# Entropy–Based Diversification Approach for Bio–Computing Methods

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Preliminaries

#### 3.1. Shannon Entropy

#### 3.2. Stagnation Problem

## 4. Developed Solution

#### 4.1. Bio–Inspired Methods

#### 4.1.1. Particle Swarm Optimization

#### 4.1.2. Black Hole Algorithm

#### 4.1.3. Bat Optimization

#### 4.1.4. Common Behavior

#### 4.2. Solving Stagnation

#### 4.2.1. Stagnation Detecting

Algorithm 1: Common work scheme used to implement the population–based algorithms |

Algorithm 2: Shannon entropy module |

#### 4.2.2. Stagnation Escaping

## 5. Experimental Setup

## 6. Discussion

## 7. Statistical Analysis

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Instance | Name | Best Known | Knapsacks | Objects |
---|---|---|---|---|

MKP01 | - | 6120 | 10 | 20 |

MKP02 | - | 12400 | 10 | 28 |

MKP03 | - | 10618 | 5 | 39 |

MKP04 | - | 16537 | 5 | 50 |

MKP05 | SENTO2 [57,58,59] | 8722 | 30 | 60 |

MKP06 | WEING5 [57,58,59] | 98796 | 2 | 28 |

MKP07 | WEING6 [57,58,59] | 130623 | 20 | 28 |

MKP08 | WEING7 [57,58,59] | 1095445 | 2 | 105 |

MKP09 | WEISH03 [58,59] | 4115 | 5 | 30 |

MKP10 | WEISH07 [58,59] | 5567 | 5 | 40 |

MKP11 | WEISH08 [58,59] | 5605 | 5 | 40 |

MKP12 | WEISH17 [58,59] | 8633 | 5 | 60 |

MKP13 | PB1 [58,59] | 3090 | 4 | 27 |

MKP14 | PB5 [58,59] | 2139 | 10 | 20 |

MKP15 | HP1 [58,59] | 3418 | 4 | 28 |

MKP16 | HP2 [58,59] | 3186 | 4 | 34 |

MKP17 | - | unknown | 5 | 100 |

MKP18 | - | unknown | 5 | 100 |

MKP19 | - | unknown | 5 | 100 |

MKP20 | - | unknown | 5 | 100 |

ID | (a) Number of Best Reached | (b) Minimum Solving Time | (c) Maximum Solving Time | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PSO | S–PSO | BA | S–BAT | BH | S–BH | PSO | S–PSO | BA | S–BAT | BH | S–BH | PSO | S–PSO | BA | S–BAT | BH | S–BH | |

MKP01 | 30 | 30 | 0 | 25 | 4 | 4 | 62 | 93 | 35 | 60 | 121 | 209 | 82 | 128 | 93 | 104 | 149 | 251 |

MKP02 | 20 | 28 | 1 | 9 | 0 | 0 | 64 | 99 | 30 | 46 | 251 | 82 | 78 | 127 | 100 | 79 | 95 | 104 |

MKP03 | 1 | 3 | 0 | 0 | 0 | 0 | 81 | 128 | 36 | 81 | 107 | 114 | 96 | 178 | 82 | 2821 | 131 | 137 |

MKP04 | 0 | 0 | 0 | 0 | 0 | 0 | 127 | 188 | 53 | 128 | 157 | 187 | 141 | 237 | 133 | 276 | 205 | 225 |

MKP05 | 0 | 0 | 0 | 0 | 0 | 0 | 412 | 421 | 8520 | 7503 | 13,827 | 13,649 | 517 | 535 | 162,779 | 60,468 | 18,624 | 17,446 |

MKP06 | 23 | 26 | 0 | 4 | 0 | 0 | 143 | 154 | 495 | 1099 | 2490 | 2536 | 180 | 203 | 1694 | 4872 | 2918 | 2772 |

MKP07 | 18 | 15 | 0 | 4 | 0 | 0 | 81 | 90 | 53 | 123 | 244 | 255 | 114 | 113 | 155 | 243 | 321 | 314 |

MKP08 | 0 | 0 | 0 | 0 | 0 | 0 | 120 | 159 | 57 | 109 | 110 | 150 | 148 | 199 | 120 | 174 | 145 | 191 |

MKP09 | 25 | 25 | 0 | 17 | 1 | 1 | 342 | 513 | 15,036 | 69,286 | 74,270 | 66,888 | 484 | 660 | 75,748 | 297,611 | 86,125 | 76,488 |

MKP10 | 23 | 23 | 2 | 16 | 0 | 0 | 559 | 456 | 12,909 | 32,863 | 41,213 | 38,791 | 456 | 696 | 323,688 | 213,580 | 53,025 | 47,676 |

MKP11 | 13 | 18 | 1 | 7 | 0 | 0 | 271 | 408 | 4639 | 6238 | 15,006 | 13,445 | 309 | 504 | 42,215 | 32,245 | 21,913 | 15,735 |

MKP12 | 0 | 0 | 0 | 7 | 0 | 0 | 304 | 216 | 240,867 | 821 | 2836 | 304 | 216 | 393 | 14,146,516 | 1955 | 3476 | 393 |

MKP13 | 1 | 4 | 1 | 4 | 0 | 4 | 51 | 89 | 35 | 99 | 82 | 89 | 76 | 131 | 101 | 142 | 100 | 131 |

MKP14 | 8 | 8 | 1 | 6 | 8 | 8 | 110 | 154 | 106 | 667 | 500 | 122 | 148 | 153 | 303 | 306 | 612 | 153 |

MKP15 | 6 | 7 | 0 | 1 | 0 | 3 | 52 | 90 | 54 | 49 | 77 | 87 | 75 | 133 | 177 | 123 | 110 | 162 |

MKP16 | 8 | 10 | 0 | 2 | 0 | 10 | 114 | 180 | 184 | 401 | 660 | 180 | 144 | 238 | 487 | 1322 | 795 | 238 |

MKP17 | 0 | 0 | 0 | 0 | 0 | 0 | 131 | 159 | 97 | 954,304 | 122 | 177 | 167 | 198 | 191 | 78,392,197 | 158 | 226 |

MKP18 | 0 | 0 | 0 | 0 | 0 | 0 | 132 | 165 | 98 | 177 | 123 | 129 | 188 | 202 | 233 | 415 | 150 | 206 |

MKP19 | 0 | 0 | 0 | 0 | 0 | 0 | 130 | 164 | 111 | 141 | 125 | 180 | 166 | 196 | 305 | 318 | 154 | 282 |

MKP20 | 0 | 0 | 0 | 0 | 0 | 0 | 112 | 155 | 105 | 167 | 127 | 184 | 174 | 203 | 467 | 541 | 161 | 214 |

ID | ${\mathit{Z}}_{\mathit{opt}}$ | Native PSO | Shannon PSO | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{Z}}_{\mathit{max}}$ | ${\mathit{RPD}}_{\mathit{max}}$ | ${\mathit{Z}}_{\mathit{med}}$ | ${\mathit{RPD}}_{\mathit{med}}$ | ${\mathit{Z}}_{\mathit{avg}}$ | ${\mathit{RPD}}_{\mathit{avg}}$ | ${\mathit{Z}}_{\mathit{sd}}$ | ${\mathit{Z}}_{\mathit{max}}$ | ${\mathit{RPD}}_{\mathit{max}}$ | ${\mathit{Z}}_{\mathit{med}}$ | ${\mathit{RPD}}_{\mathit{med}}$ | ${\mathit{Z}}_{\mathit{avg}}$ | ${\mathit{RPD}}_{\mathit{avg}}$ | ${\mathit{Z}}_{\mathit{sd}}$ | ||

MKP01 | 6120 | 6120 | 0.00 | 6120 | 0.00 | 6120 | 0.00 | 0.00 | 6120 | 0.00 | 6120 | 0.00 | 6120 | 0.00 | 0.00 |

MKP02 | 12,400 | 12,240 | 0.00 | 12,400 | 0.00 | 12,396.45 | 0.00 | 4.86 | 12,240 | 0.00 | 12,400 | 0.00 | 12,399.03 | 0.00 | 3.01 |

MKP03 | 10,618 | 10,618 | 0.00 | 10,572 | 0.00 | 10,562.70 | 0.00 | 31.92 | 10,618 | 0.00 | 10,561 | 0.00 | 10,565.51 | 0.00 | 31.29 |

MKP04 | 16,537 | 16,516 | 0.13 | 16,408 | 0.00 | 16,407.2 | 0.00 | 55.97 | 16,517 | 0.12 | 16,403 | 0.00 | 16,410.58 | 0.00 | 47.90 |

MKP05 | 8722 | 8674 | 0.55 | 8612 | 0.01 | 8609.90 | 0.01 | 27.63 | 8705 | 0.19 | 8608 | 0.01 | 8607.45 | 0.01 | 34.73 |

MKP06 | 98,796 | 98,796 | 0.00 | 98,796 | 0.00 | 97,473.16 | 0.01 | 1735.06 | 98,796 | 0.00 | 98,796 | 0.00 | 97,998.61 | 0.00 | 1503.18 |

MKP07 | 130,623 | 130,623 | 0.00 | 130,623 | 0.00 | 130,459.45 | 0.00 | 273.16 | 130,623 | 0.00 | 130,233 | 0.00 | 130,360.41 | 0.00 | 345.60 |

MKP08 | 1,095,445 | 1,074,459 | 1.92 | 1,063,435 | 0.02 | 1,063,110.38 | 0.02 | 5623.42 | 1,080,226 | 1.39 | 1,060,724 | 0.03 | 1061215.71 | 0.03 | 6497.72 |

MKP09 | 4115 | 4115 | 0.00 | 4115 | 0.00 | 4104.83 | 0.00 | 23.55 | 4115 | 0.00 | 4115 | 0.00 | 4105.74 | 0.00 | 21.94 |

MKP10 | 5567 | 5567 | 0.00 | 5567 | 0.00 | 5561.70 | 0.00 | 9.30 | 5567 | 0.00 | 5567 | 0.00 | 5561.67 | 0.00 | 9.34 |

MKP11 | 5605 | 5605 | 0.00 | 5603 | 0.00 | 5600.64 | 0.00 | 5.68 | 5605 | 0.00 | 5605 | 0.00 | 5601.45 | 0.00 | 5.43 |

MKP12 | 8633 | 8592 | 0.47 | 8523 | 0.01 | 8513.03 | 0.01 | 42.43 | 8595 | 0.44 | 8508 | 0.01 | 8507.32 | 0.01 | 42.17 |

MKP13 | 3090 | 3090 | 0.00 | 3060 | 0.00 | 3055.51 | 0.01 | 13.00 | 3090 | 0.00 | 3076 | 0.00 | 3063.06 | 0.00 | 22.04 |

MKP14 | 2139 | 2139 | 0.00 | 2122 | 0.00 | 2118.03 | 0.00 | 20.81 | 2139 | 0.00 | 2122 | 0.00 | 2118.70 | 0.00 | 17.56 |

MKP15 | 3418 | 3418 | 0.00 | 3388 | 0.00 | 3385.41 | 0.00 | 27.38 | 3418 | 0.00 | 3404 | 0.00 | 3382 | 0.01 | 26.40 |

MKP16 | 3186 | 3186 | 0.00 | 3173 | 0.00 | 3154.83 | 0.00 | 22.95 | 3186 | 0.00 | 3173 | 0.00 | 3165.03 | 0.00 | 25.08 |

MKP17 | unknown | 57,415 | - | 57,261 | - | 56,711.51 | - | 288.09 | 57,821 | - | 57,165 | - | 57,167.87 | - | 276.97 |

MKP18 | unknown | 60,421 | - | 59,544 | - | 59,505.48 | - | 342.39 | 60,423 | - | 59,743 | - | 59,766.22 | - | 268.25 |

MKP19 | unknown | 58,481 | - | 57,477 | - | 57,442.41 | - | 290.47 | 58,550 | - | 57,982 | - | 57,991.45 | - | 262.92 |

MKP20 | unknown | 58,880 | - | 58,325 | - | 58,321.22 | - | 338.59 | 59,021 | - | 58,363 | - | 58,336.61 | - | 318.37 |

ID | ${\mathit{Z}}_{\mathit{opt}}$ | Native BAT | Shannon BAT | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{Z}}_{\mathit{max}}$ | ${\mathit{RPD}}_{\mathit{max}}$ | ${\mathit{Z}}_{\mathit{med}}$ | ${\mathit{RPD}}_{\mathit{med}}$ | ${\mathit{Z}}_{\mathit{avg}}$ | ${\mathit{RPD}}_{\mathit{avg}}$ | ${\mathit{Z}}_{\mathit{sd}}$ | ${\mathit{Z}}_{\mathit{max}}$ | ${\mathit{RPD}}_{\mathit{max}}$ | ${\mathit{Z}}_{\mathit{med}}$ | ${\mathit{RPD}}_{\mathit{med}}$ | ${\mathit{Z}}_{\mathit{avg}}$ | ${\mathit{RPD}}_{\mathit{avg}}$ | ${\mathit{Z}}_{\mathit{sd}}$ | ||

MKP01 | 6120 | 6110 | 0.16 | 6010 | 0.01 | 5904.04 | 0.03 | 0.00 | 6120 | 0.00 | 6100 | 0.00 | 6017.61 | 0.01 | 0.00 |

MKP02 | 12,400 | 12,240 | 0.00 | 11,930 | 0.03 | 11,984.35 | 0.03 | 183.74 | 12,240 | 0.00 | 12,370 | 0.00 | 12,253.87 | 0.01 | 177.02 |

MKP03 | 10618 | 10,520 | 0.92 | 10,359 | 0.02 | 10,359.96 | 0.02 | 4.79 | 10,604 | 0.13 | 10,481 | 0.01 | 10,462.77 | 0.01 | 4.50 |

MKP04 | 16,537 | 16357 | 1.09 | 16,088 | 0.02 | 15,836.74 | 0.04 | 22.34 | 16,511 | 0.16 | 16,382 | 0.00 | 16,302.12 | 0.01 | 27.41 |

MKP05 | 8722 | 8568 | 1.77 | 8410 | 0.03 | 8405.77 | 0.03 | 42.56 | 8711 | 0.13 | 8663 | 0.00 | 8657.03 | 0.00 | 41.11 |

MKP06 | 98,796 | 94,348 | 4.50 | 91,618 | 0.07 | 89,691.32 | 0.09 | 196.63 | 98,796 | 0.00 | 94,738 | 0.04 | 95,067.19 | 0.03 | 35.85 |

MKP07 | 130,623 | 124,530 | 4.66 | 120,399 | 0.07 | 11,9467.67 | 0.08 | 4368.55 | 130,623 | 0.00 | 125,360 | 0.04 | 125,990.06 | 0.03 | 3655.85 |

MKP08 | 1,095,445 | 1,088,227 | 0.66 | 1,066,018 | 0.02 | 106,5867.29 | 0.02 | 4676.20 | 1,095,206 | 0.02 | 1,090,905 | 0.00 | 1,090,574.74 | 0.00 | 109.14 |

MKP09 | 4115 | 4080 | 0.85 | 4013 | 0.02 | 3983.96 | 0.03 | 56.62 | 4115 | 0.00 | 4115 | 0.00 | 4084.16 | 0.00 | 43.97 |

MKP10 | 5567 | 5567 | 0.00 | 5412 | 0.02 | 5398 | 0.03 | 1358.46 | 5567 | 0.00 | 5567 | 0.00 | 5545.80 | 0.00 | 224.29 |

MKP11 | 5605 | 5605 | 0.00 | 5452 | 0.02 | 5425.70 | 0.03 | 63.94 | 5605 | 0.00 | 5592 | 0.00 | 5557.51 | 0.00 | 20.02 |

MKP12 | 8633 | 8633 | 0.00 | 8410 | 0.02 | 8404.83 | 0.02 | 86.32 | 8633 | 0.00 | 8619 | 0.00 | 8612.48 | 0.00 | 41.79 |

MKP13 | 3090 | 3090 | 0.00 | 3008 | 0.02 | 3006 | 0.02 | 52.02 | 3090 | 0.00 | 3076 | 0.00 | 3063.06 | 0.00 | 52.16 |

MKP14 | 2139 | 2139 | 0.00 | 2079 | 0.02 | 2075.96 | 0.02 | 49.58 | 2139 | 0.00 | 2085 | 0.02 | 2097.74 | 0.01 | 56.23 |

MKP15 | 3418 | 3388 | 0.88 | 3316 | 0.02 | 3314.12 | 0.03 | 83.68 | 3418 | 0.00 | 3335 | 0.02 | 3330.09 | 0.02 | 92.92 |

MKP16 | 3186 | 3119 | 2.10 | 3073 | 0.02 | 3066.38 | 0.03 | 11210.30 | 3186 | 0.00 | 3094 | 0.02 | 3101.03 | 0.02 | 2991.02 |

MKP17 | unknown | 58,192 | - | 56,908 | - | 56,948.19 | - | 101.16 | 42,406 | - | 58,821 | - | 58,749.51 | - | 55.13 |

MKP18 | unknown | 60,502 | - | 59,380 | - | 59,374.67 | - | 92.26 | 60,423 | - | 61,098 | - | 61,041.671 | - | 56.33 |

MKP19 | unknown | 58,639 | - | 58,025 | - | 57,967.83 | - | 82.14 | 60,018 | - | 59,484 | - | 59,468.61 | - | 13.03 |

MKP20 | unknown | 59,402 | - | 58,089 | - | 58,048.77 | - | 40.61 | 60,654 | - | 60,151 | - | 60,105.80 | - | 13.47 |

ID | ${\mathit{Z}}_{\mathit{opt}}$ | Native BH | Shannon BH | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{Z}}_{\mathit{max}}$ | ${\mathit{RPD}}_{\mathit{max}}$ | ${\mathit{Z}}_{\mathit{med}}$ | ${\mathit{RPD}}_{\mathit{med}}$ | ${\mathit{Z}}_{\mathit{avg}}$ | ${\mathit{RPD}}_{\mathit{avg}}$ | ${\mathit{Z}}_{\mathit{sd}}$ | ${\mathit{Z}}_{\mathit{max}}$ | ${\mathit{RPD}}_{\mathit{max}}$ | ${\mathit{Z}}_{\mathit{med}}$ | ${\mathit{RPD}}_{\mathit{med}}$ | ${\mathit{Z}}_{\mathit{avg}}$ | ${\mathit{RPD}}_{\mathit{avg}}$ | ${\mathit{Z}}_{\mathit{sd}}$ | ||

MKP01 | 6120 | 6110 | 0.00 | 6090 | 0.00 | 6083.22 | 0.00 | 30.48 | 6120 | 0.00 | 6090 | 0.00 | 6083.22 | 0.00 | 31.82 |

MKP02 | 12,400 | 12,240 | 1.29 | 12,100 | 0.02 | 12,084.03 | 0.02 | 98.62 | 12,360 | 0.32 | 12,100 | 0.02 | 12,091.77 | 0.02 | 118.87 |

MKP03 | 10,618 | 10,584 | 0.32 | 10,374 | 0.02 | 10,385.54 | 0.02 | 57.29 | 10,532 | 0.81 | 10,388 | 0.02 | 10,394.45 | 0.02 | 52.43 |

MKP04 | 16,537 | 16,234 | 1.83 | 16,017 | 0.03 | 16,046.80 | 0.02 | 97.87 | 16,252 | 1.72 | 16,028 | 0.03 | 16,038.03 | 0.03 | 84.18 |

MKP05 | 8722 | 8293 | 4.92 | 8124 | 0.06 | 8128.12 | 0.06 | 76.63 | 8417 | 3.50 | 8123 | 0.06 | 8140.32 | 0.06 | 113.49 |

MKP06 | 98,796 | 94,348 | 4.50 | 92,942 | 0.05 | 92,906.19 | 0.05 | 644.72 | 98,346 | 0.46 | 92,777 | 0.06 | 92,927.83 | 0.05 | 1330.35 |

MKP07 | 130,623 | 127,943 | 2.05 | 123,910 | 0.05 | 124,179.48 | 0.04 | 1937.12 | 127,953 | 2.04 | 124,462 | 0.04 | 124,476.41 | 0.04 | 2036.33 |

MKP08 | 1,095,445 | 998,864 | 8.82 | 1,006,919 | 0.08 | 1,007,945.67 | 0.07 | 12,822.05 | 999,278 | 8.78 | 1,001,572 | 0.08 | 1,004,224.58 | 0.08 | 10,919.46 |

MKP09 | 4115 | 4115 | 0.00 | 4024 | 0.02 | 4014.70 | 0.02 | 63.56 | 4115 | 0.00 | 4024 | 0.02 | 4030.93 | 0.02 | 50.38 |

MKP10 | 5567 | 5381 | 3.34 | 5214 | 0.06 | 5227.35 | 0.06 | 61.07 | 5407 | 2.87 | 5233 | 0.05 | 5251.25 | 0.05 | 81.32 |

MKP11 | 5605 | 5494 | 1.98 | 5308 | 0.05 | 5317.06 | 0.05 | 76.91 | 5450 | 2.77 | 5282 | 0.05 | 5301.03 | 0.05 | 62.07 |

MKP12 | 8633 | 8170 | 5.36 | 7902 | 0.08 | 7891.19 | 0.08 | 129.37 | 8595 | 0.44 | 8508 | 0.01 | 8507.32 | 0.01 | 42.17 |

MKP13 | 3090 | 3059 | 1.00 | 3026 | 0.02 | 3024.16 | 0.02 | 19.43 | 3090 | 0.00 | 3076 | 0.00 | 3063.06 | 0.00 | 22.04 |

MKP14 | 2139 | 2139 | 0.00 | 2122 | 0.00 | 2115.48 | 0.01 | 19.06 | 2139 | 0.00 | 2122 | 0.00 | 2118.70 | 0.00 | 17.56 |

MKP15 | 3418 | 3388 | 0.88 | 3356 | 0.01 | 3351.22 | 0.01 | 20.72 | 3418 | 0.00 | 3388 | 0.00 | 3382 | 0.01 | 23.39 |

MKP16 | 3186 | 3114 | 2.26 | 3070 | 0.03 | 3071.96 | 0.03 | 20.53 | 3186 | 0.00 | 3173 | 0.00 | 3165.03 | 0.00 | 25.08 |

MKP17 | unknown | 56,455 | - | 55,719 | - | 55,784.29 | - | 303.38 | 56,633 | - | 55,784 | - | 55,865.22 | - | 340.99 |

MKP18 | unknown | 58,921 | - | 58,149 | - | 58,132.38 | - | 264.85 | 59,097 | - | 58,102 | - | 58,192.51 | - | 342.95 |

MKP19 | unknown | 57,653 | - | 56,699 | - | 56,681.19 | - | 341.39 | 57,859 | - | 56,740 | - | 56,859 | - | 370.84 |

MKP20 | unknown | 57,337 | - | 56,861 | - | 56,859.54 | - | 280.80 | 57,597 | - | 56,948 | - | 56,908.64 | - | 345.66 |

ID | Native Methods | Shannon Strategy | ||||
---|---|---|---|---|---|---|

PSO | BAT | BH | S–PSO | S–BAT | S–BH | |

MKP01 | ∼0 | – | 0.00367 | – | – | – |

MKP02 | – | 0.04057 | – | ∼0 | ∼0 | ∼0 |

MKP03 | ∼0 | – | 0.00291 | – | ∼0 | – |

MKP04 | ∼0 | ∼0 | ∼0 | 0.00065 | – | ∼0 |

MKP05 | – | – | ∼0 | 0.00982 | – | – |

MKP06 | ∼0 | 0.00083 | ∼0 | ∼0 | 0.00072 | ∼0 |

MKP07 | ∼0 | 0.00065 | ∼0 | ∼0 | 0.0026 | ∼0 |

MKP08 | ∼0 | – | ∼0 | 0.0002 | – | – |

MKP09 | – | 0.0005 | – | 0.0082 | ∼0 | ∼0 |

MKP10 | ∼0 | – | ∼0 | 0.00712 | 0.00033 | – |

MKP11 | ∼0 | 0.00629 | – | ∼0 | 0.00037 | ∼0 |

MKP12 | – | – | ∼0 | – | 0.00001 | – |

MKP13 | 0.00036 | 0.0034 | – | 0.00036 | 0.00126 | 0.00126 |

MKP14 | 0.00011 | ∼0 | 0.00086 | 0.00011 | 0.00266 | 0.00015 |

MKP15 | 0.01802 | – | 0.00917 | 0.01802 | – | 0.00257 |

MKP16 | 0.00002 | ∼0 | 0.0054 | 0.00002 | ∼0 | 0.00002 |

MKP17 | – | ∼0 | ∼0 | 0.0006 | 0.03037 | – |

MKP18 | ∼0 | ∼0 | – | 0.00054 | 0.00076 | ∼0 |

MKP19 | ∼0 | 0.00658 | ∼0 | 0.06661 | 0.0012 | ∼0 |

MKP20 | ∼0 | 0.0054 | ∼0 | 0.0004 | ∼0 | – |

ID | PSO vs. S–PSO | BAT vs. S–BAT | BH vs. S–BH |
---|---|---|---|

MKP01 | – | 2.9581384$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ | – |

MKP02 | 0.00014 | 3.9834857$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-7}$ | – |

MKP03 | – | 6.1540486$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}$ | – |

MKP04 | – | 2.9163915$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-11}$ | – |

MKP05 | – | 6.6611161$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | – |

MKP06 | 0.00573 | 1.5107026$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | – |

MKP07 | – | 9.5509242$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-8}$ | – |

MKP08 | – | 1.4444445$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ | – |

MKP09 | – | 4.7065594$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ | – |

MKP10 | – | 3.1609970$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-11}$ | – |

MKP11 | – | 4.9246126$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}$ | – |

MKP12 | – | 1.1318991$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-10}$ | 6.6650018$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-13}$ |

MKP13 | 0.00908663513 | 5.1131699$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ | 4.8034849$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-8}$ |

MKP14 | – | 0.0037256 | – |

MKP15 | – | 0.0208799 | 1.5990313$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$ |

MKP16 | – | 0.0049714 | 5.8935079$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ |

MKP17 | 2.6426213$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ | 6.6571193$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | – |

MKP18 | 1.4444445$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | 1.0824563$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | – |

MKP19 | 2.9162619$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ | 6.6688876$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | – |

MKP20 | 1.0321732$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-11}$ | 7.3535622$\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ | – |

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**MDPI and ACS Style**

Olivares, R.; Soto, R.; Crawford, B.; Riquelme, F.; Munoz, R.; Ríos, V.; Cabrera, R.; Castro, C.
Entropy–Based Diversification Approach for Bio–Computing Methods. *Entropy* **2022**, *24*, 1293.
https://doi.org/10.3390/e24091293

**AMA Style**

Olivares R, Soto R, Crawford B, Riquelme F, Munoz R, Ríos V, Cabrera R, Castro C.
Entropy–Based Diversification Approach for Bio–Computing Methods. *Entropy*. 2022; 24(9):1293.
https://doi.org/10.3390/e24091293

**Chicago/Turabian Style**

Olivares, Rodrigo, Ricardo Soto, Broderick Crawford, Fabián Riquelme, Roberto Munoz, Víctor Ríos, Rodrigo Cabrera, and Carlos Castro.
2022. "Entropy–Based Diversification Approach for Bio–Computing Methods" *Entropy* 24, no. 9: 1293.
https://doi.org/10.3390/e24091293