工程最佳化模式不確定性參數值分析 -以專案排程模式為例

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姓名

王信翔(Sin-Siang Wang) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

工程最佳化模式不確定性參數值分析 -以專案排程模式為例
(Analysis of Uncertain Parameter Values included in Engineering Optimization Models: A Case Study of a Project Scheduling Model)

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摘要(中)

決策者為了有效解決各類型的工程最佳化問題，並獲得最佳的決策方案，已將工程最佳化模式廣泛地應用於工程界中。而當面臨實務的工程問題時，最佳化模式中的某些參數可能是不確定性的，因不確定性參數值通常無法被精確估算，故將具有誤差。如果有不確定性參數被包含在工程最佳化模式中時，亦即模式輸入具有誤差時，則該模式解亦可能存在或多或少的誤差，亦即模式輸出具有誤差。在此情況下，決策者無法根據該模式解制定出最佳的決策方案。以往有關估算不確定性參數值的研究主要是使用推估或預測程序找出較合適的不確定性參數值並將其視為模式輸入資料。然而，使用那些估算的參數值所獲得的模式解的誤差仍然無法得知。因為無法知道真實的最佳解，故此等研究的模式解只能與先前所獲得的最好的解相互比較，並無法知道模式解與真實最佳解之間的差距為何，亦難以客觀證實此等研究的模式解的績效。此外，過去已有許多的研究使用近似解演算法，在給定容許誤差下以提升模式求解效率，但尚未有研究探討不同的求解容許誤差對於具有輸入誤差的模式解的影響。因此，本研究主要是探討工程最佳化模式中不確定性參數值，具有不同的可控制誤差與隨機誤差情境，並使用不同的求解容許誤差設定時，模式輸出的誤差為何，亦即評估求解之最佳性。
最佳化數學規劃模式通常具有兩類不確定性參數。一類為目標函數之不確定性參數，另一類為限制式之不確定性參數。因這兩類參數的誤差分析結果可能具有差異性，故本研究分為三個部份以分別進行探討與分析。在第一部份中，本研究發展一實驗評估方法以評估當工程最佳化模式中屬於目標函數的不確定性參數值，具有不同的可控制誤差與隨機誤差情境，並使用不同的求解容許誤差設定時，模式輸出的誤差為何。在第二部份中，本研究亦發展一實驗評估方法以評估當工程最佳化模式中屬於限制式的不確定性參數值，具有不同的可控制誤差與隨機誤差情境，並使用不同的求解容許誤差設定時，模式輸出的誤差為何。在第三部份中，本研究結合前兩部份的方法，發展一實驗評估方法以評估當工程最佳化模式中屬於目標函數及限制式的不確定性參數值，具有不同的可控制誤差與隨機誤差情境，並使用不同的求解容許誤差設定時，模式輸出的誤差為何。本研究以一工程專案最佳化排程模式作為此三部份的測試模式，以能夠方便比較此三部份的分析結果。此外，本研究為進一步了解在不同的誤差情境及使用不同的求解容許誤差設定時，模式輸入誤差、求解容許誤差與模式輸出誤差間的相關性，故將此三部份的分析結果進行迴歸分析。最後，本研究從分析結果中歸納出實務上在設計最佳化模式及求解演算法時的注意事項與管理意涵。

摘要(英)

Decision makers have widely applied engineering optimization models in the field of engineering in order to effectively solve various types of engineering optimization problems and secure optimal decisions. However, confronted with practical engineering problems, some parameters of the optimization model may be uncertain. Uncertain parameter values are hard to accurately estimate, causing that they include errors. In case there are uncertain parameters involved in the engineering optimization model (i.e., the model input includes errors), the obtained solution may also include errors (i.e., the model output includes errors). In this case, the decision makers cannot make the optimal decisions. In the past, the studies regarding estimating uncertain parameter values have chiefly utilized the estimation or prediction approach to find the proper uncertain parameter values that can be used as model input data. However, there could still be unknown errors in model solutions obtained using estimated uncertain parameter values. Since it is hard to obtain a real optimal solution for a model that contains uncertain parameters, the evaluation of these solutions is carried out mainly by comparing them with the best solution secured previously. The gap between the obtained model solution and real optimal solution is unknown, that is to say, the performance of the solutions secured from previous studies cannot be confirmed objectively. Additionally, although there have been many studies that have employed approximate solution algorithms with a solution tolerance error to enhance the solution efficiency, there have not been any studies that further explore the effect of various solution tolerance errors on model solutions with input errors. Thus, the purpose of this study is to explore the output errors for an engineering optimization model that includes uncertain parameter values under different controllable and random error scenarios, coupled with different solution tolerance error settings (i.e., this study focuses on evaluating the optimality of model solutions with input errors).
There are usually two sorts of uncertain parameters included in an optimal mathematical programming model. One is the uncertain parameters included in the objective function; the other is the uncertain parameters included in the constraint set. The results of the error analysis of the two types of uncertain parameters may be different. In order to reflect this, this dissertation is divided into three essays. In the first essay, an experimental evaluation approach is developed to evaluate the output errors of an engineering optimization model in which uncertain parameter values are included in the objective function, under various controllable and random error scenarios, coupled with various solution tolerance error settings. The second essay also develops an experimental evaluation approach to evaluate the output errors of an engineering optimization model in which uncertain parameter values are included in the constraint set, under various controllable and random error scenarios, coupled with various solution tolerance error settings. In the third essay, the methods discussed in the first two essays are combined to develop an experimental evaluation approach to evaluate the output errors of an engineering optimization model in which uncertain parameter values are included in the objective function and the constraint set, under various controllable and random error scenarios, coupled with various solution tolerance error settings. To facilitate comparison of the test results, the same engineering project optimization scheduling model is used in the testing in all three essays. In addition, regression analysis of the test results of each error scenario associated with the three essays is also implemented to further comprehend how model input errors (i.e., controllable and random errors) and solution tolerance errors affect model output errors. Finally, some useful information and managerial meanings for designing optimization models and solution algorithms in practice are extrapolated from the test results.

關鍵字(中)

★ 工程最佳化模式
★ 專案排程模式
★ 不確定性參數
★ 模式輸入誤差
★ 可控制誤差
★ 隨機誤差
★ 求解容許誤差
★ 模式輸出誤差

關鍵字(英)

★ engineering optimization model
★ project scheduling model
★ uncertain parameter
★ model input error
★ controllable error
★ random error
★ solution tolerance error
★ model output error

論文目次

摘要 i
Abstract ii
誌謝 iv
Introduction 1
Chapter 2 5
Essay 1: An Experimental Method for the Evaluation of Output Errors for Engineering Optimization Models with Uncertain Parameters 5
2.1 Introduction 5
2.2 Introduction of the tested engineering optimization model 8
2.3 Method for evaluating the model output errors 9
2.4 Error testing over uncertain parameter values 11
2.4.1 Data analysis 11
2.4.2 Test results 14
2.4.3 Regression analysis of test results 19
2.4.4 Important findings obtained from the test results 23
2.5 Conclusions 26
Chapter 3 29
Essay 2: The Development of an Output Error Evaluation Method for Engineering Optimization Models containing Uncertain Parameters 29
3.1 Introduction 29
3.2 Introduction of the tested optimization model 31
3.3 Identification of uncertain parameters included in the constraint set of the model 32
3.4 Modification of the model 33
3.5 Evaluation method for model output errors 34
3.6 Error tests to uncertain parameter values 36
3.6.1 Input data for the modified model 37
3.6.2 Test results 39
3.6.3 Regression analysis of test results 44
3.6.4 Significant findings secured from the test results 47
3.7 Conclusions 50
Chapter 4 53
Essay 3: The Exploration of the Output Errors of Engineering Optimization Models with Uncertain Parameters 53
4.1 Introduction 53
4.2 Introduction of MRCPSPDCF 56
4.3 Judgment of uncertain parameters included in the model 56
4.4 Revision of the model 58
4.5 An approach for the evaluation of model output errors 59
4.6 Error tests for uncertain parameter values 61
4.6.1 Parameter value settings for the revised model 62
4.6.2 Output results 64
4.6.3 Regression analysis for test results 69
4.6.4 Important discoveries obtained from the output results 73
4.7 Conclusions 76
Chapter 5 78
Conclusions, Suggestions and Contributions 78
5.1 Conclusions 78
5.2 Suggestions 80
5.3 Contributions 81
References 82
Appendix 1 86
Appendix 2 88
Appendix 3 92
Appendix 4 95
Appendix 5 99
Appendix 6 102
Appendix 7 106

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指導教授

顏上堯(Shangyao Yan)

審核日期

2015-7-23

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