# Adaptive Incremental Genetic Algorithm for Task Scheduling in Cloud Environments

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## Abstract

**:**

## 1. Introduction

## 2. Task Scheduling Problem

## 3. Adaptive Incremental Genetic Algorithm

#### 3.1. Encoding

#### 3.2. Fitness Function

#### 3.3. Select

#### 3.4. Crossover

#### 3.5. Mutation

- (1)
- Initialize GA parameters: Initialize the population size, crossover rate, mutation rate, max generation, etc.
- (2)
- Initialize job list: Each job is a set of tasks and the number of tasks is equal to the predefined interval size. Define the maximum iteration as the value that max generation divided by the number of jobs (also other finite bound can be used).
- (3)
- Optimization stage: For each job in the job list, use adaptive GA to optimize the scheduling problem. After randomly generating or initializing the population based on Max-Min, do select, crossover, mutation and record the best individual until the iteration reach the maximum value. Notice that, before handling the next job, the virtual machines’ occupation times should be updated by the optimal solution of the previous job.

Algorithm 1 Incremental Genetic Algorithm |

Input: Population size $Np$, max iteration, objective function, control parameters, task list T, VM types, interval size;Output: The global best solution;1: Choose tasks from T, the number of tasks equals to the interval size; 2: Initialize the population P 3: Evaluate each individual in P 4: while iteration < max generation do5: for each individual in P do6: Calculate the $probability$ to be chosen; 7: if $rand(0,1)<probability$ then8: Select the individual to the new population ${P}^{\prime}$; 9: end if10: end for11: Sort ${P}^{\prime}$ according to fitness 12: Calculate the mutation and crossover rate of each individual; 13: for each individual in ${P}^{\prime}$ do14: if $rand(0,1)<crossoverrate$ then15: Perform crossover; 16: end if17: if $rand(0,1)<mutationrate$ then18: Perform mutation; 19: end if20: end for21: Update the global best solution; iteration++; 22: end while23: Update the occupation time of each virtual machine |

## 4. Experimental Result

## 5. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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Instance Type | CU | |
---|---|---|

1 | c3:large | 7 |

2 | c3:xlarge | 14 |

3 | c3:2xlarge | 28 |

4 | c3:3xlarge | 55 |

5 | c3:4xlarge | 108 |

6 | c4:large | 8 |

7 | c4:xlarge | 16 |

8 | c4:2xlarge | 31 |

9 | c4:4xlarge | 62 |

10 | c4:8xlarge | 132 |

VM0 | VM1 | VM2 | VM3 | VM4 | VM5 | VM6 | VM7 | VM8 | VM9 | |
---|---|---|---|---|---|---|---|---|---|---|

0 | 101.75 | 50.88 | 26.26 | 13.13 | 6.17 | 116.29 | 58.14 | 29.07 | 14.8 | 7.54 |

1 | 55.88 | 27.94 | 14.42 | 7.21 | 3.39 | 63.86 | 31.93 | 15.96 | 8.13 | 4.14 |

2 | 76.25 | 38.13 | 19.68 | 9.84 | 4.62 | 87.14 | 43.57 | 21.79 | 11.09 | 5.65 |

3 | 39.88 | 19.94 | 10.29 | 5.15 | 2.42 | 45.57 | 22.79 | 11.39 | 5.8 | 2.95 |

4 | 109.5 | 54.75 | 28.26 | 14.13 | 6.64 | 125.14 | 62.57 | 31.29 | 15.93 | 8.11 |

5 | 86.5 | 43.25 | 22.32 | 11.16 | 5.24 | 98.86 | 49.43 | 24.71 | 12.58 | 6.41 |

6 | 82.88 | 41.44 | 21.39 | 10.69 | 5.02 | 94.71 | 47.36 | 23.68 | 12.05 | 6.14 |

7 | 78.88 | 39.44 | 20.35 | 10.18 | 4.78 | 90.14 | 45.07 | 22.54 | 11.47 | 5.84 |

8 | 78.25 | 39.13 | 20.19 | 10.1 | 4.74 | 89.43 | 44.71 | 22.36 | 11.38 | 5.8 |

9 | 81.88 | 40.94 | 21.13 | 10.56 | 4.96 | 93.57 | 46.79 | 23.39 | 11.91 | 6.06 |

MR | SGA | AIGA |
---|---|---|

0.1 | 594.933 | 355.407 |

0.2 | 373.862 | 350.565 |

0.3 | 372.02 | 365.267 |

0.4 | 384.447 | 374.111 |

0.5 | 376.61 | 365.998 |

0.6 | 370.013 | 366.195 |

0.7 | 365.656 | 364.522 |

0.8 | 367.732 | 366.922 |

0.9 | 353.147 | 352.397 |

CR | SGA | AIGA |
---|---|---|

0.1 | 353.558 | 338.128 |

0.2 | 372.904 | 363.381 |

0.3 | 390.524 | 371.02 |

0.4 | 363.018 | 345.526 |

0.5 | 360.534 | 354.471 |

0.6 | 369.683 | 365.282 |

0.7 | 360.473 | 343.74 |

0.8 | 369.95 | 357.186 |

0.9 | 364.27 | 352.722 |

Number of Tasks | Min-Min | Max-Min | SGA | AIGA |
---|---|---|---|---|

100 | 128.23 | 118.2 | 118.756 | 117.592 |

5000 | 5993.54 | 5986.27 | 6242.097 | 5984.747 |

10,000 | 11,978.1 | 11,973.29 | 12,408.91 | 11,971.14 |

15,000 | 17,979.93 | 17,974.44 | 22,354.83 | 17,971.24 |

20,000 | 23,691.6 | 23,689.81 | 35,008.51 | 23,686.19 |

25,000 | 29,812.08 | 29,808.85 | 50,104.01 | 29,804.54 |

30,000 | 35,720.45 | 35,722.94 | 66,403.67 | 35,717.09 |

35,000 | 41,669.28 | 41,669.37 | 82,303.76 | 41,663.41 |

40,000 | 47,685.03 | 47,689.28 | 101,092.9 | 47,682.35 |

45,000 | 53,759.32 | 53,770.26 | 122,641.1 | 53,761.93 |

50,000 | 59,652.83 | 59,661.76 | 144,997.2 | 59,653.09 |

60,000 | 71,799.67 | 71,809.81 | 195,167.3 | 71,796.99 |

70,000 | 83,595.83 | 83,607.86 | 241,417.4 | 83,590.55 |

80,000 | 95,387.53 | 95,401.51 | 292,828.4 | 95,380.96 |

90,000 | 107,296.4 | 107,312.2 | 342,214.8 | 107,287.4 |

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## Share and Cite

**MDPI and ACS Style**

Duan, K.; Fong, S.; Siu, S.W.I.; Song, W.; Guan, S.S.-U.
Adaptive Incremental Genetic Algorithm for Task Scheduling in Cloud Environments. *Symmetry* **2018**, *10*, 168.
https://doi.org/10.3390/sym10050168

**AMA Style**

Duan K, Fong S, Siu SWI, Song W, Guan SS-U.
Adaptive Incremental Genetic Algorithm for Task Scheduling in Cloud Environments. *Symmetry*. 2018; 10(5):168.
https://doi.org/10.3390/sym10050168

**Chicago/Turabian Style**

Duan, Kairong, Simon Fong, Shirley W. I. Siu, Wei Song, and Steven Sheng-Uei Guan.
2018. "Adaptive Incremental Genetic Algorithm for Task Scheduling in Cloud Environments" *Symmetry* 10, no. 5: 168.
https://doi.org/10.3390/sym10050168