以 AGE-MOEA-II與改良版環境選擇求解多目標最佳化問題

Abstract

多目標最佳化問題是現實應用的常見形式，求解問題時需要同時考慮多個目標之間的取捨關係。多目標演化演算法是求解多目標最佳化問題的常用方法，這類演算法中的關鍵機制就是平衡解族群的收斂性和多樣性。在近年發表的演算法中，AGE-MOEA-II 演算法通過估計柏拉圖前緣的形狀，並依形狀來定義解的多樣性和收斂性，展現了出色的效能表現。然而AGE-MOEA-II 仍有其值得改進之處，本論文結合了其它現有演算法的設計，一方面刪減無益於收斂性的解個體，一方面修改其應對凸型柏拉圖前緣時的多樣性評估機制。我們使用 13 個公開測試函式進行實驗，實驗結果顯示本論文所引入的機制可有效提升求解品質；與六個現有演算法相比，本論文所提出的改良版 AGE-MOEA-II 在兩項常見的效能指標 IGD 與 HV 都有更好的表現。Many real-world problems fall under the category of multiobjective optimization problems. Solving such problems requires considering trade-offs among multiple objectives simultaneously. Multiobjective evolutionary algorithms (MOEAs) are widely used for solving these problems, and the core design in these algorithms lies in balancing convergence and diversity during the search process. Among recent algorithms, AGE-MOEA-II has demonstrated promising performance by estimating the shape of the Pareto front and defining solution diversity and convergence accordingly. However, there remains room for improvement in AGE-MOEA-II. In this thesis, we improve AGE-MOEA-II by integrating the mechanisms of two other existing algorithms: one mechanism aims to remove solutions that contribute little convergence, and the other mechanism improves the diversity measure in the case of convex Pareto fronts. The performance of the proposed improved AGE-MOEA-II was verified by comparing it with six existing algorithms in solving 13 public test functions (MaF1-13). Experimental results showed that our proposed algorithm performed better regarding two popular indicators, IGD and HV.