the best candidate solution (). 1: Initialize individuals using Equation (1) and form an initialized population using Equation (2). 2: for 3: Update the best candidate solution (). 4: if 5: for 6: Hunting behavior (Exploration phase of BSFSBOA): 7: if 8: if 9: Update the position of the secret bird using Equation (4). 10: else if 11: Update the position of the secret bird using Equation (6). 12: else 13: Update the position of the secret bird using Equation (7). 14: end if 15: else 16: Update the position of the secret bird using Equation (15). 17: end if 18: Use Equation (5) to keep the position of the secret bird . 19: Escape Behavior (Exploitation Phase of BSFSBOA): 20: if 21: if 22: Update the position of the secret bird using Equation (11). 23: else 24: Update the position of the secret bird using Equation (14). 25: end if 26: else 27: Update the position of the secret bird using Equation (20). 28: end if 29: Use Equation (13) to keep the position of the secret bird . 30: end for 31: else 32: for 33: Update the position of the secret bird using Equations (18) and (19). 34: Use Equations (5) and (13) to keep the position of the secret bird . 35: end for 36: end if 37: Save the best candidate solution (). 38: end for 39: Return the best candidate solution (). |
4. Discussion of Experimental Results on the UCL Datasets
4.1. The Modeling of the FS Problems
4.2. Sensitivity Analysis of Operating Parameters
4.3. Population Diversity Analysis
4.4. Exploration/Exploitation Balance Analysis
4.5. Fitness Function Value Analysis on the UCL Datasets
4.6. Friedman Nonparametric Test Analysis on the UCL Datasets
4.7. Convergence Analysis on the UCL Datasets
4.8. Classification Accuracy and Feature Subset Size Analysis on the UCL Datasets
4.9. Runtime Analysis on the UCL Datasets
5. Discussion of Expanded Experiments on the OpenML Datasets
5.1. Fitness Function Value Analysis on the OpenML Datasets
5.2. Classification Accuracy and Feature Subset Size Analysis on the OpenML Datasets
5.3. Runtime Analysis on the OpenML Datasets
6. Conclusions and Future Work
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Categories | Datasets | Number of Features | Number of Categories | Dataset 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 | |
Exactly | 13 | 2 | 1000 | |
Wine | 13 | 3 | 178 | |
Medium | Zoo | 16 | 7 | 101 |
Vote | 16 | 2 | 435 | |
Congress | 16 | 2 | 435 | |
Lymphography | 18 | 4 | 148 | |
Vehicle | 18 | 4 | 846 | |
Ionosphere | 34 | 2 | 351 | |
Landsat | 36 | 6 | 2000 | |
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 | |
Arrhythmia | 279 | 16 | 452 | |
Isolet | 617 | 26 | 1559 |
Algorithms | Year | Parameter Settings |
---|---|---|
Particle Swarm Optimization (PSO) [39] | 1995 | |
Differential Evolution (DE) [40] | 1997 | |
Equilibrium Optimizer (EO) [41] | 2020 | |
Whale Optimization Algorithm (WOA) [42] | 2016 | |
Secretary Bird Optimization Algorithm (SBOA) | 2024 | |
Nutcracker Optimization Algorithm (NOA) [43] | 2023 | |
Electric Eel Foraging Optimization (EEFO) [44] | 2024 | |
Hippopotamus Optimization (HO) [45] | 2024 | |
Human Evolutionary Optimization Algorithm (HEOA) [46] | 2024 | |
LSHADE [47] | 2014 | |
IMODE [48] | 2022 | |
BSFSBOA | NA |
Datasets | Metrics | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Aggregation | Best | 0.100 | 0.106 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.111 | 0.100 |
Mean | 0.100 | 0.106 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.111 | 0.100 | |
Worse | 0.100 | 0.106 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.111 | 0.100 | |
Rank | 1/1/1 | 8/8/8 | 1/1/1 | 1/1/1 | 1/1/1 | 1/1/1 | 1/1/1 | 9/9/9 | 1/1/1 | |
Banana | Best | 0.201 | 0.190 | 0.198 | 0.198 | 0.199 | 0.206 | 0.196 | 0.188 | 0.187 |
Mean | 0.201 | 0.190 | 0.198 | 0.198 | 0.199 | 0.206 | 0.196 | 0.188 | 0.187 | |
Worse | 0.201 | 0.190 | 0.198 | 0.198 | 0.199 | 0.206 | 0.196 | 0.188 | 0.187 | |
Rank | 8/8/8 | 3/3/3 | 6/6/6 | 5/5/5 | 7/7/7 | 9/9/9 | 4/4/4 | 2/2/2 | 1/1/1 | |
Iris | Best | 0.050 | 0.085 | 0.085 | 0.025 | 0.025 | 0.025 | 0.080 | 0.050 | 0.025 |
Mean | 0.051 | 0.089 | 0.085 | 0.029 | 0.025 | 0.025 | 0.080 | 0.050 | 0.025 | |
Worse | 0.080 | 0.130 | 0.085 | 0.080 | 0.025 | 0.025 | 0.080 | 0.050 | 0.025 | |
Rank | 5/6/5 | 8/9/9 | 8/8/8 | 1/4/5 | 1/1/1 | 1/1/1 | 7/7/5 | 5/5/4 | 1/1/1 | |
Bupa | Best | 0.314 | 0.320 | 0.337 | 0.259 | 0.343 | 0.288 | 0.341 | 0.320 | 0.262 |
Mean | 0.316 | 0.326 | 0.342 | 0.274 | 0.346 | 0.299 | 0.341 | 0.323 | 0.264 | |
Worse | 0.344 | 0.341 | 0.399 | 0.350 | 0.393 | 0.337 | 0.341 | 0.354 | 0.272 | |
Rank | 4/4/5 | 5/6/3 | 7/8/9 | 1/2/6 | 9/9/8 | 3/3/2 | 8/7/3 | 5/5/7 | 2/1/1 | |
Glass | Best | 0.312 | 0.270 | 0.279 | 0.334 | 0.280 | 0.301 | 0.227 | 0.237 | 0.216 |
Mean | 0.323 | 0.287 | 0.279 | 0.357 | 0.291 | 0.302 | 0.229 | 0.244 | 0.219 | |
Worse | 0.377 | 0.333 | 0.280 | 0.409 | 0.398 | 0.313 | 0.248 | 0.259 | 0.259 | |
Rank | 8/8/7 | 4/5/6 | 5/4/4 | 9/9/9 | 6/6/8 | 7/7/5 | 2/2/1 | 3/3/2 | 1/1/2 | |
Breastcancer | Best | 0.068 | 0.048 | 0.068 | 0.061 | 0.059 | 0.059 | 0.042 | 0.053 | 0.040 |
Mean | 0.071 | 0.056 | 0.069 | 0.068 | 0.062 | 0.060 | 0.045 | 0.059 | 0.043 | |
Worse | 0.079 | 0.066 | 0.072 | 0.080 | 0.074 | 0.061 | 0.048 | 0.066 | 0.048 | |
Rank | 8/9/8 | 3/3/4 | 8/8/6 | 7/7/9 | 5/6/7 | 5/5/3 | 2/2/1 | 4/4/4 | 1/1/1 | |
Exactly | Best | 0.046 | 0.046 | 0.060 | 0.046 | 0.046 | 0.046 | 0.046 | 0.046 | 0.046 |
Mean | 0.172 | 0.099 | 0.167 | 0.253 | 0.159 | 0.252 | 0.151 | 0.098 | 0.054 | |
Worse | 0.299 | 0.302 | 0.291 | 0.287 | 0.287 | 0.291 | 0.291 | 0.287 | 0.287 | |
Rank | 1/7/8 | 1/3/9 | 9/6/5 | 1/9/1 | 1/5/1 | 1/8/5 | 1/4/5 | 1/2/4 | 1/1/1 | |
Wine | Best | 0.031 | 0.041 | 0.038 | 0.049 | 0.049 | 0.031 | 0.049 | 0.023 | 0.023 |
Mean | 0.047 | 0.064 | 0.045 | 0.089 | 0.058 | 0.032 | 0.052 | 0.028 | 0.024 | |
Worse | 0.134 | 0.098 | 0.049 | 0.203 | 0.082 | 0.046 | 0.075 | 0.054 | 0.031 | |
Rank | 3/5/8 | 6/8/7 | 5/4/3 | 7/9/9 | 7/7/6 | 3/3/2 | 7/6/5 | 1/2/4 | 1/1/1 | |
Mean Rank | Best | 4.750 | 4.750 | 6.125 | 4.000 | 4.625 | 3.750 | 4.000 | 3.750 | 1.125 |
Mean | 6.000 | 5.625 | 5.625 | 5.750 | 5.250 | 4.625 | 4.125 | 4.000 | 1.000 | |
Worse | 6.250 | 6.125 | 5.250 | 5.625 | 4.875 | 3.500 | 3.125 | 4.500 | 1.125 | |
Final Rank | Best | 7 | 7 | 9 | 4 | 6 | 2 | 4 | 2 | 1 |
Mean | 9 | 6 | 6 | 8 | 5 | 4 | 3 | 2 | 1 | |
Worse | 9 | 8 | 6 | 7 | 5 | 3 | 2 | 4 | 1 |
Datasets | Metrics | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Zoo | Best | 0.050 | 0.038 | 0.076 | 0.031 | 0.044 | 0.076 | 0.031 | 0.038 | 0.031 |
Mean | 0.075 | 0.062 | 0.083 | 0.054 | 0.115 | 0.079 | 0.040 | 0.079 | 0.033 | |
Worse | 0.128 | 0.128 | 0.115 | 0.095 | 0.179 | 0.089 | 0.076 | 0.108 | 0.038 | |
Rank | 7/5/7 | 4/4/7 | 8/8/6 | 1/3/4 | 6/9/9 | 8/7/3 | 1/2/2 | 4/6/5 | 1/1/1 | |
Vote | Best | 0.035 | 0.033 | 0.039 | 0.048 | 0.031 | 0.035 | 0.035 | 0.046 | 0.023 |
Mean | 0.044 | 0.044 | 0.044 | 0.049 | 0.041 | 0.038 | 0.037 | 0.048 | 0.023 | |
Worse | 0.071 | 0.054 | 0.048 | 0.070 | 0.052 | 0.046 | 0.037 | 0.054 | 0.023 | |
Rank | 4/7/9 | 3/6/7 | 7/5/4 | 9/9/8 | 2/4/5 | 4/3/3 | 4/2/2 | 8/8/6 | 1/1/1 | |
Congress | Best | 0.039 | 0.050 | 0.048 | 0.048 | 0.027 | 0.060 | 0.039 | 0.035 | 0.017 |
Mean | 0.051 | 0.063 | 0.052 | 0.051 | 0.028 | 0.060 | 0.046 | 0.046 | 0.017 | |
Worse | 0.073 | 0.081 | 0.058 | 0.073 | 0.035 | 0.066 | 0.048 | 0.058 | 0.017 | |
Rank | 4/5/7 | 8/9/9 | 7/7/4 | 6/6/7 | 2/2/2 | 9/8/6 | 4/3/3 | 3/4/5 | 1/1/1 | |
Lymphography | Best | 0.059 | 0.070 | 0.075 | 0.079 | 0.084 | 0.053 | 0.084 | 0.081 | 0.042 |
Mean | 0.081 | 0.107 | 0.090 | 0.095 | 0.110 | 0.076 | 0.092 | 0.127 | 0.046 | |
Worse | 0.138 | 0.149 | 0.126 | 0.132 | 0.146 | 0.126 | 0.132 | 0.143 | 0.053 | |
Rank | 3/3/6 | 4/7/9 | 5/4/2 | 6/6/4 | 8/8/8 | 2/2/2 | 8/5/4 | 7/9/7 | 1/1/1 | |
Vehicle | Best | 0.241 | 0.242 | 0.236 | 0.284 | 0.263 | 0.209 | 0.247 | 0.241 | 0.225 |
Mean | 0.271 | 0.267 | 0.252 | 0.315 | 0.283 | 0.250 | 0.264 | 0.273 | 0.233 | |
Worse | 0.311 | 0.322 | 0.262 | 0.364 | 0.311 | 0.273 | 0.289 | 0.300 | 0.247 | |
Rank | 4/6/7 | 6/5/8 | 3/3/2 | 9/9/9 | 8/8/6 | 1/2/3 | 7/4/4 | 4/7/5 | 2/1/1 | |
Ionosphere | Best | 0.062 | 0.072 | 0.035 | 0.015 | 0.037 | 0.037 | 0.028 | 0.022 | 0.022 |
Mean | 0.092 | 0.121 | 0.054 | 0.055 | 0.055 | 0.053 | 0.061 | 0.051 | 0.039 | |
Worse | 0.134 | 0.150 | 0.076 | 0.083 | 0.078 | 0.069 | 0.088 | 0.073 | 0.063 | |
Rank | 8/8/8 | 9/9/9 | 5/4/4 | 1/5/6 | 6/6/5 | 6/3/2 | 4/7/7 | 2/2/3 | 2/1/1 | |
landsat | Best | 0.117 | 0.112 | 0.096 | 0.105 | 0.095 | 0.099 | 0.109 | 0.094 | 0.087 |
Mean | 0.126 | 0.122 | 0.110 | 0.121 | 0.111 | 0.108 | 0.117 | 0.104 | 0.098 | |
Worse | 0.132 | 0.137 | 0.120 | 0.133 | 0.120 | 0.116 | 0.127 | 0.119 | 0.105 | |
Rank | 9/9/7 | 8/8/9 | 4/4/4 | 6/7/8 | 3/5/4 | 5/3/2 | 7/6/6 | 2/2/3 | 1/1/1 | |
SonarEW | Best | 0.049 | 0.064 | 0.040 | 0.067 | 0.015 | 0.012 | 0.020 | 0.071 | 0.008 |
Mean | 0.084 | 0.126 | 0.072 | 0.129 | 0.051 | 0.041 | 0.059 | 0.101 | 0.018 | |
Worse | 0.124 | 0.160 | 0.106 | 0.187 | 0.083 | 0.084 | 0.089 | 0.131 | 0.027 | |
Rank | 6/6/6 | 7/8/8 | 5/5/5 | 8/9/9 | 3/3/2 | 2/2/3 | 4/4/4 | 9/7/7 | 1/1/1 | |
Mean Rank | Best | 5.625 | 6.125 | 5.500 | 5.750 | 4.750 | 4.625 | 4.875 | 4.875 | 1.250 |
Mean | 6.125 | 7.000 | 5.000 | 6.750 | 5.625 | 3.750 | 4.125 | 5.625 | 1.000 | |
Worse | 7.125 | 8.250 | 3.875 | 6.875 | 5.125 | 3.000 | 4.000 | 5.125 | 1.000 | |
Final Rank | Best | 7 | 9 | 6 | 8 | 3 | 2 | 4 | 4 | 1 |
Mean | 7 | 9 | 4 | 8 | 5 | 2 | 3 | 5 | 1 | |
Worse | 8 | 9 | 3 | 7 | 5 | 2 | 4 | 5 | 1 |
Datasets | Metrics | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Libras | Best | 0.123 | 0.202 | 0.166 | 0.188 | 0.148 | 0.140 | 0.149 | 0.145 | 0.088 |
Mean | 0.143 | 0.230 | 0.196 | 0.243 | 0.190 | 0.162 | 0.179 | 0.170 | 0.126 | |
Worse | 0.169 | 0.258 | 0.222 | 0.286 | 0.235 | 0.181 | 0.215 | 0.205 | 0.151 | |
Rank | 2/2/2 | 9/8/8 | 7/7/6 | 8/9/9 | 5/6/7 | 3/3/3 | 6/5/5 | 4/4/4 | 1/1/1 | |
Hillvalley | Best | 0.340 | 0.352 | 0.345 | 0.316 | 0.308 | 0.303 | 0.296 | 0.268 | 0.250 |
Mean | 0.379 | 0.376 | 0.370 | 0.345 | 0.334 | 0.327 | 0.327 | 0.307 | 0.280 | |
Worse | 0.409 | 0.398 | 0.397 | 0.381 | 0.405 | 0.344 | 0.360 | 0.344 | 0.310 | |
Rank | 7/9/9 | 9/8/7 | 8/7/6 | 6/6/5 | 5/5/8 | 4/3/3 | 3/4/4 | 2/2/2 | 1/1/1 | |
Musk | Best | 0.071 | 0.069 | 0.023 | 0.066 | 0.055 | 0.059 | 0.064 | 0.051 | 0.026 |
Mean | 0.107 | 0.084 | 0.052 | 0.105 | 0.076 | 0.082 | 0.087 | 0.090 | 0.049 | |
Worse | 0.140 | 0.097 | 0.085 | 0.165 | 0.095 | 0.104 | 0.111 | 0.123 | 0.081 | |
Rank | 9/9/8 | 8/5/4 | 1/2/2 | 7/8/9 | 4/3/3 | 5/4/5 | 6/6/6 | 3/7/7 | 2/1/1 | |
Clean | Best | 0.070 | 0.060 | 0.036 | 0.069 | 0.043 | 0.069 | 0.029 | 0.047 | 0.024 |
Mean | 0.096 | 0.076 | 0.061 | 0.105 | 0.074 | 0.108 | 0.048 | 0.065 | 0.035 | |
Worse | 0.135 | 0.094 | 0.079 | 0.139 | 0.092 | 0.138 | 0.078 | 0.084 | 0.059 | |
Rank | 9/7/7 | 6/6/6 | 3/3/3 | 7/8/9 | 4/5/5 | 8/9/8 | 2/2/2 | 5/4/4 | 1/1/1 | |
Semeion | Best | 0.094 | 0.126 | 0.098 | 0.111 | 0.089 | 0.077 | 0.085 | 0.092 | 0.072 |
Mean | 0.113 | 0.139 | 0.111 | 0.131 | 0.098 | 0.095 | 0.102 | 0.109 | 0.089 | |
Worse | 0.129 | 0.147 | 0.120 | 0.151 | 0.110 | 0.107 | 0.117 | 0.122 | 0.104 | |
Rank | 6/7/7 | 9/9/8 | 7/6/5 | 8/8/9 | 4/3/3 | 2/2/2 | 3/4/4 | 5/5/6 | 1/1/1 | |
Arrhythmia | Best | 0.287 | 0.329 | 0.265 | 0.254 | 0.268 | 0.249 | 0.268 | 0.274 | 0.234 |
Mean | 0.322 | 0.349 | 0.291 | 0.300 | 0.298 | 0.291 | 0.302 | 0.301 | 0.269 | |
Worse | 0.350 | 0.369 | 0.322 | 0.336 | 0.325 | 0.321 | 0.324 | 0.327 | 0.296 | |
Rank | 8/8/8 | 9/9/9 | 4/2/3 | 3/5/7 | 5/4/5 | 2/3/2 | 6/7/4 | 7/6/6 | 1/1/1 | |
Isolet | Best | 0.126 | 0.176 | 0.133 | 0.148 | 0.132 | 0.115 | 0.100 | 0.151 | 0.066 |
Mean | 0.154 | 0.192 | 0.154 | 0.179 | 0.148 | 0.136 | 0.124 | 0.173 | 0.081 | |
Worse | 0.175 | 0.204 | 0.173 | 0.216 | 0.172 | 0.156 | 0.156 | 0.191 | 0.097 | |
Rank | 4/5/6 | 9/9/8 | 6/6/5 | 7/8/9 | 5/4/4 | 3/3/2 | 2/2/3 | 8/7/7 | 1/1/1 | |
Mean Rank | Best | 6.429 | 8.429 | 5.143 | 6.571 | 4.571 | 3.857 | 4.000 | 4.857 | 1.143 |
Mean | 6.714 | 7.714 | 4.714 | 7.429 | 4.286 | 3.857 | 4.286 | 5.000 | 1.000 | |
Worse | 6.714 | 7.143 | 4.286 | 8.143 | 5.000 | 3.571 | 4.000 | 5.143 | 1.000 | |
Final Rank | Best | 7 | 9 | 6 | 8 | 4 | 2 | 3 | 5 | 1 |
Mean | 7 | 9 | 5 | 8 | 3 | 2 | 3 | 6 | 1 | |
Worse | 7 | 8 | 4 | 9 | 5 | 2 | 3 | 6 | 1 |
Categories | Datasets | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Low | Aggregation | 4.30 | 7.60 | 4.18 | 4.07 | 4.15 | 3.98 | 4.12 | 8.80 | 3.80 |
Banana | 8.00 | 3.00 | 6.00 | 5.00 | 7.00 | 9.00 | 4.00 | 2.00 | 1.00 | |
Iris | 5.47 | 8.58 | 8.42 | 2.83 | 2.50 | 2.45 | 6.95 | 5.42 | 2.38 | |
Bupa | 4.00 | 5.72 | 6.88 | 1.93 | 8.80 | 3.52 | 7.70 | 5.05 | 1.40 | |
Glass | 7.90 | 5.45 | 4.38 | 8.85 | 5.65 | 6.77 | 1.98 | 2.88 | 1.13 | |
Breastcancer | 8.25 | 3.87 | 7.95 | 7.35 | 5.25 | 4.90 | 1.88 | 4.33 | 1.22 | |
Exactly | 5.23 | 4.02 | 6.27 | 6.62 | 4.63 | 7.45 | 4.32 | 4.22 | 2.25 | |
Wine | 5.07 | 7.43 | 4.87 | 8.13 | 6.97 | 2.95 | 6.05 | 2.05 | 1.48 | |
Medium | Zoo | 5.75 | 4.50 | 6.87 | 3.67 | 8.25 | 6.23 | 2.30 | 6.20 | 1.23 |
Vote | 5.87 | 6.05 | 5.97 | 7.58 | 4.38 | 3.23 | 3.60 | 7.32 | 1.00 | |
Congress | 5.35 | 8.42 | 6.43 | 5.42 | 2.00 | 8.08 | 4.07 | 4.23 | 1.00 | |
Lymphography | 3.65 | 6.73 | 4.73 | 5.30 | 7.02 | 3.52 | 4.67 | 8.35 | 1.03 | |
Vehicle | 5.83 | 5.08 | 3.13 | 8.77 | 7.10 | 3.42 | 4.65 | 5.88 | 1.13 | |
Ionosphere | 7.95 | 8.83 | 4.12 | 4.38 | 4.43 | 4.13 | 5.30 | 3.85 | 2.00 | |
landsat | 8.43 | 7.25 | 3.90 | 7.12 | 4.35 | 3.65 | 6.45 | 2.60 | 1.25 | |
SonarEW | 5.77 | 8.10 | 5.07 | 8.12 | 3.38 | 2.65 | 3.90 | 6.80 | 1.22 | |
High | Libras | 2.10 | 8.23 | 6.18 | 8.53 | 5.98 | 3.75 | 4.93 | 4.15 | 1.13 |
Hillvalley | 8.13 | 8.03 | 7.30 | 5.60 | 4.35 | 4.00 | 3.93 | 2.52 | 1.13 | |
Musk | 7.93 | 5.07 | 1.97 | 7.50 | 4.08 | 4.87 | 5.65 | 6.43 | 1.50 | |
Clean | 7.13 | 5.50 | 3.50 | 8.00 | 5.03 | 8.30 | 2.17 | 4.10 | 1.27 | |
Semeion | 6.07 | 8.77 | 5.60 | 8.03 | 3.03 | 2.37 | 3.83 | 5.53 | 1.77 | |
Arrhythmia | 7.10 | 8.90 | 3.55 | 5.10 | 4.68 | 3.70 | 5.13 | 5.10 | 1.73 | |
Isolet | 5.03 | 8.80 | 5.27 | 7.60 | 4.43 | 3.37 | 2.40 | 7.10 | 1.00 | |
Mean Rank | 6.10 | 6.69 | 5.33 | 6.33 | 5.11 | 4.62 | 4.35 | 5.00 | 1.48 | |
Final Rank | 7 | 9 | 6 | 8 | 5 | 3 | 2 | 4 | 1 |
Categories | Datasets | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Low | Aggregation | 100.00 | 99.36 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 98.73 | 100.00 |
1 | 8 | 1 | 1 | 1 | 1 | 1 | 9 | 1 | ||
Banana | 88.77 | 90.00 | 89.06 | 89.15 | 88.96 | 88.21 | 89.34 | 90.19 | 90.38 | |
8 | 3 | 6 | 5 | 7 | 9 | 4 | 2 | 1 | ||
Iris | 99.89 | 93.89 | 93.33 | 99.78 | 100.00 | 100.00 | 96.67 | 100.0 | 100.00 | |
5 | 8 | 9 | 6 | 1 | 1 | 7 | 1 | 1 | ||
Bupa | 72.32 | 68.74 | 67.49 | 74.93 | 63.86 | 73.00 | 69.57 | 67.97 | 75.94 | |
4 | 6 | 8 | 2 | 9 | 3 | 5 | 7 | 1 | ||
Glass | 67.94 | 73.33 | 71.67 | 65.48 | 72.30 | 67.78 | 80.48 | 77.46 | 80.79 | |
7 | 4 | 6 | 9 | 5 | 8 | 2 | 3 | 1 | ||
Breastcancer | 95.08 | 96.74 | 95.25 | 95.54 | 96.52 | 95.83 | 97.58 | 97.15 | 98.80 | |
9 | 4 | 8 | 7 | 5 | 6 | 2 | 3 | 1 | ||
Exactly | 84.78 | 94.60 | 85.23 | 74.90 | 85.98 | 74.67 | 87.23 | 91.35 | 95.35 | |
7 | 2 | 6 | 8 | 5 | 9 | 4 | 3 | 1 | ||
Wine | 98.29 | 96.86 | 98.38 | 93.33 | 96.57 | 97.81 | 96.95 | 99.90 | 100.00 | |
4 | 7 | 3 | 9 | 8 | 5 | 6 | 2 | 1 | ||
Medium | Zoo | 95.17 | 98.33 | 94.67 | 99.17 | 91.67 | 94.50 | 99.83 | 96.67 | 100.00 |
6 | 4 | 7 | 3 | 9 | 8 | 2 | 5 | 1 | ||
Vote | 97.16 | 98.24 | 96.55 | 95.29 | 97.55 | 97.05 | 96.63 | 95.63 | 98.85 | |
4 | 2 | 7 | 9 | 3 | 5 | 6 | 8 | 1 | ||
Congress | 96.55 | 95.94 | 96.48 | 95.33 | 97.74 | 94.75 | 95.98 | 96.05 | 98.85 | |
3 | 7 | 4 | 8 | 2 | 9 | 6 | 5 | 1 | ||
Lymphography | 94.94 | 92.76 | 94.14 | 91.49 | 91.15 | 94.71 | 92.99 | 88.28 | 96.32 | |
2 | 6 | 4 | 7 | 8 | 3 | 5 | 9 | 1 | ||
Vehicle | 74.16 | 75.96 | 75.76 | 68.48 | 72.43 | 75.56 | 74.44 | 73.71 | 75.74 | |
6 | 1 | 2 | 9 | 8 | 4 | 5 | 7 | 3 | ||
Ionosphere | 93.00 | 90.90 | 95.52 | 95.62 | 95.00 | 94.71 | 95.19 | 95.57 | 97.14 | |
8 | 9 | 4 | 2 | 6 | 7 | 5 | 3 | 1 | ||
landsat | 89.67 | 90.83 | 90.41 | 89.68 | 90.39 | 90.29 | 90.08 | 91.27 | 91.73 | |
9 | 3 | 4 | 8 | 5 | 6 | 7 | 2 | 1 | ||
SonarEW | 94.63 | 91.87 | 94.23 | 88.70 | 96.18 | 96.99 | 96.18 | 91.54 | 100.00 | |
5 | 7 | 6 | 9 | 4 | 2 | 3 | 8 | 1 | ||
High | Libras | 88.33 | 80.69 | 80.19 | 74.44 | 80.93 | 83.84 | 83.47 | 82.92 | 88.52 |
2 | 7 | 8 | 9 | 6 | 3 | 4 | 5 | 1 | ||
Hillvalley | 62.48 | 64.27 | 59.72 | 62.48 | 63.28 | 64.74 | 66.12 | 66.89 | 70.61 | |
7 | 5 | 9 | 7 | 6 | 4 | 3 | 2 | 1 | ||
Musk | 92.91 | 97.54 | 96.46 | 90.42 | 95.37 | 93.72 | 93.89 | 91.93 | 96.88 | |
7 | 1 | 3 | 9 | 4 | 6 | 5 | 8 | 2 | ||
Clean | 94.32 | 98.21 | 95.26 | 91.75 | 95.26 | 89.65 | 98.21 | 94.91 | 98.63 | |
7 | 2 | 5 | 8 | 4 | 9 | 2 | 6 | 1 | ||
Semeion | 92.66 | 91.93 | 92.78 | 90.42 | 93.98 | 93.08 | 93.95 | 92.78 | 94.08 | |
7 | 8 | 5 | 9 | 2 | 4 | 3 | 5 | 1 | ||
Arrhythmia | 69.11 | 68.04 | 69.04 | 69.44 | 69.22 | 68.37 | 70.11 | 67.85 | 71.30 | |
5 | 8 | 6 | 3 | 4 | 7 | 2 | 9 | 1 | ||
Isolet | 88.24 | 85.74 | 85.41 | 83.07 | 86.62 | 87.43 | 90.03 | 83.28 | 93.29 | |
3 | 6 | 7 | 9 | 5 | 4 | 2 | 8 | 1 | ||
Mean Rank | 5.48 | 5.13 | 5.57 | 6.78 | 5.09 | 5.35 | 3.96 | 5.22 | 1.13 | |
Final Rank | 7 | 4 | 8 | 9 | 3 | 6 | 2 | 5 | 1 |
Categories | Datasets | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Low | Aggregation | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||
Banana | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | 2.00 | |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||
Iris | 2.00 | 1.37 | 1.00 | 1.07 | 1.00 | 1.17 | 2.00 | 2.00 | 1.00 | |
7 | 6 | 1 | 4 | 1 | 5 | 7 | 7 | 1 | ||
Bupa | 4.03 | 2.70 | 2.97 | 2.90 | 1.23 | 3.33 | 4.00 | 2.07 | 3.90 | |
9 | 3 | 5 | 4 | 1 | 6 | 8 | 2 | 7 | ||
Glass | 3.13 | 4.23 | 2.20 | 4.17 | 3.77 | 3.33 | 4.80 | 3.67 | 4.17 | |
2 | 8 | 1 | 6 | 5 | 3 | 9 | 4 | 6 | ||
Breastcancer | 2.43 | 2.43 | 2.40 | 2.50 | 2.77 | 2.57 | 2.10 | 3.00 | 2.87 | |
3 | 3 | 2 | 5 | 7 | 6 | 1 | 9 | 8 | ||
Exactly | 4.53 | 6.57 | 4.43 | 3.47 | 4.30 | 3.17 | 4.67 | 7.27 | 6.73 | |
5 | 7 | 4 | 2 | 3 | 1 | 6 | 9 | 8 | ||
Wine | 4.13 | 4.60 | 3.93 | 3.77 | 3.57 | 4.53 | 3.17 | 3.53 | 3.17 | |
7 | 9 | 6 | 5 | 4 | 8 | 1 | 3 | 1 | ||
Medium | Zoo | 5.10 | 7.53 | 5.63 | 7.37 | 6.43 | 7.53 | 6.13 | 7.77 | 5.33 |
1 | 7 | 3 | 6 | 5 | 7 | 4 | 9 | 2 | ||
Vote | 3.03 | 4.43 | 2.00 | 1.13 | 2.97 | 3.90 | 1.10 | 1.33 | 2.00 | |
7 | 9 | 4 | 2 | 6 | 8 | 1 | 3 | 4 | ||
Congress | 3.20 | 4.17 | 3.23 | 1.47 | 1.17 | 3.10 | 1.53 | 1.70 | 1.00 | |
7 | 9 | 8 | 3 | 2 | 6 | 4 | 5 | 1 | ||
Lymphography | 6.30 | 7.60 | 6.67 | 3.23 | 5.53 | 5.07 | 5.17 | 3.90 | 4.63 | |
7 | 9 | 8 | 1 | 6 | 4 | 5 | 2 | 3 | ||
Vehicle | 6.97 | 9.13 | 6.03 | 5.60 | 6.30 | 5.40 | 6.10 | 6.57 | 5.77 | |
8 | 9 | 4 | 2 | 6 | 1 | 5 | 7 | 3 | ||
Ionosphere | 9.83 | 13.43 | 4.60 | 5.13 | 3.33 | 5.00 | 6.00 | 3.73 | 4.43 | |
8 | 9 | 4 | 6 | 1 | 5 | 7 | 2 | 3 | ||
landsat | 11.70 | 14.27 | 8.60 | 10.23 | 8.97 | 10.17 | 10.03 | 9.13 | 8.57 | |
8 | 9 | 2 | 7 | 3 | 6 | 5 | 4 | 1 | ||
SonarEW | 21.43 | 31.73 | 12.27 | 16.57 | 9.83 | 16.23 | 14.60 | 14.90 | 10.53 | |
8 | 9 | 3 | 7 | 1 | 6 | 4 | 5 | 2 | ||
High | Libras | 35.70 | 50.20 | 16.13 | 11.67 | 16.33 | 27.73 | 27.60 | 15.03 | 18.90 |
8 | 9 | 3 | 1 | 4 | 7 | 6 | 2 | 5 | ||
Hillvalley | 41.20 | 54.23 | 7.37 | 7.70 | 3.40 | 25.40 | 22.33 | 8.63 | 15.40 | |
8 | 9 | 2 | 3 | 1 | 7 | 6 | 4 | 5 | ||
Musk | 70.97 | 103.50 | 33.70 | 31.53 | 57.37 | 63.17 | 53.97 | 29.63 | 34.53 | |
8 | 9 | 3 | 2 | 6 | 7 | 5 | 1 | 4 | ||
Clean | 74.37 | 100.80 | 31.23 | 51.80 | 52.37 | 58.07 | 60.10 | 32.50 | 32.30 | |
8 | 9 | 1 | 4 | 5 | 6 | 7 | 3 | 2 | ||
Semeion | 121.03 | 168.90 | 116.67 | 114.93 | 112.77 | 108.83 | 121.47 | 113.63 | 91.20 | |
7 | 9 | 6 | 5 | 3 | 2 | 8 | 4 | 1 | ||
Arrhythmia | 121.90 | 171.00 | 34.33 | 68.60 | 58.13 | 64.97 | 91.20 | 32.93 | 29.47 | |
8 | 9 | 3 | 6 | 4 | 5 | 7 | 2 | 1 | ||
Isolet | 294.87 | 392.77 | 138.10 | 163.63 | 172.63 | 197.47 | 213.40 | 138.17 | 126.93 | |
8 | 9 | 2 | 4 | 5 | 6 | 7 | 3 | 1 | ||
Mean Rank | 6.26 | 7.43 | 3.35 | 3.78 | 3.52 | 4.96 | 5.00 | 4.00 | 3.09 | |
Final Rank | 8 | 9 | 2 | 4 | 3 | 6 | 7 | 5 | 1 |
Categories | Datasets | PSO | DE | EO | WOA | SBOA | NOA | EEFO | HO | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|---|
Low | Aggregation | 7.51 | 4.94 | 3.42 | 4.50 | 4.05 | 5.39 | 3.72 | 11.22 | 3.46 |
8 | 6 | 1 | 5 | 4 | 7 | 3 | 9 | 2 | ||
Banana | 5.89 | 12.38 | 9.19 | 11.74 | 12.2 | 18.88 | 10.94 | 30.71 | 23.06 | |
1 | 6 | 2 | 4 | 5 | 7 | 3 | 9 | 8 | ||
Iris | 8.11 | 4.24 | 4.26 | 4.02 | 2.98 | 4.73 | 3.21 | 10.23 | 3.32 | |
8 | 5 | 6 | 4 | 1 | 7 | 2 | 9 | 3 | ||
Bupa | 8.23 | 3.93 | 4.65 | 4.46 | 3.10 | 5.03 | 4.38 | 11.73 | 3.38 | |
8 | 3 | 6 | 5 | 1 | 7 | 4 | 9 | 2 | ||
Glass | 7.99 | 4.18 | 4.57 | 4.03 | 3.80 | 4.94 | 4.16 | 10.77 | 3.30 | |
8 | 5 | 6 | 3 | 2 | 7 | 4 | 9 | 1 | ||
Breastcancer | 9.16 | 4.41 | 4.63 | 4.33 | 3.97 | 5.36 | 3.85 | 12.02 | 3.56 | |
8 | 5 | 6 | 4 | 3 | 7 | 2 | 9 | 1 | ||
Exactly | 9.31 | 4.91 | 5.91 | 4.43 | 3.83 | 5.90 | 4.22 | 13.33 | 3.88 | |
8 | 5 | 7 | 4 | 1 | 6 | 3 | 9 | 2 | ||
Wine | 7.99 | 4.32 | 4.78 | 4.69 | 3.60 | 4.99 | 3.52 | 11.12 | 3.36 | |
8 | 4 | 6 | 5 | 3 | 7 | 2 | 9 | 1 | ||
Medium | Zoo | 7.77 | 4.12 | 4.43 | 4.30 | 3.76 | 4.91 | 3.40 | 11.17 | 3.30 |
8 | 4 | 6 | 5 | 3 | 7 | 2 | 9 | 1 | ||
Vote | 7.85 | 4.55 | 4.44 | 4.12 | 3.55 | 5.10 | 3.68 | 9.90 | 3.32 | |
8 | 6 | 5 | 4 | 2 | 7 | 3 | 9 | 1 | ||
Congress | 8.32 | 4.26 | 4.80 | 4.16 | 3.23 | 6.05 | 3.75 | 9.93 | 3.34 | |
8 | 5 | 6 | 4 | 1 | 7 | 3 | 9 | 2 | ||
Lymphography | 8.56 | 4.34 | 4.39 | 4.00 | 4.07 | 5.94 | 4.02 | 9.59 | 3.36 | |
8 | 5 | 6 | 2 | 4 | 7 | 3 | 9 | 1 | ||
Vehicle | 11.28 | 5.17 | 6.77 | 5.41 | 4.41 | 5.92 | 6.19 | 12.61 | 3.53 | |
8 | 3 | 7 | 4 | 2 | 5 | 6 | 9 | 1 | ||
Ionosphere | 8.41 | 4.25 | 4.53 | 3.89 | 3.48 | 5.06 | 4.72 | 10.05 | 3.37 | |
8 | 4 | 5 | 3 | 2 | 7 | 6 | 9 | 1 | ||
landsat | 15.02 | 6.18 | 7.74 | 5.36 | 5.46 | 7.62 | 7.05 | 16.49 | 4.14 | |
8 | 4 | 7 | 2 | 3 | 6 | 5 | 9 | 1 | ||
SonarEW | 8.59 | 3.71 | 4.51 | 3.3 | 3.56 | 4.54 | 4.31 | 10.24 | 3.09 | |
8 | 4 | 6 | 2 | 3 | 7 | 5 | 9 | 1 | ||
High | Libras | 11.98 | 4.37 | 4.56 | 3.36 | 3.73 | 4.85 | 6.47 | 10.28 | 3.15 |
9 | 4 | 5 | 2 | 3 | 6 | 7 | 8 | 1 | ||
Hillvalley | 8.97 | 5.57 | 5.30 | 3.61 | 3.42 | 5.41 | 5.37 | 11.81 | 3.57 | |
8 | 7 | 4 | 3 | 1 | 6 | 5 | 9 | 2 | ||
Musk | 8.49 | 6.02 | 5.13 | 3.65 | 4.28 | 6.05 | 4.70 | 14.48 | 3.59 | |
8 | 6 | 5 | 2 | 3 | 7 | 4 | 9 | 1 | ||
Clean | 8.51 | 5.93 | 5.81 | 3.88 | 4.13 | 5.95 | 4.74 | 14.63 | 3.60 | |
8 | 6 | 5 | 2 | 3 | 7 | 4 | 9 | 1 | ||
Semeion | 24.19 | 16.08 | 12.98 | 13.68 | 13.39 | 19.85 | 13.63 | 38.71 | 8.44 | |
8 | 6 | 2 | 5 | 3 | 7 | 4 | 9 | 1 | ||
Arrhythmia | 8.56 | 6.78 | 4.98 | 4.30 | 4.97 | 6.53 | 6.11 | 13.50 | 4.05 | |
8 | 7 | 4 | 2 | 3 | 6 | 5 | 9 | 1 | ||
Isolet | 30.65 | 26.41 | 15.27 | 16.97 | 20.85 | 28.96 | 19.29 | 57.06 | 16.12 | |
8 | 6 | 1 | 3 | 5 | 7 | 4 | 9 | 2 | ||
Mean Rank | 7.74 | 5.04 | 4.96 | 3.43 | 2.65 | 6.70 | 3.87 | 8.96 | 1.65 | |
Final Rank | 8 | 6 | 5 | 3 | 2 | 7 | 4 | 9 | 1 |
Datasets | Number of Features | Number of Categories | Dataset Size |
---|---|---|---|
Titanic | 3 | 2 | 2201 |
Balance-scale | 4 | 3 | 625 |
Diabetes | 8 | 2 | 768 |
Breast-w | 9 | 2 | 699 |
HeartEW | 13 | 2 | 270 |
KC1 | 21 | 2 | 2109 |
PC1 | 21 | 2 | 1109 |
Parkinsons | 22 | 2 | 195 |
BreastEW | 30 | 2 | 569 |
PC2 | 36 | 2 | 5589 |
PC4 | 37 | 2 | 1458 |
Piechart3 | 37 | 2 | 1077 |
Pizzacutter3 | 37 | 2 | 1043 |
Datasets | Metrics | DE | EO | WOA | SBOA | HEOA | LSHADE | IMODE | BSFSBOA |
---|---|---|---|---|---|---|---|---|---|
Titanic | Best | 0.269 | 0.256 | 0.232 | 0.228 | 0.246 | 0.254 | 0.234 | 0.224 |
Mean | 0.294 | 0.256 | 0.232 | 0.228 | 0.246 | 0.254 | 0.234 | 0.224 | |
Worse | 0.455 | 0.256 | 0.232 | 0.228 | 0.246 | 0.254 | 0.234 | 0.224 | |
Rank | 8/8/8 | 7/7/7 | 3/3/3 | 2/2/2 | 5/5/5 | 6/6/6 | 4/4/4 | 1/1/1 | |
Balance-Scale | Best | 0.222 | 0.237 | 0.237 | 0.222 | 0.215 | 0.215 | 0.280 | 0.208 |
Mean | 0.222 | 0.237 | 0.237 | 0.222 | 0.215 | 0.215 | 0.280 | 0.208 | |
Worse | 0.222 | 0.237 | 0.237 | 0.222 | 0.215 | 0.215 | 0.280 | 0.208 | |
Rank | 4/4/4 | 6/6/6 | 6/6/6 | 4/4/4 | 2/2/2 | 2/2/2 | 8/8/8 | 1/1/1 | |
Diabetes | Best | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.072 |
Mean | 0.078 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.074 | |
Worse | 0.090 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | 0.077 | |
Rank | 2/8/8 | 2/2/1 | 2/2/1 | 2/2/1 | 2/2/1 | 2/2/1 | 2/2/1 | 1/1/1 | |
Breast-w | Best | 0.068 | 0.046 | 0.042 | 0.066 | 0.048 | 0.066 | 0.059 | 0.040 |
Mean | 0.069 | 0.054 | 0.056 | 0.067 | 0.048 | 0.067 | 0.061 | 0.045 | |
Worse | 0.079 | 0.061 | 0.077 | 0.072 | 0.057 | 0.072 | 0.066 | 0.053 | |
Rank | 8/8/8 | 3/3/3 | 2/4/7 | 6/7/5 | 4/2/2 | 6/6/5 | 5/5/4 | 1/1/1 | |
HeartEW | Best | 0.172 | 0.121 | 0.129 | 0.140 | 0.138 | 0.147 | 0.181 | 0.090 |
Mean | 0.201 | 0.129 | 0.148 | 0.152 | 0.148 | 0.161 | 0.192 | 0.109 | |
Worse | 0.263 | 0.173 | 0.197 | 0.190 | 0.258 | 0.196 | 0.223 | 0.172 | |
Rank | 7/8/8 | 2/2/2 | 3/4/5 | 5/5/3 | 4/3/7 | 6/6/4 | 8/7/6 | 1/1/1 | |
KC1 | Best | 0.163 | 0.155 | 0.164 | 0.166 | 0.136 | 0.180 | 0.167 | 0.135 |
Mean | 0.177 | 0.159 | 0.175 | 0.171 | 0.144 | 0.191 | 0.177 | 0.142 | |
Worse | 0.188 | 0.162 | 0.192 | 0.177 | 0.155 | 0.208 | 0.188 | 0.151 | |
Rank | 4/6/5 | 3/3/3 | 5/5/7 | 6/4/4 | 2/2/2 | 8/8/8 | 7/7/6 | 1/1/1 | |
PC1 | Best | 0.058 | 0.051 | 0.063 | 0.063 | 0.067 | 0.058 | 0.046 | 0.050 |
Mean | 0.068 | 0.053 | 0.073 | 0.068 | 0.069 | 0.060 | 0.057 | 0.052 | |
Worse | 0.076 | 0.054 | 0.083 | 0.071 | 0.070 | 0.062 | 0.066 | 0.054 | |
Rank | 5/5/7 | 3/2/2 | 6/8/8 | 6/6/6 | 8/7/5 | 4/4/3 | 1/3/4 | 2/1/1 | |
Parkinsons | Best | 0.069 | 0.051 | 0.078 | 0.055 | 0.069 | 0.046 | 0.041 | 0.032 |
Mean | 0.092 | 0.057 | 0.100 | 0.055 | 0.115 | 0.079 | 0.083 | 0.034 | |
Worse | 0.106 | 0.083 | 0.143 | 0.055 | 0.152 | 0.097 | 0.101 | 0.051 | |
Rank | 6/6/6 | 4/3/3 | 8/7/7 | 5/2/2 | 6/8/8 | 3/4/4 | 2/5/5 | 1/1/1 | |
BreastEW | Best | 0.061 | 0.035 | 0.029 | 0.020 | 0.020 | 0.039 | 0.013 | 0.010 |
Mean | 0.073 | 0.044 | 0.053 | 0.035 | 0.029 | 0.051 | 0.029 | 0.021 | |
Worse | 0.084 | 0.056 | 0.076 | 0.052 | 0.039 | 0.064 | 0.043 | 0.035 | |
Rank | 8/8/8 | 6/5/5 | 5/7/7 | 3/4/4 | 3/3/2 | 7/6/6 | 2/2/3 | 1/1/1 | |
PC2 | Best | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 |
Mean | 0.019 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | |
Worse | 0.031 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | |
Rank | 1/8/8 | 1/1/1 | 1/1/1 | 1/1/1 | 1/1/1 | 1/1/1 | 1/1/1 | 1/1/1 | |
PC4 | Best | 0.098 | 0.097 | 0.085 | 0.082 | 0.084 | 0.082 | 0.073 | 0.072 |
Mean | 0.120 | 0.107 | 0.108 | 0.091 | 0.097 | 0.094 | 0.092 | 0.089 | |
Worse | 0.145 | 0.113 | 0.123 | 0.111 | 0.111 | 0.111 | 0.111 | 0.108 | |
Rank | 8/8/8 | 7/6/6 | 6/7/7 | 3/2/3 | 5/5/3 | 3/4/3 | 2/3/2 | 1/1/1 | |
Piechart3 | Best | 0.122 | 0.103 | 0.100 | 0.095 | 0.095 | 0.090 | 0.092 | 0.093 |
Mean | 0.137 | 0.110 | 0.114 | 0.107 | 0.106 | 0.105 | 0.104 | 0.104 | |
Worse | 0.155 | 0.114 | 0.120 | 0.118 | 0.114 | 0.114 | 0.112 | 0.110 | |
Rank | 8/8/8 | 7/6/4 | 6/7/7 | 4/5/6 | 4/4/3 | 1/3/4 | 2/2/2 | 3/1/1 | |
Pizzacutter3 | Best | 0.108 | 0.086 | 0.086 | 0.095 | 0.084 | 0.095 | 0.092 | 0.086 |
Mean | 0.124 | 0.099 | 0.103 | 0.103 | 0.099 | 0.103 | 0.107 | 0.091 | |
Worse | 0.136 | 0.108 | 0.124 | 0.111 | 0.107 | 0.110 | 0.114 | 0.108 | |
Rank | 8/8/8 | 2/2/2 | 2/6/7 | 6/4/5 | 1/3/1 | 6/5/4 | 5/7/6 | 2/1/2 | |
MeanRank | Best | 5.92 | 4.08 | 4.23 | 4.08 | 3.62 | 4.23 | 3.77 | 1.31 |
Mean | 7.15 | 3.69 | 5.15 | 3.69 | 3.62 | 4.38 | 4.31 | 1.00 | |
Worse | 7.23 | 3.46 | 5.62 | 3.54 | 3.23 | 3.92 | 4.00 | 1.08 | |
FinalRank | Best | 8 | 4 | 6 | 4 | 2 | 6 | 3 | 1 |
Mean | 8 | 3 | 7 | 3 | 2 | 6 | 5 | 1 | |
Worse | 8 | 3 | 7 | 4 | 2 | 5 | 6 | 1 |
Datasets | DE | EO | WOA | SBOA | HEOA | LSHADE | IMODE | BSFSBOA |
---|---|---|---|---|---|---|---|---|
Titanic | 75.68 | 74.74 | 75.23 | 77.95 | 76.36 | 75.45 | 77.73 | 78.86 |
5 | 8 | 7 | 2 | 4 | 6 | 3 | 1 | |
Balance-scale | 87.20 | 86.40 | 84.80 | 84.80 | 87.20 | 87.20 | 80.00 | 88.00 |
2 | 5 | 6 | 6 | 2 | 2 | 8 | 1 | |
Diabetes | 92.81 | 92.81 | 92.81 | 92.81 | 92.81 | 92.81 | 92.81 | 92.81 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Breast-w | 95.11 | 98.01 | 98.18 | 97.27 | 97.17 | 96.31 | 96.71 | 98.20 |
8 | 3 | 2 | 4 | 5 | 7 | 6 | 1 | |
HeartEW | 88.64 | 83.15 | 88.77 | 85.99 | 88.09 | 85.74 | 81.79 | 90.56 |
3 | 7 | 2 | 5 | 4 | 6 | 8 | 1 | |
KC1 | 82.69 | 83.34 | 84.54 | 82.48 | 85.53 | 81.40 | 82.47 | 87.02 |
5 | 4 | 3 | 6 | 2 | 8 | 7 | 1 | |
PC1 | 93.50 | 94.10 | 94.86 | 92.58 | 92.94 | 93.92 | 94.80 | 94.80 |
6 | 4 | 1 | 8 | 7 | 5 | 2 | 2 | |
Parkinsons | 93.85 | 92.56 | 94.53 | 90.94 | 88.29 | 93.42 | 91.88 | 97.35 |
3 | 5 | 2 | 7 | 8 | 4 | 6 | 1 | |
BreastEW | 98.76 | 96.55 | 97.32 | 97.02 | 99.00 | 97.11 | 98.88 | 99.76 |
4 | 8 | 5 | 7 | 2 | 6 | 3 | 1 | |
PC2 | 99.64 | 99.64 | 99.64 | 99.64 | 99.64 | 99.64 | 99.64 | 99.64 |
1 | 8 | 1 | 1 | 1 | 1 | 1 | 1 | |
PC4 | 88.00 | 88.91 | 90.52 | 88.49 | 90.58 | 90.26 | 90.80 | 91.36 |
8 | 6 | 4 | 7 | 3 | 5 | 2 | 1 | |
Piechart3 | 88.79 | 88.37 | 88.79 | 87.88 | 89.07 | 88.96 | 89.29 | 89.09 |
5 | 7 | 5 | 8 | 3 | 4 | 1 | 2 | |
Pizzacutter3 | 89.28 | 89.71 | 89.31 | 89.10 | 89.73 | 89.36 | 88.85 | 90.64 |
6 | 3 | 5 | 7 | 2 | 4 | 8 | 1 | |
Mean Rank | 4.38 | 5.31 | 3.38 | 5.31 | 3.38 | 4.54 | 4.31 | 1.15 |
Final Rank | 5 | 7 | 2 | 7 | 2 | 6 | 4 | 1 |
Datasets | DE | EO | WOA | SBOA | HEOA | LSHADE | IMODE | BSFSBOA |
---|---|---|---|---|---|---|---|---|
Titanic | 1.00 | 2.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
1 | 8 | 1 | 1 | 1 | 1 | 1 | 1 | |
Balance-scale | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 | 4.00 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
Diabetes | 1.00 | 1.03 | 1.0 | 1.00 | 1.57 | 1.00 | 1.00 | 1.00 |
1 | 7 | 1 | 1 | 8 | 1 | 1 | 1 | |
Breast-w | 2.23 | 2.57 | 3.37 | 2.83 | 2.63 | 3.00 | 2.83 | 2.70 |
1 | 2 | 8 | 5 | 3 | 7 | 5 | 4 | |
HeartEW | 4.47 | 6.37 | 3.57 | 2.87 | 2.80 | 4.20 | 3.67 | 3.07 |
7 | 8 | 4 | 2 | 1 | 6 | 5 | 3 | |
KC1 | 4.70 | 5.70 | 4.20 | 3.70 | 2.80 | 5.00 | 4.13 | 3.17 |
6 | 8 | 5 | 3 | 1 | 7 | 4 | 2 | |
PC1 | 2.93 | 3.07 | 1.43 | 1.20 | 1.80 | 1.03 | 2.13 | 1.03 |
7 | 8 | 4 | 3 | 5 | 1 | 6 | 1 | |
Parkinsons | 4.23 | 5.60 | 1.73 | 4.00 | 2.17 | 4.37 | 2.20 | 2.00 |
6 | 8 | 1 | 5 | 3 | 7 | 4 | 2 | |
BreastEW | 10.70 | 12.43 | 5.97 | 7.90 | 6.03 | 7.57 | 5.63 | 6.10 |
7 | 8 | 2 | 6 | 3 | 5 | 1 | 4 | |
PC2 | 3.53 | 5.63 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
7 | 8 | 1 | 1 | 1 | 1 | 1 | 1 | |
PC4 | 8.93 | 2.67 | 4.00 | 1.60 | 3.23 | 2.43 | 3.33 | 13.00 |
7 | 3 | 6 | 1 | 4 | 2 | 5 | 8 | |
Piechart3 | 7.30 | 11.83 | 3.20 | 1.80 | 2.17 | 2.20 | 2.73 | 1.97 |
7 | 8 | 6 | 1 | 3 | 4 | 5 | 2 | |
Pizzacutter3 | 10.07 | 2.50 | 2.53 | 1.97 | 2.77 | 2.67 | 2.53 | 10.40 |
7 | 2 | 3 | 1 | 6 | 5 | 3 | 8 | |
Mean Rank | 5.00 | 6.08 | 3.31 | 2.38 | 3.08 | 3.69 | 3.23 | 2.92 |
Final Rank | 7 | 8 | 5 | 1 | 3 | 6 | 4 | 2 |
Datasets | DE | EO | WOA | SBOA | HEOA | LSHADE | IMODE | BSFSBOA |
---|---|---|---|---|---|---|---|---|
Titanic | 6.15 | 5.33 | 4.92 | 11.73 | 11.08 | 12.21 | 4.72 | 4.26 |
5 | 4 | 3 | 7 | 6 | 8 | 2 | 1 | |
Balance-scale | 5.09 | 4.83 | 5.14 | 10.48 | 10.46 | 10.96 | 4.59 | 4.60 |
4 | 3 | 5 | 7 | 6 | 8 | 1 | 2 | |
Diabetes | 4.68 | 4.72 | 4.51 | 10.40 | 9.45 | 9.92 | 3.84 | 4.08 |
4 | 5 | 3 | 8 | 6 | 7 | 1 | 2 | |
Breast-w | 4.77 | 5.02 | 5.06 | 10.66 | 10.24 | 10.44 | 4.58 | 4.38 |
3 | 4 | 5 | 8 | 6 | 7 | 2 | 1 | |
HeartEW | 4.43 | 4.80 | 4.67 | 9.74 | 8.63 | 10.22 | 4.49 | 4.11 |
2 | 5 | 4 | 7 | 6 | 8 | 3 | 1 | |
KC1 | 4.78 | 5.33 | 5.24 | 12.12 | 9.25 | 13.19 | 5.06 | 4.81 |
1 | 5 | 4 | 7 | 6 | 8 | 3 | 2 | |
PC1 | 4.74 | 4.83 | 4.82 | 10.29 | 9.26 | 10.16 | 4.50 | 4.06 |
3 | 5 | 4 | 8 | 6 | 7 | 2 | 1 | |
Parkinsons | 4.57 | 4.44 | 4.48 | 9.51 | 8.56 | 9.57 | 3.92 | 4.05 |
5 | 3 | 4 | 7 | 6 | 8 | 1 | 2 | |
BreastEW | 4.01 | 4.19 | 4.29 | 10.21 | 8.83 | 9.65 | 4.45 | 3.70 |
2 | 3 | 4 | 8 | 6 | 7 | 5 | 1 | |
PC2 | 13.60 | 12.46 | 11.81 | 23.46 | 20.99 | 33.45 | 9.16 | 8.00 |
5 | 4 | 3 | 7 | 6 | 8 | 2 | 1 | |
PC4 | 4.30 | 4.68 | 4.39 | 10.50 | 8.66 | 14.12 | 4.89 | 4.82 |
1 | 3 | 2 | 7 | 6 | 8 | 5 | 4 | |
Piechart3 | 4.51 | 4.07 | 4.78 | 10.44 | 9.32 | 13.70 | 4.58 | 4.98 |
2 | 1 | 4 | 7 | 6 | 8 | 3 | 5 | |
Pizzacutter3 | 4.22 | 4.4 | 5.17 | 10.35 | 9.45 | 13.50 | 4.51 | 4.82 |
1 | 2 | 5 | 7 | 6 | 8 | 3 | 4 | |
Mean Rank | 2.92 | 3.62 | 3.85 | 7.31 | 6.00 | 7.69 | 2.54 | 2.08 |
Final Rank | 3 | 4 | 5 | 7 | 6 | 8 | 2 | 1 |
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Chen, F.; Ye, S.; Wang, J.; Luo, J. Multi-Strategy Improved Binary Secretarial Bird Optimization Algorithm for Feature Selection. Mathematics 2025, 13, 668. https://doi.org/10.3390/math13040668
Chen F, Ye S, Wang J, Luo J. Multi-Strategy Improved Binary Secretarial Bird Optimization Algorithm for Feature Selection. Mathematics. 2025; 13(4):668. https://doi.org/10.3390/math13040668
Chicago/Turabian StyleChen, Fuqiang, Shitong Ye, Jianfeng Wang, and Jia Luo. 2025. "Multi-Strategy Improved Binary Secretarial Bird Optimization Algorithm for Feature Selection" Mathematics 13, no. 4: 668. https://doi.org/10.3390/math13040668
APA StyleChen, F., Ye, S., Wang, J., & Luo, J. (2025). Multi-Strategy Improved Binary Secretarial Bird Optimization Algorithm for Feature Selection. Mathematics, 13(4), 668. https://doi.org/10.3390/math13040668