臺灣博碩士論文加值系統

近期有許多版本之改良式株落選擇演算法已經被大量地運用到理論和實際的應用上。然而，這些研究中卻少有被應用到結構拓樸最佳化問題及多台冰水主機負載最佳化問題的求解上。此外對於使用二進位編碼表示且以群體為基礎(population-based)的結構拓樸最佳化方法而言，結構設計連結情況的處理及單點連結的預防是十分重要的一個環節，卻尚未被考量於文獻上的類免疫演算法。本研究提出一個應力強化的株落選擇演算法(stress-enhanced clonal selection algorithm, SECSA)，其結合了使用以支配為基礎的限制條件處理機制(dominance-based constraint-handling)和新的應力強化之超突變操作機制(stress-enhanced hypermutation operator)等於類免疫演算法中。為了展示所提出之方法的高可行性，本研究所提出之SECSA將和其他基因遺傳演算法類的方法在最小撓度問題(二維度及三維度)和最小重量問題(單一負載及多負載)等基準結構拓樸設計問題(benchmark structural topology design problems)上進行比較。而從這些比較中得到的結果可以發現到，本研究所提出之SECSA和其他方法相比較，不論在收斂的速度上及答案品質上皆具有不錯的競爭力。

對於冰水主機負載分配最佳化 (Optimal Chiller Loading, OCL) 問題的求解上，本研究先藉由把問題指定之限制條件(冷卻需求)視為一個新增加的求解目標，而將原本具有限制條件的單目標冰水主機負載分配最佳化的問題，轉成無限制條件的多目標冰水主機負載分配最佳化的問題。然後，再以一改良式株落選擇演算來求解此問題。一旦取得了這個多目標最佳化問題的一系列妥協解後，便可直接從中挑選出最符合冷卻需求的妥協解，作為原來冰水主機負載分配最佳化問題的最佳解。此外，運用此一相同系列的妥協解和挑選流程，不但可直接求解符合不同冷卻需求條件的冰水主機負載分配最佳化問題，甚至是擁有大量變數和等式限制條件之高難度的每日冰水主機負載分配最佳化問題，也只需要按各時間之冷卻需求的條件，逐一挑選出相符合的妥協解即可。其所得之結果和文獻進行比較，顯示出本研究所提出之方法，能夠穩健地以較少的計算次數，找出每日冰水主機負載分配最佳化問題的最佳部分負載組合。

本研究不但探索類免疫演算法的能力之外，還展示出類免疫演算法搭配適當之加強機制可發展出效能與求解品質都很優異的最佳化求解方法。

Recently, numerous modified versions of clonal selection algorithms (CSAs) have been adopted in both theoretical and practical applications. However, few have been proposed for solving structural topology optimization problems and optimal chiller loading problems. In addition, the design connectivity handling and one-node connected hinge prevention, which are vital in the application of population-based methods with binary representation for structural topology optimization, have not been applied to IAs in literature. A stress-enhanced clonal selection algorithm (SECSA) incorporating an IA with a dominance-based constraint-handling technique and a new stress-enhanced hypermutation operator is proposed to rectify those deficiencies. To demonstrate the high viability of the presented method, comparisons between the presented SECSA and GA-based methods were made on minimum compliance and minimum weight benchmark structural topology design problems in 2D, 3D, and multi-loading cases. In each case, SECSA was shown to be competitive in terms of convergence speed and solution quality.

In solving optimal chiller loading (OCL) problems, the original constrained single-objective problem is firstly transformed into an unconstrained multi-objective optimization problem by defining the given constraint (cooling demand) as an additional objective. Then this transformed unconstraint multi-objective optimization problem is solved by the adopted modified clonal selection algorithm. Once a series of compromise solutions for this multi-objective optimization problem is obtained, the compromise solution with closest matching cooling load to the given cooling demand can be directly selected as the optimal solution to the original OCL problem. Furthermore, by the same series of compromise solutions and selection process, a new multiple chiller loading optimization problem with a different cooling demand can be directly handled. Even for the more complex daily optimal chiller loading (DOCL) problem with excessive decision variables and equality constraints, it still works by individually selecting the compromise solution with closest matching cooling load to the given cooling demand at each time interval merely. The obtained results, compared with those reported in the literature, show that the adopted approach can robustly find the optimal solution to a DOCL problem with less function evaluations.

The main goal of this study is not only to further explore the capabilities of IAs, but also to show that an IA with appropriate enhancements can lead to the development of attractive optimization computational tools.

ACKNOWLEDGEMENT i
摘要 ii
ABSTRACT iv
TABLE OF CONTENTS vi
LIST OF TABLES viii
LIST OF FIGURES ix
NOMENCLATURE xi
CHAPTER 1 INTRODUCTION 1
1.1 STRUCTURAL TOPOLOGY OPTIMIZATION 2
1.2 OPTIMAL CHILLER LOADING PROBLEM 5
CHAPTER 2 OVERVIEW OF THE CLONAL SELECTION ALGORITHM 9
2.1 CLONAL SELECTION THEORY 10
2.2 CLONAL SELECTION ALGORITHM 13
CHAPTER 3 STRESS-ENHANCED CLONAL SELECTION ALGORITHM 15
3.1 DESIGN PROBLEM REPRESENTATION 15
3.2 CONNECTIVITY ANALYSIS 17
3.3 CONNECTIVITY HANDLING TECHNIQUE 18
3.4 DOMINANCE-BASED CONSTRAINT-HANDLING TECHNIQUE 20
3.5 CLONING OPERATOR 21
3.6 ENHANCED HYPERMUTATION OPERATOR 23
3.7 ELITIST AGING OPERATOR 27
3.8 OUTLINE OF THE PRESENTED SECSA 28
CHAPTER 4 MODIFIED CSA APPROACH FOR OPTIMAL CHILLER LOADING OPTIMIZATION 30
4.1 MULTIPLE CHILLER SYSTEM 31
4.2 MULTI-OBJECTIVE OPTIMIZATION CONSTRAINT-HANDLING TECHNIQUE 34
4.3 DESIGN PROBLEM REPRESENTATION 35
4.4 AFFINITY EVALUATION AND NON-DOMINATED SORTING 36
4.5 CLONING OPERATOR 37
4.6 HYPERMUTATION OPERATOR 38
4.7 MEMORY CELL MATURATION OPERATOR 39
4.8 PSEUDO CODE OF MODIFIED CSA FOR OCL PROBLEM 39
CHAPTER 5 RESULTS AND DISCUSSIONS 41
5.1 STRUCTURAL TOPOLOGY OPTIMIZATION USING SECSA 41
5.1.1 MINIMUM COMPLIANCE DESIGN 42
5.1.2 MINIMUM WEIGHT DESIGN 49
5.2 OPTIMAL CHILLER LOADING USING MODIFIED CSA APPROACH 56
CHAPTER 6 CONCLUSIONS 66
REFERENCES 69

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