雲端計算是資訊科技領域的熱門話題。雲端計算是一種商業模型，其可以動態且靈活地提供用戶大規模的計算和儲存服務。任務調度問題在雲端計算環境非常重要，因為它直接影響雲端計算系統的服務績效。在當前關於雲計算的任務調度問題的研究中，大多數學者僅考慮單一目標，例如最小化總成本或最小化完工時間。在現實世界中，雲端服務用戶或雲端服務提供商傾向於從多個方面衡量雲服務的質量。對於用戶而言，他們專注於如何以最低的價格獲得最快的服務，而雲端服務公司在追求客戶重視的目標時，也必須重視VM負載平衡的問題，因為VM負載不平衡可能會造成資源浪費，甚至會降低雲端系統的績效。為了解決上述問題，本研究建立了兩個最小化完工時間和最小化成本的目標及一個負載平衡的限制。此外，本研究採用簡化群體演算法中簡單且有效率的更新機制並結合非支配排序基因演算法（NSGAII）的非支配排序概念，發展了一種適用於多目標問題的非支配排序簡化群優化算法（NSSSO）。關於如何提高解的多樣性議題，本研究使用Cluster degree排序方法而非NSGAII的擁擠距離排序方法挑選解，因為使用擁擠距離排序法來挑選解可能會導致解的分佈較不均勻。

Cloud computing is a hot topic in the field of Information Technology. Cloud computing is a business model that provides users with large-scale computing and storage services in a dynamic and flexible way. Task scheduling problem in cloud computing is significantly important because it directly affects a cloud systems performance. In the current research on the task scheduling problem of cloud computing, most scholars only consider single goal, such as minimizing total cost or minimizing makespan. In the real world, cloud service users or cloud service providers tend to measure the quality of cloud services in many aspects. For users, they always focus on how to get the fastest service under the lowest price. In addition, cloud services company must put emphasis on the issue of VM load balancing while pursuing the goals that customers value because the uneven distribution of load to VMs will cause waste of resources and even degrade the performance of the cloud system. To solve the problems mentioned above, the study sets up two objectives of minimizing makespan and minimizing cost while setting the limit of degree of imbalance. Besides, this paper develops an algorithm called Non-dominated Sorting Simplified Swarm Optimization (NSSSO) for multi-objective problems, learning from the simple and efficient update mechanism of Simplified Swarm Optimization (SSO) algorithm, combining with the idea of non-dominated sorting of the Non-dominated Sorting Genetic Algorithm II (NSGAII). About how to enhance the diversity of solutions, the study uses the cluster degree sorting method instead of crowding distance sorting method to select solutions because crowding distance sorting method may result that solutions distribution is quite uneven.

Abstract I
List of Tables VI
List of Figures VII
Chaper 1 Introduction 1
1.1 Background and Motivation 1
1.2 Structure 5
Chaper 2 Literature Review 6
2.1 Task Scheduling Problem in Cloud Computing 6
2.2 Multi-Objective Algorithm in Task Scheduling Problem 7
2.3 NSGAII 8
2.3.1 Non-dominated sorting 9
2.3.2 Crowding-distance Sorting 10
2.4 Simplified Swarm Optimization 12
Chaper 3 Problem Statement 15
3.1 System Model 15
3.2 Notations 16
3.3 Mathematical Model 17
3.3.1 Makespan 17
3.3.2 Cost 18
3.3.3 Load Balancing 18
Chaper 4 Methodology 20
4.1 Cluster degree 20
4.2 Novel update mechanism of SSO 21
4.3 Proposed Non-dominated Sorting Simple Swarm Optimization 23
Chaper 5 Experiment Results & Analysis 28
5.1 Experiment Data 28
5.2 Performance metrics 28
5.3 Parameter Design 30
5.4 Experiment Result and Analysis 35
Chaper 6 Conclusion and Future works 42
6.1 Conclusion 42
6.2 Future Work 43
Reference 44
APPENDIX 48

1. Shawish, A. and M. Salama, Cloud computing: paradigms and technologies, in Inter-cooperative collective intelligence: Techniques and applications. 2014, Springer. p. 39-67.
2. Li, X., Cloud Computing: Introduction, Application and Security from Industry Perspectives. International Journal of Computer Science and Network Security, 2011. 11(5): p. 224-228.
3. Hunziker, D., et al. Rapyuta: The roboearth cloud engine. in 2013 IEEE international conference on robotics and automation. 2013. IEEE.
4. Sowmya, S., P. Deepika, and J. Naren, Layers of cloud–iaas, paas, and saas: A survey. International Journal of Computer Science and Information Technologies, 2014. 5(3): p. 4477-4480.
5. Rani, D. and R.K. Ranjan, A comparative study of SaaS, PaaS and IaaS in cloud computing. International Journal of Advanced Research in Computer Science and Software Engineering, 2014. 4(6).
6. Soltani, N., B. Soleimani, and B. Barekatain, Heuristic algorithms for task scheduling in cloud computing: a survey. International Journal of Computer Network and Information Security, 2017. 11(8): p. 16.
7. Buyya, R., R. Ranjan, and R.N. Calheiros. Modeling and simulation of scalable Cloud computing environments and the CloudSim toolkit: Challenges and opportunities. in 2009 international conference on high performance computing & simulation. 2009. IEEE.
8. Li, K., et al. Cloud task scheduling based on load balancing ant colony optimization. in 2011 Sixth Annual ChinaGrid Conference. 2011. IEEE.
9. Zhao, C., et al. Independent tasks scheduling based on genetic algorithm in cloud computing. in 2009 5th International Conference on Wireless Communications, Networking and Mobile Computing. 2009. IEEE.
10. Tawfeek, M.A., et al. Cloud task scheduling based on ant colony optimization. in 2013 8th international conference on computer engineering & systems (ICCES). 2013. IEEE.
11. Ramezani, F., J. Lu, and F.K. Hussain, Task-based system load balancing in cloud computing using particle swarm optimization. International journal of parallel programming, 2014. 42(5): p. 739-754.
12. Ding, J., L. Sha, and X. Chen. Modeling and evaluating IaaS Cloud using performance evaluation process Algebra. in 2016 22nd Asia-Pacific Conference on Communications (APCC). 2016. IEEE.
13. Mishra, S.K., et al. Time efficient dynamic threshold-based load balancing technique for Cloud Computing. in 2017 International Conference on Computer, Information and Telecommunication Systems (CITS). 2017. IEEE.
14. Ghomi, E.J., A.M. Rahmani, and N.N. Qader, Load-balancing algorithms in cloud computing: A survey. Journal of Network and Computer Applications, 2017. 88: p. 50-71.
15. Wu, Z., et al. A revised discrete particle swarm optimization for cloud workflow scheduling. in 2010 International Conference on Computational Intelligence and Security. 2010. IEEE.
16. Babu, K.R. and P. Samuel, Enhanced bee colony algorithm for efficient load balancing and scheduling in cloud, in Innovations in bio-inspired computing and applications. 2016, Springer. p. 67-78.
17. Panda, S.K. and P.K. Jana. A multi-objective task scheduling algorithm for heterogeneous multi-cloud environment. in 2015 International Conference on Electronic Design, Computer Networks & Automated Verification (EDCAV). 2015. IEEE.
18. Deb, K., et al., A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 2002. 6(2): p. 182-197.
19. Chen, B., et al., Modified differential evolution algorithm using a new diversity maintenance strategy for multi-objective optimization problems. Applied Intelligence, 2015. 43(1): p. 49-73.
20. Kukkonen, S. and K. Deb. Improved pruning of non-dominated solutions based on crowding distance for bi-objective optimization problems. in 2006 IEEE International Conference on Evolutionary Computation. 2006. IEEE.
21. Attiya, G. and Y. Hamam, Task allocation for maximizing reliability of distributed systems: A simulated annealing approach. Journal of parallel and Distributed Computing, 2006. 66(10): p. 1259-1266.
22. Singh, S. and M. Kalra. Scheduling of independent tasks in cloud computing using modified genetic algorithm. in 2014 International Conference on Computational Intelligence and Communication Networks. 2014. IEEE.
23. Zhan, S. and H. Huo, Improved PSO-based task scheduling algorithm in cloud computing. Journal of Information & Computational Science, 2012. 9(13): p. 3821-3829.
24. Liu, N., Z. Dong, and R. Rojas-Cessa. Task scheduling and server provisioning for energy-efficient cloud-computing data centers. in 2013 IEEE 33rd International Conference on Distributed Computing Systems Workshops. 2013. IEEE.
25. Mao, M. and M. Humphrey. Auto-scaling to minimize cost and meet application deadlines in cloud workflows. in SC'11: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis. 2011. IEEE.
26. Liu, J., et al., Job scheduling model for cloud computing based on multi-objective genetic algorithm. International Journal of Computer Science Issues (IJCSI), 2013. 10(1): p. 134.
27. Ramezani, F., J. Lu, and F. Hussain. Task scheduling optimization in cloud computing applying multi-objective particle swarm optimization. in International Conference on Service-oriented computing. 2013. Springer.
28. Xue, S., F. Liu, and X. Xu, An Improved Algorithm Based on NSGA-II for Cloud PDTs Scheduling. JSW, 2014. 9(2): p. 443-450.
29. Zuo, L., et al., A multi-objective optimization scheduling method based on the ant colony algorithm in cloud computing. Ieee Access, 2015. 3: p. 2687-2699.
30. Fieldsend, J.E. and S. Singh, A multi-objective algorithm based upon particle swarm optimisation, an efficient data structure and turbulence. 2002.
31. Coello, C.A.C., G.T. Pulido, and M.S. Lechuga, Handling multiple objectives with particle swarm optimization. IEEE Transactions on evolutionary computation, 2004. 8(3): p. 256-279.
32. Huang, C.-L., et al. Multi Objective Scheduling in Cloud Computing Using MOSSO. in 2018 IEEE Congress on Evolutionary Computation (CEC). 2018. IEEE.
33. Yeh, W.-C., A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems. Expert Systems with Applications, 2009. 36(5): p. 9192-9200.
34. Lai, C.-M., W.-C. Yeh, and Y.-C. Huang, Entropic simplified swarm optimization for the task assignment problem. Applied Soft Computing, 2017. 58: p. 115-127.
35. Yeh, W.-C. and J.-S. Lin, New parallel swarm algorithm for smart sensor systems redundancy allocation problems in the Internet of Things. The Journal of Supercomputing, 2018. 74(9): p. 4358-4384.
36. Yeh, W.-C., Simplified swarm optimization in disassembly sequencing problems with learning effects. Computers & Operations Research, 2012. 39(9): p. 2168-2177.
37. Ever, Y.K., Using simplified swarm optimization on path planning for intelligent mobile robot. Procedia computer science, 2017. 120: p. 83-90.
38. Yeh, W.-C., Novel swarm optimization for mining classification rules on thyroid gland data. Information Sciences, 2012. 197: p. 65-76.
39. Lin, P., et al., Parameters extraction of solar cell models using a modified simplified swarm optimization algorithm. Solar Energy, 2017. 144: p. 594-603.
40. Liu, W.-C., 應用非支配排序簡化群體演算法求解多目標多階層有限容量設施選址問題. 清華大學工業工程與工程管理學系學位論文, 2018: p. 1-84.
41. Lai, C.-M., et al., A novel nondominated sorting simplified swarm optimization for multi-stage capacitated facility location problems with multiple quantitative and qualitative objectives. Applied Soft Computing, 2019. 84: p. 105684.
42. Wei, S.-C., W.-C. Yeh, and T.-J. Yen. Pareto simplified swarm optimization for grid-computing reliability and service makspan in grid-RMS. in 2014 IEEE Congress on Evolutionary Computation (CEC). 2014. IEEE.
43. Al-Qerem, A. and A. Hamarsheh, Statistical-Based Heuristic for Tasks Scheduling in Cloud Computing Environment. International Journal of Communication Networks and Information Security, 2018. 10(2): p. 358-365.
44. Ibrahim, E., N.A. El-Bahnasawy, and F.A. Omara. Task scheduling algorithm in cloud computing environment based on cloud pricing models. in 2016 World Symposium on Computer Applications & Research (WSCAR). 2016. IEEE.
45. Riquelme, N., C. Von Lücken, and B. Baran. Performance metrics in multi-objective optimization. in 2015 Latin American Computing Conference (CLEI). 2015. IEEE.
46. Van Veldhuizen, D.A. and G.B. Lamont, Multiobjective evolutionary algorithm research: A history and analysis. 1998, Citeseer.
47. Jiang, S., et al., Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE transactions on cybernetics, 2014. 44(12): p. 2391-2404.
48. Schott, J.R., Fault tolerant design using single and multicriteria genetic algorithm optimization. 1995, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH.
49. Liu, D., et al. On solving multiobjective bin packing problems using particle swarm optimization. in 2006 IEEE International Conference on Evolutionary Computation. 2006. IEEE.