# Adaptive Incremental Genetic Algorithm for Task Scheduling in Cloud Environments

^{1}

^{2}

^{3}

^{*}

## 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

- Mell, P.; Grance, T. The NIST Definition of Cloud Computing. Available online: http://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-145.pdf (accessed on 15 March 2018).
- Radu, L.D. Green Cloud Computing: A Literature Survey. Symmetry
**2017**, 9, 295. [Google Scholar] [CrossRef] - Encalada, W.L.; Sequera, J.L.C. Model to Implement Virtual Computing Labs via Cloud Computing Services. Symmetry
**2017**, 9, 117. [Google Scholar] [CrossRef] - Gao, J.; Yi, R. Cloud generalized power ordered weighted average operator and its application to linguistic group decision-making. Symmetry
**2017**, 9, 156. [Google Scholar] [CrossRef] - Chu, P.M.; Cho, S.; Fong, S.; Park, Y.W.; Cho, K. 3D Reconstruction Framework for Multiple Remote Robots on Cloud System. Symmetry
**2017**, 9, 55. [Google Scholar] [CrossRef] - Aarts, E.; Korst, J.; Michiels, W. Simulated annealing. In Search Methodologies; Springer: Boston, MA, USA, 2005; pp. 187–210. [Google Scholar]
- He, X.; Sun, X.; Von Laszewski, G. QoS guided min-min heuristic for grid task scheduling. J. Comput. Sci. Tech.
**2003**, 18, 442–451. [Google Scholar] [CrossRef] - Mao, Y.; Chen, X.; Li, X. Max-min task scheduling algorithm for load balance in cloud computing. In Proceedings of the International Conference on Computer Science and Information Technology, Barcelona, Spain, 22–24 December 2014; Springer: New Delhi, India, 2014; pp. 457–465. [Google Scholar]
- Zhan, S.; Huo, H. Improved PSO-based task scheduling algorithm in cloud computing. J. Inf. Comput. Sci.
**2012**, 9, 3821–3829. [Google Scholar] - Zuo, X.; Zhang, G.; Tan, W. Self-adaptive learning PSO-based deadline constrained task scheduling for hybrid IaaS cloud. IEEE Trans. Autom. Sci. Eng.
**2014**, 11, 564–573. [Google Scholar] [CrossRef] - Chen, S.M.; Chien, C.Y. Parallelized genetic ant colony systems for solving the traveling salesman problem. Expert Syst. Appl.
**2011**, 38, 3873–3883. [Google Scholar] [CrossRef] - Tsai, P.W.; Pan, J.S.; Chen, S.M.; Liao, B.Y.; Hao, S.P. Parallel cat swarm optimization. In Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, China, 12–15 July 2008; pp. 3328–3333. [Google Scholar]
- Tsai, P.W.; Pan, J.S.; Chen, S.M.; Liao, B.Y. Enhanced parallel cat swarm optimization based on the Taguchi method. Expert Syst. Appl.
**2012**, 39, 6309–6319. [Google Scholar] [CrossRef] - Wu, L.; Wang, Y.J.; Yan, C.K. Performance Comparison of Energy-aware task scheduling with GA and CRO algorithms in Cloud Environment. Appl. Mech. Mater.
**2014**, 596, 204–208. [Google Scholar] [CrossRef] - Mahmood, A.; Khan, S.A. Hard Real-Time Task Scheduling in Cloud Computing Using an Adaptive Genetic Algorithm. Computers
**2017**, 6, 15. [Google Scholar] [CrossRef] - Karaboga, D.; Basturk, B. A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. J. Glob. Optim.
**2007**, 39, 459–471. [Google Scholar] [CrossRef] - Babu, K.R.; Samuel, P. Enhanced bee colony algorithm for efficient load balancing and scheduling in cloud. In Innovations in Bio-Inspired Computing and Applications; Springer: Cham, Switzerland, 2016; pp. 67–78. [Google Scholar]
- Navimipour, N.J. Task scheduling in the cloud environments based on an artificial bee colony algorithm. In Proceedings of the 2015 International Conference on Image Processing, Production and Computer Science, Istanbul, Turkey, 3–4 June 2015; pp. 38–44. [Google Scholar]
- Fidanova, S. Simulated annealing for grid scheduling problem. In Proceedings of the IEEE John Vincent Atanasoff 2006 International Symposium on Modern Computing, Sofia, Bulgaria, 3–6 October 2006; pp. 41–45. [Google Scholar]
- Mandal, T.; Acharyya, S. Optimal task scheduling in cloud computing environment: Meta heuristic approaches. In Proceedings of the 2015 2nd International Conference on Electrical Information and Communication Technology (EICT), Khulna, Bangladesh, 10–12 December 2015; pp. 24–28. [Google Scholar]
- Wang, S.; Liang, K.; Liu, J.K.; Chen, J.; Yu, J.; Xie, W. Attribute-based data sharing scheme revisited in cloud computing. IEEE Trans. Inf. Forensics Secur.
**2016**, 11, 1661–1673. [Google Scholar] [CrossRef] - Liang, K.; Liu, J.K.; Lu, R.; Wong, D.S. Privacy concerns for photo sharing in online social networks. IEEE Internet Comput.
**2015**, 19, 58–63. [Google Scholar] [CrossRef] - Liu, J.; Huang, X.; Liu, J.K. Secure sharing of personal health records in cloud computing: Ciphertext-policy attribute-based signcryption. Future Gener. Comput. Syst.
**2015**, 52, 67–76. [Google Scholar] [CrossRef] - Wen, J.; Lu, L.; Casale, G.; Smirni, E. Less can be more: Micro-managing vms in amazon EC2. In Proceedings of the 2015 IEEE 8th International Conference on Cloud Computing, New York, NY, USA, 27 June–2 July 2015; pp. 317–324. [Google Scholar]
- Amazon EC2 Pricing. Available online: https://aws.amazon.com/ec2/pricing/on-demand/?nc1=h_ls (accessed on 1 April 2018).
- Previous Generation Instances. Available online: https://aws.amazon.com/ec2/previous-generation/?nc1=h_ls (accessed on 1 April 2018).
- Srinivas, M.; Patnaik, L.M. Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans. Syst. Man Cybern.
**1994**, 24, 656–667. [Google Scholar] [CrossRef]

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 |

© 2018 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**

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