能源相關排程問題中的挑戰與演算法｜國立清華大學博碩士論文庫

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研究生：	劉向瑄 Liu, Hsiang-Hsuan
論文名稱：	能源相關排程問題中的挑戰與演算法 Combinatorial Challenges and Algorithms in New Energy Aware Scheduling Problems
指導教授：	韓永楷 Hon, Wing-Kai
口試委員:	謝孫源 Hsieh, Sun-Yuan 李哲榮 Lee, Che-Rung 廖崇碩 Liao, Chung-Shou 彭勝龍 Peng, Sheng-Lung 蔡明哲 Tsai, Ming-Jer 楊得年 Yang, De-Nian
學位類別：	博士 Doctor
系所名稱：
論文出版年：	2017
畢業學年度：	105
語文別：	英文
論文頁數：	128
中文關鍵詞：	排程、即時演算法、需求響應管理、智慧電網、電力成本、精確演算法
外文關鍵詞：	scheduling, online algorithm, demand response management, smart grid, electricity cost, exact algorithm
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在本論文中,我們呈現現代智慧電網“需求響應管理”(demand response management) 中出現的節能排程問題的理論研究。消費者發送電力需求與這些需求可被執行的時間區間。智慧電網控制中心在接收到電力需求後,會在指定的時間區間內調度這些需求。每個時間點的電費是由當時的電力負載的凸函數來測量的。在這個最佳化問題中,我們的目標是以最小的總電力成本安排所有需求。

我們研究了不同模型中的智慧電網排程問題。在 offline model 中,我們證明這個智慧電網排程問題在一般情況下是 NP-hard。對於特殊的需求,例如當所有需求的功率和持續時間都是一單位,我們提出了一種多項式時間演算法。利用這個多項式時間演算法,我們更提出了一種近似演算法可以解決任意的需求。另一方面,我們還提出了一個精確的演算法來找出任意需求的最佳解。

對於 online model,我們提出了一種可以用在任意需求的即時演算法。我們還證明了智慧電網排程問題的競爭比(competitive ratio)的下限。對於特殊情況,我們設計許多不同,競爭比更好的即時演算法。

最後,我們轉向其他最佳化問題,並展示如何通過調整我們的演算法來解決它們。我們證明我們的即時演算法能夠以趨近最優競爭比解決機器最小化問題(machine minimization problem)。另外我們還證明,我們的精確演算法可以用於解決其他需求響應管理問題。

In this thesis, we study the theoretical approach on energy-efficient scheduling problems arising in demand response management in the modern electrical smart grid. Consumers send in power requests with flexible feasible timeslots during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost.

We study the smart grid scheduling problem in different models. For the offline model, we prove the problem is NP-hard for the general case. We propose a polynomial time algorithm for special input where jobs have unit power request and unit time duration. By adapting the polynomial time algorithm for unit-size jobs, we propose an approximation algorithm for more general input. On the other hand, we also present an exact algorithm to find the optimal schedule for the problem with general input.

For the online model, we propose an online algorithm for jobs with jobs with arbitrary power request, arbitrary time duration, and arbitrary contiguous feasible intervals. We also show a lower bound of the competitive ratio for the smart grid scheduling problem with unit height and arbitrary width. For special cases, we design different online algorithms with better competitive ratios.

Finally, we look at other optimization problems and show how to solve them by adapting our techniques. We prove that our online algorithm can solve the machine minimization problem with an asymptotically optimal competitive ratio. We also show that our exact algorithm can be adapted to solve other demand response management problems.

Notations    ix
Preface    xi
Abstract    xiii
Acknowledgements    xvi
Introduction    1
1 Smart Grid Scheduling and Demand Respond Management . . . . . . . . 1
2 Our contribution ................................ 3
3 Organization of the Thesis........................... 6
  Preliminaries and Definitions    9
1 Offline algorithms and class NP........................ 9
1.1 Approximation algorithms....................... 10
1.2 Fixed-parameter algorithms...................... 10
2 Online algorithms................................ 11
3 Scheduling.................................... 12
4 Smart Grid Scheduling Problem and Definitions. . . . . . . . . . . . . . . 13
  Literature Review    15
1 Previous Workon Smart Grid Scheduling .................. 16
1.1 Minimizing peak power demand ................... 16
1.2 Minimizing total cost over time.................... 17
2 Dynamic Voltage/Speed Scaling Problem .................. 19
2.1 Algorithms for the DVS Problem ................... 20
2.2 Discrete dynamic voltage/speed scheduling . . . . . . . . . . . . . 22
2.3 Non-preemptive dynamic voltage/speed scheduling . . . . . . . . . 23
3 Related Scheduling Problems ......................... 25
3.1 Machine minimization ......................... 25
3.2 BinPackingproblem.......................... 27
3.3 Load Balancing problem........................ 28
4 Related Graph Algorithms........................... 30
4.1 Flow problem.............................. 30
4.2 Matching problem ........................... 30
4.3 Interval graphs ............................. 31
5 Summary .................................... 33
  Offline Algorithms for The GRID Problem    35
1 NP-hardness .................................. 35
2 UnitCase.................................... 37
2.1 Feasibility graph Algorithm...................... 38
2.2 Correctness ............................... 40
2.3 TimeComplexity............................ 51
Noncontiguous Feasible Timeslots .................. 51
Contiguous Intervals.......................... 52
2.4 Using a Discrete DVS Algorithm ................... 55
3 Exact Algorithms for Jobs with Arbitrary Widths and Heights . . . . . . 59
3.1 Key notions............................... 59
3.2 Framework of the algorithms ..................... 61
3.3 An algorithm with three parameters ................. 67
3.4 An algorithm with two parameters.................. 69
4    An (36(1 + ⌈log wmax / wmin ⌉)(1 + ⌈log hmax / hmin ⌉))α-Approximation Algorithm for General Case.................................. 71
4.1 Uniform Widths and Uniform Heights Jobs . . . . . . . . . . . . . 72
4.2 General Input.............................. 79
5 Summary .................................... 85
  Online Algorithms for The GRID Problem    87
1 General Case .................................. 90
1.1 Unit width and arbitrary height ................... 90
1.2 Uniform width and arbitrary height ................. 92
1.3 Arbitrary Input............................. 94
2 Lower Bound .................................. 99
3 Special Cases ..................................101
3.1 Unit-width and uniform-height ....................102
3.2 Uniform-height, arbitrary widths and agreeable deadlines . . . . . 103
3.3 Uniform height job set with common feasible intervals . . . . . . . 106
3.4 Unit width job set with common feasible intervals    . . . . . . . . . 107
4 Summary ....................................109
  Extensions to Other Problems    111
1 Online algorithm: Minimizing the peak power request . . . . . . . . . . . 111
2 The interval graph approach on other problems . . . . . . . . . . . . . . .116
2.1    Minimizing the peak power request. . . . . . . . . . . . . . . . . .117
2.2 Minimizing the total cost with limited power . . . . . . . . . . . .117
3 Summary ....................................118
Conclusion 119
Bibliography 121
                                

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