# A Reward Population-Based Differential Genetic Harmony Search Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Harmony Search Algorithm

#### 2.1. Parameters Involved in Harmony Search Algorithm

#### 2.2. Flow of Harmony Search Algorithm

Algorithm 1: HS Algorithm | |

1: | Initialize the algorithm parameters HMS, HMCR, PAR, BW, ${T}_{max}$ |

2: | Initialize the harmony memory. |

3: | Repeat |

4: | Improvise a new harmony as: |

5: | for all i, do |

6: | ${x}_{i}^{new}\to \left\{\begin{array}{c}\mathrm{memory}\phantom{\rule{4.pt}{0ex}}\mathrm{consideration}\phantom{\rule{4.pt}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}\mathrm{HMCR}\hfill \\ \mathrm{random}\phantom{\rule{4.pt}{0ex}}\mathrm{selection}\phantom{\rule{4.pt}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}1-\mathrm{HMCR}\hfill \end{array}\right.$ |

7: | $if\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}{x}_{i}^{new}\in $ HM, then |

8: | ${{x}^{\prime}}_{i}^{new}=\left\{\begin{array}{c}{x}_{i}^{new}\pm r\ast BW\phantom{\rule{2.em}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}\mathrm{PAR}\hfill \\ {x}_{i}^{new}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}1-\mathrm{PAR}\hfill \end{array}\right.$ |

9: | end if |

10: | end for |

11: | if the new harmony vector is better than the worst |

12: | one in the original HM, then |

13: | update harmony memory |

14: | end if |

15: | Until ${T}_{max}$ is fulfilled |

16: | Return best harmony |

## 3. Improved Harmony Search Algorithm

#### 3.1. Reward Population Harmony Search Algorithm (RHS)

#### 3.2. Differential Genetic Harmony Search Algorithm (DEGA-HS)

#### 3.2.1. Mutation of Differential Evolution

#### 3.2.2. Partheno-Genetic Algorithm

#### 3.2.3. Flow of DEGA-HS Algorithm

#### 3.3. Reward Population-Based Differential Genetic Harmony Search Algorithm (RDEGA-HS)

Algorithm 2: RDEGA-HS Algorithm | |

1: | Initialize the algorithm parameters |

2: | Initialize the total harmony memory |

3: | For $Pop=\cup Po{p}_{i}$ |

4: | Repeat |

5: | While time(2) $<{T}_{max}^{2}$, do |

6: | Improvise each new harmony as follows: |

7: | While time(1)$<{T}_{max}^{1}$ |

8: | For all j, do |

9: | ${x}_{j}^{new}=\left\{\begin{array}{c}{x}_{j}^{best}+F({x}_{j}^{k}-{x}_{j}^{l})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}\mathrm{HMCR}\hfill \\ \mathrm{random}\phantom{\rule{4.pt}{0ex}}\mathrm{selection}\phantom{\rule{4.pt}{0ex}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{2.em}{0ex}}\hspace{1em}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}1-\mathrm{HMCR}\hfill \end{array}\right.$ |

10: | If with probability HMCR, then |

11: | ${{x}^{\prime}}_{j}^{new}=\left\{\begin{array}{c}{x}_{j}^{rand}+F({x}_{j}^{k}-{x}_{j}^{l})\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}\mathrm{PAR}\hfill \\ {x}_{j}^{new}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{2.em}{0ex}}\hspace{1em}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}1-\mathrm{PAR}\hfill \end{array}\right.$ |

12: | Else, do |

13: | ${{x}^{\prime}}_{j}^{new}=\left\{\begin{array}{c}operation\phantom{\rule{3.33333pt}{0ex}}of\phantom{\rule{3.33333pt}{0ex}}parthenogenetic\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\hspace{1em}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}\mathrm{PAR}\hfill \\ {x}_{j}^{new}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{with}\phantom{\rule{4.pt}{0ex}}\mathrm{probability}\phantom{\rule{4.pt}{0ex}}1-\mathrm{PAR}\hfill \end{array}\right.$ |

14: | End If |

15: | End For |

16: | If the new harmony vector is better than the worst one in the |

17: | original HM, then |

18: | update the harmony memory |

19: | End If |

20: | End while |

21: | Update the reward harmony memory |

22: | End While |

23: | End For |

24: | Return best harmony |

## 4. Experiments

#### 4.1. Effects of HMS and HMCR on Performance of RDEGA-HS

#### 4.2. Comparative Study on RDEGA-HS and HS Variants

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Change in average optimal fitness value of the Schwefel function with the number of iterations.

Function Name | Formulation | Search Range |
---|---|---|

Ackley | $\begin{array}{c}f\left(x\right)=-20exp\left(-0.2\sqrt{\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{x}_{i}^{2}}\right)\hfill \\ \phantom{\rule{2.em}{0ex}}\phantom{\rule{1.em}{0ex}}-exp\left(\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}cos\left(2\pi {x}_{i}\right)\right)+20\hfill \end{array}$ | ${x}_{i}\in [-32,32]$ |

Griewank | $f\left(x\right)=1+\frac{1}{4000}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{x}_{i}^{2}-{\displaystyle {\displaystyle \prod}_{i=1}^{n}}cos\left(\frac{{x}_{i}}{\sqrt{i}}\right)$ | ${x}_{i}\in [-600,600]$ |

Rastrigin | $f\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{n}}[{x}_{i}^{2}-10cos\left(2\pi {x}_{i}\right)+10]$ | ${x}_{i}\in [-5.12,5.12]$ |

Rosenbrock | $f\left(x\right)={{\displaystyle \sum}}_{i=1}^{n}\left[100{\left({x}_{i+1}-{x}_{i}^{2}\right)}^{2}+{\left(1-{x}_{i}\right)}^{2}\right]$ | ${x}_{i}\in [-30,30]$ |

Sphere | $f\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{n}}{x}_{i}^{2}$ | ${x}_{i}\in [-100,100]$ |

Schwefel | $f\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{n}}\left|x\right|+{\displaystyle {\displaystyle \prod}_{i=1}^{n}}\left|x\right|$ | ${x}_{i}\in [-10,10]$ |

Funtion | HMS | |||||
---|---|---|---|---|---|---|

100 | 80 | 50 | 20 | 10 | 5 | |

Ackley | 9.26 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 5.44 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 1.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 5.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 1.02 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 8.84 |

1.20 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 5.57 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 8.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 1.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 9.54 | 2.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

Griewank | 5.16 $\times \phantom{\rule{4pt}{0ex}}{10}^{-10}$ | 1.35 $\times \phantom{\rule{4pt}{0ex}}{10}^{-11}$ | 2.46 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 9.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 8.89 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 5.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

9.25 | 1.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 5.12 | 1.26 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 5.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 6.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

Rastrigin | 1.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 1.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 1.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 1.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 1.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 1.91 |

3.21 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 5.57 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 1.05 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 5.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 4.89 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 6.27 | |

Rosenbrock | 9.99 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 8.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 1.38 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 7.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 3.63 | 8.74 |

7.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 1.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 4.21 | 2.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 9.79 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 1.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

Sphere | 3.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-37}$ | 1.03 $\times \phantom{\rule{4pt}{0ex}}{10}^{-40}$ | 5.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 6.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 7.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 8.47 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ |

6.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ | 5.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | 7.48 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ | 6.42 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | 3.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-24}$ | 5.49 $\times \phantom{\rule{4pt}{0ex}}{10}^{-20}$ | |

Schwefel | 5.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 2.51 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 4.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 7.69 $\times \phantom{\rule{4pt}{0ex}}{10}^{-31}$ | 3.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | 4.16 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ |

5.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | 4.87 $\times \phantom{\rule{4pt}{0ex}}{10}^{-31}$ | 7.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | 1.36 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | 8.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | 2.65 $\times \phantom{\rule{4pt}{0ex}}{10}^{-24}$ |

Function | HMCR | |||||
---|---|---|---|---|---|---|

0.9 | 0.8 | 0.6 | 0.5 | 0.3 | 0.1 | |

Ackley | 4.26 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 8.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 9.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 3.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 9.88 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 6.54 |

9.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 4.51 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 5.89 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 5.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 1.25 | 6.66 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

Griewank | 2.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-10}$ | 7.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 1.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 5.65 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 6.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 2.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ |

7.33 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 9.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 1.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 6.85 | 8.98 | 4.65 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

Rastrigin | 9.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-9}$ | 7.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 8.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 3.69 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 9.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 7.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ |

2.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 8.96 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 2.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 6.66 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 2.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 8.95 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | |

Rosenbrock | 7.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 8.75 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 2.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 9.87 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 2.6 | 8.74 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ |

1.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 6.87 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 8.95 | 6.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 1.26 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 9.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

Sphere | 2.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-39}$ | 8.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 5.64 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 9.87 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 6.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-31}$ | 5.36 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ |

7.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | 5.42 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | 6.46 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | 3.38 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | 5.10 $\times \phantom{\rule{4pt}{0ex}}{10}^{-23}$ | 3.86 $\times \phantom{\rule{4pt}{0ex}}{10}^{-21}$ | |

Schwefel | 5.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 6.04 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 9.40 $\times \phantom{\rule{4pt}{0ex}}{10}^{-31}$ | 3.20 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | 1.65 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | 9.69 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ |

2.31 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | 3.94 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ | 4.48 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | 9.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | 4.31 $\times \phantom{\rule{4pt}{0ex}}{10}^{-23}$ | 1.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-22}$ |

Algorithm | Dimensions | Theoretical Optimum | Mean Optimum | Standard Deviation |
---|---|---|---|---|

HS | 30 | 0 | 3.66 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 2.35 |

40 | 0 | 3.55 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 3.51 | |

50 | 0 | 1.25 | 4.21 | |

60 | 0 | 3.35 | 3.23 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

70 | 0 | 8.70 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 5.64 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

80 | 0 | 9.49 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 6.43 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

RHS | 30 | 0 | 2.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 5.33 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 1.02 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 6.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 1.01 | 4.22 | |

60 | 0 | 8.25 | 1.10 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

70 | 0 | 6.59 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 4.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

80 | 0 | 1.88 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 3.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{3}$ | |

DEGA-HS | 30 | 0 | 8.20 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 2.03 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 1.22 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 6.01 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | |

50 | 0 | 1.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 8.85 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

60 | 0 | 7.22 | 6.43 | |

70 | 0 | 6.96 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 7.80 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

80 | 0 | 1.69 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 9.72 $\times \phantom{\rule{4pt}{0ex}}{10}^{3}$ | |

RDEGA-HS | 30 | 0 | 2.67 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 1.22 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ |

40 | 0 | 5.44 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 3.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | |

50 | 0 | 9.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 5.26 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

60 | 0 | 2.29 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 4.14 | |

70 | 0 | 9.61 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 2.34 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

80 | 0 | 5.77 | 1.22 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ |

Algorithm | Dimensions | Theoretical Optimum | Average Optimum | Standard Deviation |
---|---|---|---|---|

HS | 30 | 0 | 4.00 $\times \phantom{\rule{4pt}{0ex}}{10}^{-11}$ | 1.00 |

40 | 0 | 6.02 $\times \phantom{\rule{4pt}{0ex}}{10}^{-9}$ | 1.50 | |

50 | 0 | 1.38 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 2.64 | |

60 | 0 | 4.86 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 7.16 | |

70 | 0 | 5.99 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 5.99 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

80 | 0 | 6.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 7.94 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

RHS | 30 | 0 | 3.13 $\times \phantom{\rule{4pt}{0ex}}{10}^{-10}$ | 5.19 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ |

40 | 0 | 1.66 $\times \phantom{\rule{4pt}{0ex}}{10}^{-9}$ | 7.73 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 7.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-9}$ | 1.15 | |

60 | 0 | 2.06 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 7.52 | |

70 | 0 | 6.34 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 7.93 | |

80 | 0 | 4.54 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 1.87 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

DEGA-HS | 30 | 0 | 8.82 $\times \phantom{\rule{4pt}{0ex}}{10}^{-11}$ | 2.15 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ |

40 | 0 | 2.08 $\times \phantom{\rule{4pt}{0ex}}{10}^{-10}$ | 5.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 1.08 $\times \phantom{\rule{4pt}{0ex}}{10}^{-9}$ | 7.96 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

60 | 0 | 8.90 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 8.11 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

70 | 0 | 8.22 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 4.48 | |

80 | 0 | 7.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 5.21 | |

RDEGA-HS | 30 | 0 | 1.13 $\times \phantom{\rule{4pt}{0ex}}{10}^{-12}$ | 1.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 1.35 $\times \phantom{\rule{4pt}{0ex}}{10}^{-11}$ | 1.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 1.35 $\times \phantom{\rule{4pt}{0ex}}{10}^{-10}$ | 2.29 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

60 | 0 | 7.44 $\times \phantom{\rule{4pt}{0ex}}{10}^{-9}$ | 7.67 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

70 | 0 | 4.93 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 9.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

80 | 0 | 8.01 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 1.36 |

Algorithm | Dimensions | Theoretical Optimum | Average Optimum | Standard Deviation |
---|---|---|---|---|

HS | 30 | 0 | 1.39 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 3.32 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 8.52 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 4.98 | |

50 | 0 | 2.86 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 8.75 | |

60 | 0 | 5.20 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 6.11 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

70 | 0 | 5.38 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 4.85 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

80 | 0 | 3.59 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 8.09 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

RHS | 30 | 0 | 4.02 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 1.72 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ |

40 | 0 | 8.30 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 2.56 | |

50 | 0 | 3.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 3.80 | |

60 | 0 | 4.32 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 8.60 | |

70 | 0 | 2.73 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 4.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

80 | 0 | 5.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 5.87 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

DEGA-HS | 30 | 0 | 9.46 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 7.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 2.09 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 1.74 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 1.03 $\times \phantom{\rule{4pt}{0ex}}{10}^{-5}$ | 2.64 | |

60 | 0 | 4.81 $\times \phantom{\rule{4pt}{0ex}}{10}^{-4}$ | 7.34 | |

70 | 0 | 9.85 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 1.67 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

80 | 0 | 6.95 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 5.74 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

RDEGA-HS | 30 | 0 | 1.46 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 4.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ |

40 | 0 | 1.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-8}$ | 5.57 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | |

50 | 0 | 1.06 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 7.60 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

60 | 0 | 8.34 $\times \phantom{\rule{4pt}{0ex}}{10}^{-7}$ | 4.21 | |

70 | 0 | 4.63 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 7.84 | |

80 | 0 | 9.85 $\times \phantom{\rule{4pt}{0ex}}{10}^{-6}$ | 8.73 |

Algorithm | Dimensions | Theoretical Optimum | Average Optimum | Standard Deviation |
---|---|---|---|---|

HS | 30 | 0 | 8.43 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 6.36 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 4.82 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 4.65 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 2.86 | 6.80 | |

60 | 0 | 7.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 9.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

70 | 0 | 7.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 9.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

80 | 0 | 5.23 $\times \phantom{\rule{4pt}{0ex}}{10}^{3}$ | 7.35 $\times \phantom{\rule{4pt}{0ex}}{10}^{3}$ | |

RHS | 30 | 0 | 4.08 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 2.77 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 4.68 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 8.47 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

50 | 0 | 6.93 | 3.72 | |

60 | 0 | 9.63 | 5.71 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

70 | 0 | 3.72 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 6.62 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

80 | 0 | 7.52 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 5.04 $\times \phantom{\rule{4pt}{0ex}}{10}^{3}$ | |

DEGA-HS | 30 | 0 | 7.77 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 7.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ |

40 | 0 | 2.67 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 2.91 | |

50 | 0 | 6.12 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 6.84 | |

60 | 0 | 1.55 | 8.15 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

70 | 0 | 7.15 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 3.43 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | |

80 | 0 | 7.02 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ | 1.48 $\times \phantom{\rule{4pt}{0ex}}{10}^{3}$ | |

RDEGA-HS | 30 | 0 | 2.21 $\times \phantom{\rule{4pt}{0ex}}{10}^{-3}$ | 9.98 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ |

40 | 0 | 9.04 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | 4.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-2}$ | |

50 | 0 | 2.53 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | 9.10 $\times \phantom{\rule{4pt}{0ex}}{10}^{-1}$ | |

60 | 0 | 5.90 | 5.78 | |

70 | 0 | 1.31 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 1.74 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | |

80 | 0 | 8.33 $\times \phantom{\rule{4pt}{0ex}}{10}^{1}$ | 4.77 $\times \phantom{\rule{4pt}{0ex}}{10}^{2}$ |

Algorithm | Dimensions | Theoretical Optimum | Average Optimum | Standard Deviation |
---|---|---|---|---|

HS | 30 | 0 | 8.72 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 3.26 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ |

40 | 0 | 9.21 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 1.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

50 | 0 | 4.11 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 3.67 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

60 | 0 | 8.42 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 1.63 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

70 | 0 | 8.16 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 1.09 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | |

80 | 0 | 2.91 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 1.28 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | |

RHS | 30 | 0 | 2.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 2.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ |

40 | 0 | 6.49 $\times \phantom{\rule{4pt}{0ex}}{10}^{-37}$ | 2.06 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

50 | 0 | 1.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 1.63 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

60 | 0 | 4.80 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 3.32 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

70 | 0 | 7.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 2.46 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

80 | 0 | 3.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 2.33 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

DEGA-HS | 30 | 0 | 9.17 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 3.63 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ |

40 | 0 | 3.90 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 1.40 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

50 | 0 | 6.56 $\times \phantom{\rule{4pt}{0ex}}{10}^{-37}$ | 3.06 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

60 | 0 | 8.62 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 3.05 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

70 | 0 | 1.07 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 1.73 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

80 | 0 | 1.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 2.39 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

RDEGA-HS | 30 | 0 | 7.00 $\times \phantom{\rule{4pt}{0ex}}{10}^{-40}$ | 6.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-31}$ |

40 | 0 | 2.66 $\times \phantom{\rule{4pt}{0ex}}{10}^{-39}$ | 5.84 $\times \phantom{\rule{4pt}{0ex}}{10}^{-30}$ | |

50 | 0 | 2.77 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 2.27 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ | |

60 | 0 | 3.92 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 3.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

70 | 0 | 1.01 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 3.69 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ | |

80 | 0 | 3.89 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 8.51 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ |

Algorithm | Dimensions | Theoretical Optimum | Average Optimum | Standard Deviation |
---|---|---|---|---|

HS | 30 | 0 | 3.93 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 7.20 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ |

40 | 0 | 3.36 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 3.55 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | |

50 | 0 | 7.14 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 3.82 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | |

60 | 0 | 2.59 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 2.93 $\times \phantom{\rule{4pt}{0ex}}{10}^{-24}$ | |

70 | 0 | 1.58 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 3.07 $\times \phantom{\rule{4pt}{0ex}}{10}^{-23}$ | |

80 | 0 | 5.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-31}$ | 3.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-23}$ | |

RHS | 30 | 0 | 2.44 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 6.47 $\times \phantom{\rule{4pt}{0ex}}{10}^{-28}$ |

40 | 0 | 3.70 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 1.69 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | |

50 | 0 | 1.60 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 1.23 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | |

60 | 0 | 4.13 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 3.01 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | |

70 | 0 | 2.17 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 1.79 $\times \phantom{\rule{4pt}{0ex}}{10}^{-23}$ | |

80 | 0 | 4.43 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 3.38 $\times \phantom{\rule{4pt}{0ex}}{10}^{-23}$ | |

DEGA-HS | 30 | 0 | 4.63 $\times \phantom{\rule{4pt}{0ex}}{10}^{-38}$ | 9.70 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ |

40 | 0 | 9.97 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 1.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

50 | 0 | 3.25 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 8.49 $\times \phantom{\rule{4pt}{0ex}}{10}^{-27}$ | |

60 | 0 | 1.13 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 8.16 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | |

70 | 0 | 1.97 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 3.24 $\times \phantom{\rule{4pt}{0ex}}{10}^{-24}$ | |

80 | 0 | 5.93 $\times \phantom{\rule{4pt}{0ex}}{10}^{-32}$ | 2.29 $\times \phantom{\rule{4pt}{0ex}}{10}^{-22}$ | |

RDEGA-HS | 30 | 0 | 1.52 $\times \phantom{\rule{4pt}{0ex}}{10}^{-39}$ | 2.19 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ |

40 | 0 | 5.42 $\times \phantom{\rule{4pt}{0ex}}{10}^{-36}$ | 8.45 $\times \phantom{\rule{4pt}{0ex}}{10}^{-29}$ | |

50 | 0 | 3.76 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 3.19 $\times \phantom{\rule{4pt}{0ex}}{10}^{-26}$ | |

60 | 0 | 6.41 $\times \phantom{\rule{4pt}{0ex}}{10}^{-35}$ | 2.42 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | |

70 | 0 | 1.09 $\times \phantom{\rule{4pt}{0ex}}{10}^{-34}$ | 1.53 $\times \phantom{\rule{4pt}{0ex}}{10}^{-25}$ | |

80 | 0 | 3.20 $\times \phantom{\rule{4pt}{0ex}}{10}^{-33}$ | 2.06 $\times \phantom{\rule{4pt}{0ex}}{10}^{-24}$ |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Li, J.; Li, L.
A Reward Population-Based Differential Genetic Harmony Search Algorithm. *Algorithms* **2022**, *15*, 23.
https://doi.org/10.3390/a15010023

**AMA Style**

Zhang Y, Li J, Li L.
A Reward Population-Based Differential Genetic Harmony Search Algorithm. *Algorithms*. 2022; 15(1):23.
https://doi.org/10.3390/a15010023

**Chicago/Turabian Style**

Zhang, Yang, Jiacheng Li, and Lei Li.
2022. "A Reward Population-Based Differential Genetic Harmony Search Algorithm" *Algorithms* 15, no. 1: 23.
https://doi.org/10.3390/a15010023