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研究生: 曾則儒
Tseng, Tser-Ru
論文名稱: 求解高維多目標最佳化問題的演化演算法效能評析
Large-Scale Evolutionary Multiobjective Optimization: An Experimental Study
指導教授: 蔣宗哲
Chiang, Tsung-Che
口試委員: 蔣宗哲
Chiang, Tsung-Che
鄒慶士
Tsou, Ching-Shih
廖容佐
Liaw, Rung-Tzuo
口試日期: 2024/07/17
學位類別: 碩士
Master
系所名稱: 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年: 2024
畢業學年度: 112
語文別: 中文
論文頁數: 67
中文關鍵詞: 演化演算法多目標最佳化高維多目標最佳化
英文關鍵詞: Evolutionary Algorithms, Multiobjective Optimization, Large Scale
研究方法: 實驗設計法
DOI URL: http://doi.org/10.6345/NTNU202401528
論文種類: 學術論文
相關次數: 點閱:140下載:2
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  • 演化演算法在求解多目標最佳化問題有很好的表現,也被廣泛使用於各領域的實際應用問題。然而當決策變數的個數增加至數百個甚至數千個時,指數成長的搜尋空間會對多目標演化演算法的求解能力形成嚴峻的挑戰;因此,近年來演化計算領域有越來越多的學者投入高維多目標演化演算法的設計。然而,我們發現到此領域的研究文獻在評估演算法效能時未能使用統一的實驗設定,此舉可能造成實驗結果的偏頗與失真。本論文自文獻中挑選八個具有代表性的高維多目標演化演算法,使用兩套公開測試函式集 LSMOP 與 LMF,檢視這些演算法在四種問題維度和四種計算資源所組合的十六種實驗環境下的求解效能。經由公平且完整的實驗測試,我們得以正確評比演算法的效能與特質,也對各種演算法設計的異同處與其對於求解效能的影響提出解釋與探討。

    Evolutionary algorithms have shown promising performance in addressing multiobjective optimization problems (MOPs) and are widely applied across various domains. However, as the number of decision variables grows into the hundreds or even thousands, the exponentially growing search space poses significant challenges to the searching capabilities of multiobjective evolutionary algorithms (MOEAs). In response, recent years have seen a growing focus within the evolutionary computation community on designing MOEAs tailored for large-scale MOPs. One issue we have identified in this research area is the inconsistent experimental settings when evaluating algorithm performance, which can result in biased and misleading outcomes. In this thesis, we select eight representative MOEAs from the literature and employ two publicly available test function sets, LSMOP and LMF, to assess the performance of these algorithms across sixteen experimental scenarios, each defined by a combination of four problem dimensions and four levels of computational budgets. Through rigorous and comprehensive testing, we provide a fair comparison of the algorithms' performance and offer insights into the differences in algorithm design and their implications for solving efficiency.

    誌謝 i 中文摘要 ii Abstract iii 目錄 iv 附表目錄 vi 附圖目錄 vii 第一章 緒論 1 1.1 研究背景與動機 1 1.2 研究問題定義 2 1.3 多目標演化演算法 2 1.4 研究目的與方法 3 第二章 文獻探討 4 2.1 變數分群途徑 4 2.1.1 隨機分群類 5 2.1.2 變數分析類 6 2.2 空間限縮途徑 8 2.2.1 問題轉換類 8 2.2.2 維度限縮類 9 2.3 新穎搜尋策略途徑 10 2.3.1 進階操作類 10 2.3.2 特殊問題類 12 第三章 高維多目標演化演算法 13 3.1 演算法概念和關係 13 3.2 WOF 15 3.3 LSMOF 17 3.4 LMOEA-DS 19 3.5 DGEA 21 3.6 FLEA 22 3.7 LMOCSO 24 3.8 ALMOEA 25 3.9 LERD 26 第四章 實驗設計與結果 29 4.1 測試問題集 29 4.2 實驗設定 29 4.3 實驗結果與分析 31 4.4 演算法特性觀察與探討 40 4.4.1 使用問題轉換的演算法比較 40 4.4.2 使用邊界點的演算法比較 40 4.4.3 使用方向向量抽樣的演算法比較 41 4.4.4 使用收斂方向學習策略的演算法比較 42 4.5 實驗結果和原始論文差異之探討 42 4.6 測試函式設計問題探討 45 第五章 結論與未來研究方向 49 參考文獻 50 附錄 1:LSMOP 測試函式定義 54 附錄 2:LMF 測試函式定義 64

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