雖然單目標函式最佳化為一相當傳統的問題，但是直至今日，單目標的函式最佳化問題在各個不同的領域仍扮演相當重要的角色，並且有相當多的學者致力於研究這個問題。然而在真實世界中，不管是工程、科學、數學等不同領域的研究中往往會遇到一些更為困難的問題，目前遭遇的問題不僅僅只是單一目標函式的最佳化，而是必需同時滿足兩個以上的目標函式，又稱之為多目標問題。因為多目標問題一般不存在單一全域最佳解，而是一組柏拉圖最佳解集合(Pareto Optimal Set)，所以如何得到均勻且完整的解集合是目前相當重要的研究之一。本文提出一個以螢火蟲演算法與快速非支配排序型精英策略的多目標基因演算法為基礎的新型演算法，並加入一個適用於高維度的擁擠距離計算公式來得到分佈更為平均且完整的柏拉圖最佳解集合，以保持解的多樣性分佈。本研究使用數個較為常見的多目標問題，並與其他演算法做比較，實驗結果顯示，此演算法能提供較為完整且分佈更為平均的柏拉圖最佳解集合。

The so-called multi-objective optimization problem (MOP) has become a critical research subject because many multi-objective optimization problems exist in our daily life. Unlike solving a single-objective problem, solving a multi-objective optimization problem requires that many conflicting objectives be optimized altogether at the same time. Instead of finding a single solution as in the single-objective problem, how to find approximate solutions or a pareto set within a reasonable time has become an active research topic in recent years. In this thesis, we present a high-performance algorithm that leverages the strengths of firefly algorithm (FA) and a fast and elitist non-dominated sorting genetic algorithm (NSGA-II). In order to get a more uniformly distributed and completed pareto set, we also propose a new way to determine the crowding distance. Simulation results show that the proposed algorithm can provide a better result than all the state-of-the-art multi-objective optimization algorithms compared in this thesis in most cases.

i. 論文審定書
i. 論文公開授權書
iv. 誌謝
v. 摘要
vi. Abstract
ix. List of Figures
xi. List of Tables
Chapter 1 [簡介......1]
1.1 [動機......2]
1.2 [論文貢獻......2]
1.3 [論文架構......3]
Chapter 2 [相關文獻探討......4]
2.1 [函式最佳化問題......4]
2.2 [多目標最佳化問題......5]
2.2.1 [支配（Domination）......6]
2.2.2 [柏拉圖最佳化（Pareto Optimization）......8]
2.3 [演化式計算求解多目標最佳化問題......9]
2.3.1 [A Fast and Elitist Non-dominated sorting genetic algorithm......10]
2.3.2 [Multiple Objective Particles Swarm Optimization......12]
2.4 [螢火蟲相關演算法......14]
2.4.1 [螢火蟲演算法......14]
2.4.2 [多目標螢火蟲演算法......16]
2.5 [結論......18]
Chapter 3 [非支配排序型螢火蟲演算法......19]
3.1 [演算法設計概念......19]
3.2 [演算法流程......20]
3.2.1 [初始設定......21]
3.2.2 [螢火蟲移動......21]
3.2.2.1 [受支配......22]
3.2.2.2 [未受支配......22]
3.2.3 [更新......24]
3.3 [範例......28]
Chapter 4 [實驗結果......31]
4.1 [執行環境、參數設定......31]
4.2 [模擬結果......33]
4.2.1 [問題介紹與實驗結果圖......33]
4.2.2 [實驗數據分析......39]
4.2.2.1 [多目標評估方式......39]
4.2.2.2 [數據分析......39]
4.3 [總結......41]
4.4 [其他問題探討......41]
Chapter 5 [結論與未來展望......44]
5.1 [結論......44]
5.2 [未來展望......44]
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