# Binary Competitive Swarm Optimizer Approaches for Feature Selection

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Competitive Swarm Optimizer

_{l}is the velocity of loser particle, x

_{w}is the position of the winner particle, x

_{l}is the position of the loser particle, $\overline{x}$ is the mean position of the current swarm, r

_{1}, r

_{2}, and r

_{3}are three independent random vectors in [0, 1], $\varphi $ is the social factor, d is the dimension of search space, and t is the iteration number. The pseudocode of the CSO is presented in Algorithm 1.

Algorithm 1. Competitive swarm optimizer |

Input parameter:N, T_{max} and $\varphi $ |

(1) Initialize a population of particles, x |

(2) Calculate the fitness of particles, F(x) |

(3) Define the best particle as gbest |

(4) for t = 1 to maximum number of iterations, T_{max} |

// Competition Strategy // |

(5) for i = 1 to half of population, N/2 |

(6) Random select two particles, x_{k} and x_{m} |

(7) if F(x_{k}) better than F(x_{m}) |

(8) x_{w} = x_{k}, x_{l} = x_{m} |

(9) else |

(10) x_{w} = x_{m}, x_{l} = x_{k} |

(11) end if |

(12) Add x_{w} into new population |

(13) Remove x_{k} and x_{m} from the population |

(14) next i |

//Velocity and Position Update // |

(15) for i = 1 to half of population, N/2 |

(16) for d = 1 to the dimension of search space, D |

(17) Update velocity of loser using Equation (1) |

(18) Update position of loser as shown in Equation (2) |

(19) next d |

(20) Calculate the fitness of new loser, F(x_{l}) |

(21) Move new loser into new population |

(22) Update gbest if there is better solution |

(23) next i |

(24) Pass new population to next iteration |

(25) next t |

Output: Global best solution |

## 3. Binary Version of the Competitive Swarm Optimizer

#### 3.1. S-Shaped Family

_{l}is the velocity of loser particle, d is the dimension, and t is the iteration number. The illustrations of the S-shaped transfer functions are presented in Figure 1. In these approaches, the velocity of the loser is first calculated as shown in Equation (1). The transfer function is then used to convert the velocity into a probability value between [0, 1]. After that, the position of the loser is updated as:

_{4}is a random vector distributed in [0, 1].

#### 3.2. V-Shaped Family

_{l}is the velocity of loser particle, d is the dimension, and t is the iteration number. The illustrations of the V-shaped transfer functions are shown in Figure 2. Unlike the S-shaped transfer function, the V-shaped transfer function does not force the search agents to move on the binary search space. In this approach, the position of loser particle is updated as:

_{5}is a random vector distributed in [0, 1].

_{max}are the number of particles and the maximum number of iterations. In the first step, a population of N particles is randomly initialized, and the velocity of each particle is initialized as zero. Then, the fitness of each particle is evaluated. The best particle is defined as the global best, gbest. For each iteration, the particles are randomly divided into two groups, and the competition is made between two coupled particles. From the competition, the winners are directly passed into the new population. On the other hand, the losers update their velocity using Equation (1). Then, the velocity is converted into a probability value by employing S-shaped or V-shaped transfer functions. Afterward, the position of the loser particle is updated using Equation (7) or Equation (12). Next, the fitness of each new loser is evaluated, and the new losers are moved into the new population for the next iteration. At the end of each iteration, the global best solution gbest is updated. The procedure is repeated iteratively until the maximum number of iterations is reached. Finally, the global best solution is achieved.

Algorithm 2. Binary competitive swarm optimizer. |

Input parameter:N, T_{max} and $\varphi $ |

(1) Initialize a population of particles, x |

(2) Calculate the fitness of particles, F(x) |

(3) Define the best particle as gbest |

(4) for t = 1 to maximum number of iterations, T_{max} |

// Competition Strategy // |

(5) for i = 1 to half of population, N/2 |

(6) Random select two particles, x_{k} and x_{m} |

(7) if F(x_{k}) better than F(x_{m}) |

(8) x_{w} = x_{k}, x_{l} = x_{m} |

(9) else |

(10) x_{w} = x_{m}, x_{l} = x_{k} |

(11) end if |

(12) Add x_{w} into new population |

(13) Remove x_{k} and x_{m} from the population |

(14) next i |

//Velocity and Position Update // |

(15) for i = 1 to half of population, N/2 |

(16) for d = 1 to the dimension of search space, D |

(17) Update velocity of loser using Equation (1) |

(18) Convert velocity into probability using S-shaped or V-shaped transfer function |

(19) Update position of loser as shown in Equation (7) or Equation (12) |

(20) next d |

(21) Calculate the fitness of new loser, F(x_{l}) |

(22) Move new loser into new population |

(23) Update gbest if there is better solution |

(24) next i |

(25) Pass new population to next iteration |

(26) next t |

Output: Global best solution |

## 4. Application of the Binary Competitive Swarm Optimizer for Feature Selection

^{D}– 1, which is impractical for searching exhaustively. Therefore, the proposed approaches are used to evaluate the best feature subset. In this paper, the fitness function that considers both classification error rate and number of features is applied. Mathematically, the fitness function can be expressed as:

## 5. Experimental Results and Discussions

#### 5.1. Experiment Setup

#### 5.2. Comparison Algorithms and Evaluation Metrics

_{max}) are fixed at 10 and 100, respectively [23]. On one hand, the dimension of the search space (D) is equal to the total number of features in each dataset. Table 2 exhibits the parameter settings for the utilized approaches. Note that there is no additional parameter setting for BSSA.

#### 5.3. Assessments of the BCSO in Feature Selection

#### 5.4. Comparison with Other Algorithms

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Mafarja, M.; Aljarah, I.; Heidari, A.A.; Hammouri, A.I.; Faris, H.; Al-Zoubi, A.M.; Mirjalili, S. Evolutionary Population Dynamics and Grasshopper Optimization approaches for feature selection problems. Knowl.-Based Syst.
**2018**, 145, 25–45. [Google Scholar] [CrossRef] [Green Version] - Arora, S.; Anand, P. Binary butterfly optimization approaches for feature selection. Expert Syst. Appl.
**2019**, 116, 147–160. [Google Scholar] [CrossRef] - Hafiz, F.; Swain, A.; Patel, N.; Naik, C. A two-dimensional (2-D) learning framework for Particle Swarm based feature selection. Pattern Recognit.
**2018**, 76, 416–433. [Google Scholar] [CrossRef] [Green Version] - Lin, K.C.; Hung, J.C.; Wei, J. Feature selection with modified lion’s algorithms and support vector machine for high-dimensional data. Appl. Soft Comput.
**2018**, 68, 669–676. [Google Scholar] [CrossRef] - Lin, K.C.; Zhang, K.Y.; Huang, Y.H.; Hung, J.C.; Yen, N. Feature selection based on an improved cat swarm optimization algorithm for big data classification. J. Supercomput.
**2016**, 72, 3210–3221. [Google Scholar] [CrossRef] - Chen, Y.P.; Li, Y.; Wang, G.; Zheng, Y.F.; Xu, Q.; Fan, J.H.; Cui, X.T. A novel bacterial foraging optimization algorithm for feature selection. Expert Syst. Appl.
**2017**, 83, 1–17. [Google Scholar] [CrossRef] - Xue, B.; Zhang, M.; Browne, W.N. Particle Swarm Optimization for Feature Selection in Classification: A Multi-Objective Approach. IEEE Trans. Cybern.
**2013**, 43, 1656–1671. [Google Scholar] [CrossRef] [PubMed] - Emary, E.; Zawbaa, H.M.; Hassanien, A.E. Binary ant lion approaches for feature selection. Neurocomputing
**2016**, 213, 54–65. [Google Scholar] [CrossRef] - Emary, E.; Zawbaa, H.M.; Hassanien, A.E. Binary grey wolf optimization approaches for feature selection. Neurocomputing
**2016**, 172, 371–381. [Google Scholar] [CrossRef] - Huang, C.L.; Wang, C.J. A GA-based feature selection and parameters optimization for support vector machines. Expert Syst. Appl.
**2006**, 31, 231–240. [Google Scholar] [CrossRef] - De Stefano, C.; Fontanella, F.; Marrocco, C.; Scotto di Freca, A. A GA-based feature selection approach with an application to handwritten character recognition. Pattern Recognit. Lett.
**2014**, 35, 130–141. [Google Scholar] [CrossRef] - Ghareb, A.S.; Bakar, A.A.; Hamdan, A.R. Hybrid feature selection based on enhanced genetic algorithm for text categorization. Expert Syst. Appl.
**2016**, 49, 31–47. [Google Scholar] [CrossRef] - Ma, B.; Xia, Y. A tribe competition-based genetic algorithm for feature selection in pattern classification. Appl. Soft Comput.
**2017**, 58, 328–338. [Google Scholar] [CrossRef] [Green Version] - Al-Sharhan, S.; Bimba, A. Adaptive multi-parent crossover GA for feature optimization in epileptic seizure identification. Appl. Soft Comput.
**2019**, 75, 575–587. [Google Scholar] [CrossRef] - Chuang, L.Y.; Chang, H.W.; Tu, C.J.; Yang, C.H. Improved binary PSO for feature selection using gene expression data. Comput. Biol. Chem.
**2008**, 32, 29–38. [Google Scholar] [CrossRef] - Tan, T.Y.; Zhang, L.; Neoh, S.C.; Lim, C.P. Intelligent skin cancer detection using enhanced particle swarm optimization. Knowl.-Based Syst.
**2018**, 158, 118–135. [Google Scholar] [CrossRef] - Chuang, L.Y.; Yang, C.H.; Li, J.C. Chaotic maps based on binary particle swarm optimization for feature selection. Appl. Soft Comput.
**2011**, 11, 239–248. [Google Scholar] [CrossRef] - Jain, I.; Jain, V.K.; Jain, R. Correlation feature selection based improved-Binary Particle Swarm Optimization for gene selection and cancer classification. Appl. Soft Comput.
**2018**, 62, 203–215. [Google Scholar] [CrossRef] - Too, J.; Abdullah, A.R.; Mohd Saad, N.; Tee, W. EMG Feature Selection and Classification Using a Pbest-Guide Binary Particle Swarm Optimization. Computation
**2019**, 7, 12. [Google Scholar] [CrossRef] - Cheng, R.; Jin, Y. A Competitive Swarm Optimizer for Large Scale Optimization. IEEE Trans. Cybern.
**2015**, 45, 191–204. [Google Scholar] [CrossRef] - Mirjalili, S.; Lewis, A. S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization. Swarm Evol. Comput.
**2013**, 9, 1–14. [Google Scholar] [CrossRef] - Saremi, S.; Mirjalili, S.; Lewis, A. How important is a transfer function in discrete heuristic algorithms. Neural Comput. Appl.
**2015**, 26, 625–640. [Google Scholar] [CrossRef] - Faris, H.; Mafarja, M.M.; Heidari, A.A.; Aljarah, I.; Al-Zoubi, A.M.; Mirjalili, S.; Fujita, H. An efficient binary Salp Swarm Algorithm with crossover scheme for feature selection problems. Knowl.-Based Syst.
**2018**, 154, 43–67. [Google Scholar] [CrossRef] - Mafarja, M.; Aljarah, I.; Faris, H.; Hammouri, A.I.; Al-Zoubi, A.M.; Mirjalili, S. Binary grasshopper optimisation algorithm approaches for feature selection problems. Expert Syst. Appl.
**2019**, 117, 267–286. [Google Scholar] [CrossRef] - Rashedi, E.; Nezamabadi-pour, H.; Saryazdi, S. BGSA: Binary gravitational search algorithm. Nat. Comput.
**2010**, 9, 727–745. [Google Scholar] [CrossRef] - Emary, E.; Zawbaa, H.M. Feature selection via Lèvy Antlion optimization. Pattern Anal. Appl.
**2018**, 19, 1–20. [Google Scholar] [CrossRef] - UCI Machine Learning Repository. Available online: https://archive.ics.uci.edu/ml/index.php (accessed on 24 March 2019).
- Zorarpacı, E.; Özel, S.A. A hybrid approach of differential evolution and artificial bee colony for feature selection. Expert Syst. Appl.
**2016**, 62, 91–103. [Google Scholar] [CrossRef] - Zawbaa, H.M.; Emary, E.; Grosan, C. Feature Selection via Chaotic Antlion Optimization. PLoS ONE
**2016**, 11, e0150652. [Google Scholar] [CrossRef] - Too, J.; Abdullah, A.R.; Mohd Saad, N. A New Co-Evolution Binary Particle Swarm Optimization with Multiple Inertia Weight Strategy for Feature Selection. Informatics
**2019**, 6, 21. [Google Scholar] [CrossRef]

No. | Dataset | Number of Instances | Number of Features | Number of Classes |
---|---|---|---|---|

1 | Arrhythmia | 452 | 279 | 16 |

2 | Breast Cancer Wisconsin | 699 | 9 | 2 |

3 | Dermatology | 366 | 34 | 6 |

4 | Diabetic Retinopathy Debrecen | 1151 | 19 | 2 |

5 | Hepatitis | 155 | 19 | 2 |

6 | Ionosphere | 351 | 34 | 2 |

7 | Libras Movement | 360 | 90 | 15 |

8 | LSVT Voice Rehabilitation | 126 | 309 | 2 |

9 | SCADI | 70 | 205 | 7 |

10 | Wine | 178 | 13 | 3 |

11 | Breast Cancer Coimbra | 116 | 9 | 2 |

12 | Iris | 150 | 4 | 3 |

13 | Lung Cancer | 32 | 56 | 2 |

14 | Musk 1 | 476 | 167 | 2 |

15 | Seeds | 210 | 7 | 3 |

Algorithm | Parameter | Value |
---|---|---|

BPSO | Inertia weight, w | [0.9–0.4] |

Acceleration coefficient, c_{1} and c_{2} | 2 | |

Maximum velocity, V_{max} | 6 | |

GA | Crossover rate, CR | 0.8 |

Mutation rate, MR | 0.01 | |

BDE | Crossover rate, CR | 0.9 |

BCSO | Social factor, $\varphi $ | 0.2 |

Maximum velocity, V_{max} | 6 |

Dataset | Metrics | Binary Version of Competitive Swarm Optimizer (BCSO) | |||||||
---|---|---|---|---|---|---|---|---|---|

S1 | S2 | S3 | S4 | V1 | V2 | V3 | V4 | ||

1 | Best fitness | 0.3927 | 0.3947 | 0.4008 | 0.4015 | 0.3656 | 0.3645 | 0.3641 | 0.3656 |

Worst fitness | 0.4030 | 0.4041 | 0.4052 | 0.4045 | 0.4035 | 0.4031 | 0.4034 | 0.4023 | |

Mean fitness | 0.3945 | 0.3974 | 0.4013 | 0.4020 | 0.3717 | 0.3709 | 0.3703 | 0.3726 | |

STD | 0.0027 | 0.0031 | 0.0009 | 0.0006 | 0.0096 | 0.0095 | 0.0096 | 0.0094 | |

Feature size | 133.00 | 138.07 | 134.57 | 134.17 | 134.03 | 132.70 | 132.17 | 133.57 | |

2 | Best fitness | 0.0286 | 0.0301 | 0.0316 | 0.0316 | 0.0215 | 0.0221 | 0.0219 | 0.0201 |

Worst fitness | 0.0314 | 0.0308 | 0.0319 | 0.0320 | 0.0302 | 0.0304 | 0.0304 | 0.0306 | |

Mean fitness | 0.0291 | 0.0301 | 0.0316 | 0.0316 | 0.0223 | 0.0231 | 0.0228 | 0.0213 | |

STD | 0.0007 | 0.0001 | 0.0001 | 0.0001 | 0.0019 | 0.0020 | 0.0020 | 0.0026 | |

Feature size | 3.50 | 3.33 | 4.43 | 4.47 | 3.47 | 3.57 | 3.57 | 3.63 | |

3 | Best fitness | 0.0064 | 0.0067 | 0.0069 | 0.0069 | 0.0173 | 0.0182 | 0.0201 | 0.0214 |

Worst fitness | 0.0295 | 0.0261 | 0.0224 | 0.0197 | 0.0437 | 0.0437 | 0.0437 | 0.0437 | |

Mean fitness | 0.0080 | 0.0074 | 0.0073 | 0.0072 | 0.0209 | 0.0217 | 0.0240 | 0.0259 | |

STD | 0.0046 | 0.0030 | 0.0022 | 0.0018 | 0.0058 | 0.0057 | 0.0057 | 0.0067 | |

Feature size | 21.63 | 22.83 | 23.47 | 23.53 | 15.90 | 15.83 | 16.17 | 15.73 | |

4 | Best fitness | 0.2976 | 0.3033 | 0.3056 | 0.3056 | 0.2874 | 0.2885 | 0.2828 | 0.2863 |

Worst fitness | 0.3047 | 0.3057 | 0.3056 | 0.3056 | 0.3094 | 0.3092 | 0.3101 | 0.3101 | |

Mean fitness | 0.2979 | 0.3034 | 0.3056 | 0.3056 | 0.2897 | 0.2904 | 0.2858 | 0.2891 | |

STD | 0.0013 | 0.0006 | 0.0000 | 0.0000 | 0.0046 | 0.0038 | 0.0064 | 0.0055 | |

Feature size | 8.70 | 10.80 | 11.23 | 11.23 | 7.87 | 7.63 | 7.33 | 7.20 | |

5 | Best fitness | 0.1300 | 0.1443 | 0.1464 | 0.1464 | 0.1222 | 0.1263 | 0.1276 | 0.1245 |

Worst fitness | 0.1355 | 0.1465 | 0.1465 | 0.1465 | 0.1433 | 0.1434 | 0.1434 | 0.1434 | |

Mean fitness | 0.1306 | 0.1444 | 0.1464 | 0.1464 | 0.1256 | 0.1289 | 0.1294 | 0.1274 | |

STD | 0.0015 | 0.0004 | 0.0000 | 0.0000 | 0.0063 | 0.0047 | 0.0041 | 0.0049 | |

Feature size | 6.37 | 7.17 | 7.10 | 7.13 | 5.73 | 5.37 | 5.77 | 5.93 | |

6 | Best fitness | 0.1207 | 0.1393 | 0.1423 | 0.1432 | 0.0886 | 0.0868 | 0.0894 | 0.0890 |

Worst fitness | 0.1423 | 0.1429 | 0.1437 | 0.1437 | 0.1423 | 0.1423 | 0.1419 | 0.1428 | |

Mean fitness | 0.1252 | 0.1400 | 0.1425 | 0.1435 | 0.1005 | 0.0980 | 0.1016 | 0.1035 | |

STD | 0.0056 | 0.0010 | 0.0005 | 0.0003 | 0.0139 | 0.0152 | 0.0152 | 0.0146 | |

Feature size | 11.30 | 13.47 | 14.03 | 14.00 | 11.03 | 11.33 | 10.77 | 11.03 | |

7 | Best fitness | 0.2321 | 0.2356 | 0.2428 | 0.2410 | 0.2004 | 0.1991 | 0.2060 | 0.2107 |

Worst fitness | 0.2643 | 0.2666 | 0.2702 | 0.2698 | 0.2696 | 0.2683 | 0.2683 | 0.2683 | |

Mean fitness | 0.2386 | 0.2401 | 0.2471 | 0.2463 | 0.2190 | 0.2181 | 0.2219 | 0.2266 | |

STD | 0.0083 | 0.0069 | 0.0071 | 0.0080 | 0.0192 | 0.0194 | 0.0158 | 0.0153 | |

Feature size | 46.67 | 49.63 | 48.47 | 48.93 | 38.47 | 38.57 | 38.63 | 39.67 | |

8 | Best fitness | 0.0935 | 0.1146 | 0.1449 | 0.1595 | 0.1049 | 0.1114 | 0.1022 | 0.1062 |

Worst fitness | 0.1648 | 0.1701 | 0.1622 | 0.1701 | 0.1871 | 0.1857 | 0.1857 | 0.1844 | |

Mean fitness | 0.1033 | 0.1193 | 0.1483 | 0.1596 | 0.1261 | 0.1272 | 0.1215 | 0.1273 | |

STD | 0.0162 | 0.0107 | 0.0045 | 0.0012 | 0.0205 | 0.0193 | 0.0237 | 0.0218 | |

Feature size | 156.60 | 155.57 | 155.80 | 156.37 | 140.60 | 140.27 | 141.00 | 142.63 | |

9 | Best fitness | 0.2169 | 0.2217 | 0.2287 | 0.2288 | 0.2086 | 0.2040 | 0.2063 | 0.2063 |

Worst fitness | 0.2358 | 0.2358 | 0.2358 | 0.2288 | 0.2403 | 0.2404 | 0.2427 | 0.2427 | |

Mean fitness | 0.2181 | 0.2234 | 0.2295 | 0.2288 | 0.2126 | 0.2097 | 0.2132 | 0.2138 | |

STD | 0.0043 | 0.0045 | 0.0022 | 0.0000 | 0.0073 | 0.0094 | 0.0091 | 0.0088 | |

Feature size | 97.57 | 98.77 | 98.50 | 99.07 | 73.17 | 74.17 | 74.33 | 73.90 | |

10 | Best fitness | 0.0741 | 0.0799 | 0.0878 | 0.0878 | 0.0524 | 0.0514 | 0.0497 | 0.0472 |

Worst fitness | 0.0863 | 0.0845 | 0.0880 | 0.0880 | 0.0848 | 0.0848 | 0.0904 | 0.0906 | |

Mean fitness | 0.0742 | 0.0799 | 0.0878 | 0.0878 | 0.0550 | 0.0549 | 0.0533 | 0.0502 | |

STD | 0.0014 | 0.0005 | 0.0000 | 0.0000 | 0.0068 | 0.0069 | 0.0079 | 0.0079 | |

Feature size | 5.73 | 4.90 | 4.47 | 4.53 | 4.90 | 4.87 | 5.07 | 5.30 | |

11 | Best fitness | 0.1352 | 0.1352 | 0.1357 | 0.1358 | 0.1467 | 0.1455 | 0.1495 | 0.1456 |

Worst fitness | 0.1537 | 0.1425 | 0.1385 | 0.1358 | 0.2101 | 0.2101 | 0.2101 | 0.2100 | |

Mean fitness | 0.1355 | 0.1353 | 0.1357 | 0.1358 | 0.1499 | 0.1501 | 0.1529 | 0.1491 | |

STD | 0.0021 | 0.0009 | 0.0003 | 0.0000 | 0.0120 | 0.0135 | 0.0114 | 0.0118 | |

Feature size | 5.47 | 5.47 | 5.90 | 6.00 | 4.17 | 4.37 | 4.10 | 4.47 | |

12 | Best fitness | 0.0025 | 0.0025 | 0.0025 | 0.0025 | 0.0037 | 0.0037 | 0.0039 | 0.0038 |

Worst fitness | 0.0091 | 0.0066 | 0.0061 | 0.0061 | 0.0099 | 0.0099 | 0.0099 | 0.0099 | |

Mean fitness | 0.0026 | 0.0025 | 0.0025 | 0.0025 | 0.0039 | 0.0039 | 0.0040 | 0.0040 | |

STD | 0.0007 | 0.0004 | 0.0004 | 0.0004 | 0.0009 | 0.0009 | 0.0009 | 0.0009 | |

Feature size | 1.00 | 1.00 | 1.00 | 1.00 | 1.03 | 1.03 | 1.10 | 1.07 | |

13 | Best fitness | 0.0321 | 0.2409 | 0.2077 | 0.2685 | 0.0031 | 0.0031 | 0.0032 | 0.0088 |

Worst fitness | 0.2577 | 0.2632 | 0.2631 | 0.2741 | 0.2740 | 0.2740 | 0.2684 | 0.2631 | |

Mean fitness | 0.0868 | 0.2471 | 0.2136 | 0.2689 | 0.0282 | 0.0346 | 0.0326 | 0.0422 | |

STD | 0.0781 | 0.0082 | 0.0158 | 0.0014 | 0.0638 | 0.0655 | 0.0644 | 0.0648 | |

Feature size | 25.57 | 24.77 | 23.67 | 25.10 | 17.53 | 17.60 | 17.93 | 18.60 | |

14 | Best fitness | 0.0742 | 0.0824 | 0.0924 | 0.0969 | 0.0667 | 0.0622 | 0.0645 | 0.0674 |

Worst fitness | 0.1043 | 0.1078 | 0.1055 | 0.1048 | 0.1071 | 0.1074 | 0.1077 | 0.1067 | |

Mean fitness | 0.0812 | 0.0882 | 0.0942 | 0.0983 | 0.0767 | 0.0737 | 0.0747 | 0.0779 | |

STD | 0.0078 | 0.0063 | 0.0035 | 0.0021 | 0.0106 | 0.0124 | 0.0107 | 0.0103 | |

Feature size | 84.87 | 82.6 | 81.03 | 81.70 | 82.07 | 82.10 | 79.40 | 81.97 | |

15 | Best fitness | 0.0517 | 0.0517 | 0.0517 | 0.0517 | 0.0504 | 0.0504 | 0.0503 | 0.0504 |

Worst fitness | 0.0556 | 0.0517 | 0.0517 | 0.0517 | 0.0652 | 0.0652 | 0.0652 | 0.0660 | |

Mean fitness | 0.0517 | 0.0517 | 0.0517 | 0.0517 | 0.0509 | 0.0510 | 0.0509 | 0.0510 | |

STD | 0.0004 | 0.0000 | 0.0000 | 0.0000 | 0.0023 | 0.0024 | 0.0025 | 0.0026 | |

Feature size | 3.17 | 3.20 | 3.20 | 3.20 | 2.30 | 2.30 | 2.20 | 2.27 |

Dataset | Metrics | Feature Selection Method | ||||
---|---|---|---|---|---|---|

BDE | BPSO | BSSA | GA | BCSO | ||

1 | Best fitness | 0.3965 | 0.3604 | 0.3854 | 0.3806 | 0.3645 |

Worst fitness | 0.4034 | 0.3994 | 0.4071 | 0.4013 | 0.4031 | |

Mean fitness | 0.3966 | 0.3631 | 0.3862 | 0.3811 | 0.3709 | |

STD | 0.0009 | 0.0073 | 0.0032 | 0.0027 | 0.0095 | |

Feature size | 156.97 | 131.73 | 102.43 | 132.67 | 132.70 | |

2 | Best fitness | 0.0279 | 0.0259 | 0.0260 | 0.0228 | 0.0221 |

Worst fitness | 0.0297 | 0.0262 | 0.0320 | 0.0254 | 0.0304 | |

Mean fitness | 0.0279 | 0.0259 | 0.0264 | 0.0228 | 0.0231 | |

STD | 0.0002 | 0.0000 | 0.0011 | 0.0003 | 0.0020 | |

Feature size | 4.53 | 4.43 | 3.87 | 3.77 | 3.57 | |

3 | Best fitness | 0.0291 | 0.028 | 0.0358 | 0.0203 | 0.0182 |

Worst fitness | 0.0365 | 0.042 | 0.0445 | 0.0346 | 0.0437 | |

Mean fitness | 0.0292 | 0.0289 | 0.0366 | 0.0206 | 0.0217 | |

STD | 0.0009 | 0.0021 | 0.0019 | 0.0017 | 0.0057 | |

Feature size | 19.10 | 15.13 | 14.30 | 15.33 | 15.83 | |

4 | Best fitness | 0.306 | 0.2986 | 0.2945 | 0.3043 | 0.2885 |

Worst fitness | 0.3103 | 0.3151 | 0.3151 | 0.3118 | 0.3092 | |

Mean fitness | 0.3061 | 0.3004 | 0.2967 | 0.3044 | 0.2904 | |

STD | 0.0006 | 0.0039 | 0.0049 | 0.0009 | 0.0038 | |

Feature size | 10.80 | 8.13 | 6.77 | 8.97 | 7.63 | |

5 | Best fitness | 0.1425 | 0.1296 | 0.1216 | 0.1343 | 0.1263 |

Worst fitness | 0.1446 | 0.1466 | 0.1466 | 0.1411 | 0.1434 | |

Mean fitness | 0.1426 | 0.1304 | 0.1223 | 0.1344 | 0.1289 | |

STD | 0.0003 | 0.0030 | 0.0032 | 0.0008 | 0.0047 | |

Feature size | 7.90 | 5.47 | 4.47 | 6.40 | 5.37 | |

6 | Best fitness | 0.1359 | 0.1016 | 0.1095 | 0.1184 | 0.0868 |

Worst fitness | 0.1402 | 0.1398 | 0.1438 | 0.1341 | 0.1423 | |

Mean fitness | 0.1360 | 0.1045 | 0.1103 | 0.1186 | 0.0980 | |

STD | 0.0006 | 0.0078 | 0.0044 | 0.0020 | 0.0152 | |

Feature size | 16.47 | 15.23 | 8.60 | 12.90 | 11.33 | |

7 | Best fitness | 0.2611 | 0.2269 | 0.2433 | 0.2430 | 0.1991 |

Worst fitness | 0.2669 | 0.2708 | 0.2733 | 0.2628 | 0.2683 | |

Mean fitness | 0.2612 | 0.2313 | 0.2450 | 0.2433 | 0.2181 | |

STD | 0.0008 | 0.0091 | 0.0049 | 0.0025 | 0.0194 | |

Feature size | 48.03 | 45.93 | 28.23 | 41.60 | 38.57 | |

8 | Best fitness | 0.1653 | 0.1065 | 0.1418 | 0.1379 | 0.1114 |

Worst fitness | 0.1809 | 0.1806 | 0.1923 | 0.1830 | 0.1857 | |

Mean fitness | 0.1656 | 0.1187 | 0.1473 | 0.1393 | 0.1272 | |

STD | 0.0021 | 0.0184 | 0.0120 | 0.0069 | 0.0193 | |

Feature size | 171.73 | 151.27 | 99.73 | 141.50 | 140.27 | |

9 | Best fitness | 0.2335 | 0.2256 | 0.2170 | 0.2142 | 0.2040 |

Worst fitness | 0.2382 | 0.2451 | 0.2451 | 0.2332 | 0.2404 | |

Mean fitness | 0.2336 | 0.2286 | 0.2175 | 0.2146 | 0.2097 | |

STD | 0.0007 | 0.0055 | 0.0032 | 0.0024 | 0.0094 | |

Feature size | 99.07 | 81.7 | 51.23 | 91.47 | 74.17 | |

10 | Best fitness | 0.0752 | 0.0531 | 0.0613 | 0.0511 | 0.0514 |

Worst fitness | 0.0835 | 0.0980 | 0.0980 | 0.0678 | 0.0848 | |

Mean fitness | 0.0754 | 0.0574 | 0.0628 | 0.0514 | 0.0549 | |

STD | 0.0012 | 0.0103 | 0.0054 | 0.0022 | 0.0069 | |

Feature size | 6.03 | 4.63 | 4.67 | 5.60 | 4.87 | |

11 | Best fitness | 0.1739 | 0.1812 | 0.1710 | 0.1556 | 0.1455 |

Worst fitness | 0.1993 | 0.2259 | 0.2259 | 0.1831 | 0.2101 | |

Mean fitness | 0.1744 | 0.1840 | 0.1724 | 0.1561 | 0.1501 | |

STD | 0.0035 | 0.0089 | 0.0068 | 0.0035 | 0.0135 | |

Feature size | 5.40 | 4.27 | 4.10 | 4.47 | 4.37 | |

12 | Best fitness | 0.0114 | 0.0059 | 0.0073 | 0.0051 | 0.0037 |

Worst fitness | 0.0115 | 0.0126 | 0.0126 | 0.0064 | 0.0099 | |

Mean fitness | 0.0114 | 0.0069 | 0.0074 | 0.0051 | 0.0039 | |

STD | 0.0000 | 0.0021 | 0.0006 | 0.0001 | 0.0009 | |

Feature size | 1.47 | 1.03 | 1.17 | 1.17 | 1.03 | |

13 | Best fitness | 0.1647 | 0.0918 | 0.1241 | 0.1419 | 0.0031 |

Worst fitness | 0.2196 | 0.0975 | 0.2742 | 0.2026 | 0.2740 | |

Mean fitness | 0.1661 | 0.0951 | 0.1326 | 0.1429 | 0.0346 | |

STD | 0.0079 | 0.0027 | 0.0252 | 0.0071 | 0.0655 | |

Feature size | 29.23 | 21.47 | 17.53 | 24.43 | 17.60 | |

14 | Best fitness | 0.0878 | 0.0692 | 0.0899 | 0.0816 | 0.0622 |

Worst fitness | 0.1015 | 0.1005 | 0.1099 | 0.1012 | 0.1074 | |

Mean fitness | 0.0881 | 0.0742 | 0.0911 | 0.0822 | 0.0737 | |

STD | 0.0018 | 0.0074 | 0.0033 | 0.0029 | 0.0124 | |

Feature size | 108.63 | 82.43 | 63.23 | 80.80 | 82.10 | |

15 | Best fitness | 0.0599 | 0.0624 | 0.0554 | 0.0520 | 0.0504 |

Worst fitness | 0.0611 | 0.0667 | 0.0667 | 0.0602 | 0.0652 | |

Mean fitness | 0.0600 | 0.0625 | 0.0556 | 0.0521 | 0.0510 | |

STD | 0.0002 | 0.0006 | 0.0013 | 0.0010 | 0.0024 | |

Feature size | 2.90 | 3.00 | 2.47 | 2.83 | 2.30 |

**Table 5.**p-values of the Wilcoxon rank sum test of the BCSO accuracy results versus other algorithms.

Dataset | P-Value | |||
---|---|---|---|---|

BDE | BPSO | BSSA | GA | |

1 | 0.000000 | 0.380188 | 6.00 × 10^{−6} | 0.000434 |

2 | 3.70 × 10^{−5} | 0.000532 | 0.001921 | 0.630455 |

3 | 0.001156 | 0.017644 | 2.60 × 10^{−5} | 0.107494 |

4 | 0.000000 | 0.016211 | 0.012478 | 1.38 × 10^{−4} |

5 | 0.016281 | 0.587798 | 0.546144 | 0.214683 |

6 | 0.000000 | 0.001541 | 4.00 × 10^{−6} | 0.000000 |

7 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |

8 | 0.000000 | 0.356995 | 5.70 × 10^{−5} | 0.001066 |

9 | 0.000591 | 0.003016 | 0.013394 | 0.090513 |

10 | 0.033928 | 0.919999 | 0.151188 | 0.797191 |

11 | 0.004939 | 0.000866 | 3.20 × 10^{−5} | 0.319416 |

12 | 0.024637 | 0.312817 | 0.169401 | 0.570163 |

13 | 0.000000 | 4.00 × 10^{−6} | 2.00 × 10^{−6} | 0.000000 |

14 | 0.000000 | 0.170318 | 0.000000 | 3.00 × 10^{−6} |

15 | 0.005555 | 5.80 × 10^{−5} | 0.021498 | 0.333711 |

w/t/l | 15/0/0 | 9/6/0 | 12/3/0 | 7/8/0 |

Dataset | Average Computational Time (s) | ||||
---|---|---|---|---|---|

BDE | BPSO | BSSA | GA | BCSO | |

1 | 1.9970 | 2.2986 | 1.8710 | 3.4647 | 1.4204 |

2 | 2.6003 | 2.5338 | 2.3849 | 4.3947 | 1.2760 |

3 | 1.5281 | 1.4024 | 1.3335 | 2.4316 | 0.7592 |

4 | 7.3024 | 7.0196 | 6.6112 | 12.305 | 3.6870 |

5 | 0.8450 | 0.7938 | 0.7571 | 0.9028 | 0.4451 |

6 | 1.3588 | 1.3879 | 1.2595 | 2.2471 | 0.7262 |

7 | 1.4888 | 1.5563 | 1.3818 | 2.4323 | 0.8689 |

8 | 0.8920 | 1.1479 | 0.9308 | 1.4286 | 0.9336 |

9 | 0.6814 | 0.8616 | 0.7186 | 1.2021 | 0.6763 |

10 | 0.8608 | 0.8524 | 0.8020 | 1.2649 | 0.4529 |

11 | 0.6864 | 0.6677 | 0.6298 | 1.2466 | 0.3558 |

12 | 0.7488 | 0.7489 | 0.7048 | 1.0054 | 0.3944 |

13 | 0.5667 | 0.6357 | 0.5720 | 0.8743 | 0.3884 |

14 | 2.0475 | 2.0989 | 1.8085 | 3.6051 | 1.2123 |

15 | 0.9156 | 0.8726 | 0.8549 | 1.5100 | 0.4702 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Too, J.; Abdullah, A.R.; Mohd Saad, N.
Binary Competitive Swarm Optimizer Approaches for Feature Selection. *Computation* **2019**, *7*, 31.
https://doi.org/10.3390/computation7020031

**AMA Style**

Too J, Abdullah AR, Mohd Saad N.
Binary Competitive Swarm Optimizer Approaches for Feature Selection. *Computation*. 2019; 7(2):31.
https://doi.org/10.3390/computation7020031

**Chicago/Turabian Style**

Too, Jingwei, Abdul Rahim Abdullah, and Norhashimah Mohd Saad.
2019. "Binary Competitive Swarm Optimizer Approaches for Feature Selection" *Computation* 7, no. 2: 31.
https://doi.org/10.3390/computation7020031