隨著網路社會的蓬勃發展，資料的傳輸量日益漸增，網路綿密交織，各式各樣的物聯網裝置相互連結，點連著點形成線、線交線形成面、面與面形成網。如此龐大複雜的網路使的傳統中心化的雲計算架構無法負荷，資料傳遞延遲隨規模成長。因此越來越多的學者開始研究去中心化的網路架構概念──霧計算。
在霧計算的應用場景中，許多應用對於時間延遲的容忍度非常低。而演算法又會因問題規模而使得模擬時間增長，使得任務分配無法在可容忍時間內完成。然而過往的研究中，尚無學者對此提出相關解決方案。因此本研究針對演算法時間複雜度以及演算法求解效率兩方面著手，分別提出快速菁英挑選法(Fast Elite Selecting)以及理牌搜尋演算法 (Card Sorting Local Search)。 本研究提出快速菁英挑選法取代快速非支配排序(Fast Non-dominated Sorting)使得篩選非支配解之時間複雜度從O(N^2 )降至 O(〖N_F〗^2 )。另一新提出的區域搜尋法──理牌搜尋演算法根據霧計算任務分配問題特性，加強雙目標簡化群體演算法(Bi-Objective Simplified Swarm Optimization)之區域搜尋能力。結合雙目標簡化群體演算法、快速菁英挑選法、理牌搜尋演算法及CPU平行處理的技巧，形成本篇研究針對霧計算任務分配所提出的菁英簡化群體演算法(EliteSSO)策略。
本研究的實驗結果顯示，本研究所提的策略在時間上及求解品質上皆勝過其他演算法如：NSGA-II以及MOPSO。其優勢隨著問題的規模及複雜度的增加而逐漸擴大。

With the dramatic growth of data volume, the cloud computing structure has faced a severe difficulty, the latency. In order to deal with this problem, researchers have proposed the fog computing structure, which can successfully release the computation loads from one data center of cloud to multiple local fog devices. Hence, the tasks will be processed at the local fog device and avoid transmitting to data center which is not cost-effective, and the results can be transmitted to the users immediately. In this way, fog computing not only shorten the latency but achieved cost reduction.
In fog computing paradigm, many applications are time sensitive. However, most of the research so far haven’t presented a time-efficient and well-customized algorithm especially for fog computing task scheduling problem. Hence, we focused on time-efficiency issue and proposed a novel local search mechanism, Card Sorting Local Search (CSLS), which effectively improved the non-dominated solutions found by Bi-objective Simplified Swarm Optimization (BSSO). Moreover, we also proposed a one-front non-dominated sorting method, Fast Elite Selecting (FES), reduce the time complexity of non-dominated sorting technique. We Combine BSSO, CSLS and FES, and proposed a new algorithm for this study, Elite Swarm Simplified Optimization (EliteSSO), to overcome difficulties in time-efficiency and number of non-dominated solutions especially in large scale problems like fog computing task scheduling problem.
In the end of this work, computational results demonstrated that the proposed algorithm is time-efficiency and significantly outperformed other algorithms.

Abstract I
List of Tables V
List of Figures VI
Chaper 1 Introduction 1
Background 1
1.2 Motivation 4
1.3 Purpose 6
1.4 Structure 7
Chaper 2 Literature Review 9
2.1 Task Scheduling Problem in Fog Computing 9
2.2 Multi-Objective Algorithm in Task Scheduling Problem 10
2.3 Simplified Swarm Optimization 11
Chaper 3 Problem Statement 15
3.1 System Model 15
3.2 Notations 16
3.3 Mathematical Model 17
Chaper 4 Methodology 20
4.1 Non-dominated Sorting 20
4.2 Fast Elite Selecting 22
4.3 Card Sorting Local Search 24
4.4 Proposed strategy 33
Chaper 5 Experiments 35
5.1 Datasets 35
5.2 Performance Metrics 37
5.3 CSLS Parameter Design 38
5.4 Experimental Results 45
5.5 Statistical Verification 55
Chaper 6 Conclusion and Future works 57
6.1 Conclusion 57
6.2 Future Work 58
Reference 59
APPENDIX A 62
APPENDIX B 69

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