運用柔性演算法求解最佳參數設計

Abstract

在快速的市場環境變遷下，促使製造商必須迅速的開發出新產品並提供高品質的商品來滿足顧客善變的需求，以持續保有競爭力。對製造商而言，要同時縮短上市時間（time-to-market）及提昇產品與製程品質，參數設計是一個重要的課題。然而，參數設計最佳化的問題由於系統內存在著高度複雜的非線性關係以及參數間的交互作用，使得最佳參數設計不容易達成。工程師最近常運用田口方法（Taguchi method）來求得最佳參數設計，不過，田口方法在實務應用上仍然有一些限制。本論文企圖運用三種柔性演算法（soft computing, SC）的技術以克服這些限制。這三種方法分別是類神經網路（neural network, NN）、基因演算法（genetic algorithm, GA）以及模擬退火法（simulated annealing, SA）。為了達成參數設計最佳化，本論文提出三個以柔性演算法為基（SC-based）的求解程序。這三個程序分別是NNs為基的程序（NNs-based）、結合NN與GA的程序（NN-GA）以及結合NN與SA的程序（NN-SA）。本論文所提的最佳化參數設計程序提供另一種相對簡單且有效率的方法，並能放寬以往統計方法在實務應用上的一些限制。最後，並以文獻中五個參數設計問題探討所提出之最佳化方法的有效性，經由模擬實驗結果顯示本文所提的方法優於傳統田口方法。

The fast change of environment makes manufacturers have to promptly develop new products and provide high quality products to meet customers’ requirements so as to keep the competitive edges. Parameter design is critical for manufacturers to simultaneously achieve both the time-to-market reduction and the quality enhancement of the products and processes. However, the parameter design optimization problems are difficult owing to that nonlinear relationships exist in the system and interactions may occur among parameters. Engineers conventionally apply the Taguchi method to optimize parameter design; however, the Taguchi method has some limitations in practice. This dissertation attempts to release those limitations by using three techniques of soft computing (SC), i.e., neural network (NN), genetic algorithm (GA), and simulated annealing (SA). To achieve optimal parameter design, three SC-based procedures are proposed herein: (1) Neural networks based procedure (named NNs-based), (2) combined NN with GA procedure (named NN-GA), and (3) combined NN with SA procedure (named NN-SA). The proposed procedures in this dissertation provide the relatively simple and efficient methods, and are able to release the limitations of the statistical methods in solving the practical problems. Five numerical examples adopted from literature are resolved to illustrate the proposed procedures’ effectiveness. The computational results show that the proposed procedures in this dissertation excel the Taguchi method. 1.1 Overview 1 1.2 Research Motivations 3 1.3 Research Objectives 5 1.4 Organization 6 CHAPTER 2 LITERATURE REVIEW 7 2.1 Overview of the Taguchi Method 7 2.2 Earlier Improvements on the Taguchi Method 10 2.2.1 Qualitative quality characteristic 10 2.2.2 Multiple responses 11 2.2.3 Optimization procedure 13 2.2.4 Dynamic characteristic problems 14 2.2.5 Others 15 2.3 Applications of Soft Computing in Parameter Design 16 2.3.1 Neural network 16 2.3.2 Genetic algorithm and simulated annealing 18 CHAPTER 3 BACKGROUND OF SOFT COMPUTING 19 3.1 Introduction 19 3.2 Neural Network 19 3.3 Genetic Algorithm 22 3.4 Simulated Annealing 24 CHAPTER 4 PROPOSED PROCEDURES 26 4.1 Neural Networks Based (NNs-based) Procedure 26 4.2 Combination of NN and GA (NN-GA) Procedure 28 4.3 Combination of NN and SA (NN-SA) Procedure 32 4.4 Transformations of the Objective Function 35 4.4.1 Transformations of the fitness function 35 4.4.2 Transformations of the energy function 37 CHAPTER 5 NUMERICAL ILLUSTRATIONS 40 5.1 Introduction 40 5.2 Basic Information 40 5.2.1 Example 1 (static LTB problem) 40 5.2.2 Example 2 (static STB problem) 43 5.2.3 Example 3 (static NTB problem) 45 5.2.4 Example 4 (dynamic LTB problem) 47 5.2.5 Example 5 (dynamic NTB problem) 49 5.3 Implementation Results by NNs-based Procedure 51 5.3.1 Example 1 (static LTB problem) 51 5.3.2 Example 2 (static STB problem) 53 5.3.3 Example 3 (static NTB problem) 56 5.3.4 Example 4 (dynamic LTB problem) 59 5.3.5 Example 5 (dynamic NTB problem) 63 5.4 Implementation Results by NN-GA Procedure 67 5.4.1 Example 1 (static LTB problem) 67 5.4.2 Example 2 (static STB problem) 69 5.4.3 Example 3 (static NTB problem) 70 5.4.4 Example 4 (dynamic LTB problem) 72 5.4.5 Example 5 (dynamic NTB problem) 74 5.5 Implementation Results by NN-SA Procedure 76 5.5.1 Example 1 (static LTB problem) 76 5.5.2 Example 2 (static STB problem) 77 5.5.3 Example 3 (static NTB problem) 79 5.5.4 Example 4 (dynamic LTB problem) 80 5.5.5 Example 5 (dynamic NTB problem) 83 CHAPTER 6 COMPARISON AND DISCUSSION 86 6.1 Introduction 86 6.2 Comparison and discussion 86 6.2.1 Example 1 (static LTB problem) 86 6.2.2 Example 2 (static STB problem) 87 6.2.3 Example 3 (static NTB problem) 88 6.2.4 Example 4 (dynamic LTB problem) 89 6.2.5 Example 5 (dynamic NTB problem) 90 6.3 Summary 92 CHAPTER 7 CONCLUSIONS 93 APPENDIX A The main genetic operators 96 REFERENCES 97