具動態變數分群與繁衍機制的大規模多目標演化演算法

Abstract

大規模多目標最佳化問題 (large-scale multi-objective optimization problems, LSMOPs) 因其高維決策空間給傳統演化算子帶來「維度災難」，難以兼顧收斂速度與解集多樣性。為此，本文在 LVIDE 框架上提出一種動態切換變數分群的演化演算法 LVIDE-DGR。首先，我們量化每個變數對多目標問題的重要性，並生成全域重要性分群 (importance based variable grouping, IVG) 與目標專屬分群 (objective-based IVG, OIVG)，同時引入線性分群 (linear grouping, LG)。演算法依設定週期在 LG 與 IVG/OIVG 之間動態切換，前期側重IVG、後期轉向各目標 OIVG，以聚焦不同搜尋階段所需的子空間。其次，我們設計了以上下界點作為導引的雙階段 VIDE 子代生成機制，在子空間內精細推進收斂；並以低機率插入差分演化 (differential evolution, DE) 運算子以補充全維度多樣性。演化過程還包括按目標拆分子族群並定期跨群交流，使算法在提速收斂的同時保持均勻的柏拉圖前緣覆蓋。實驗結果證明，本演算法在LSMOP 的 9 個測試問題中有 8 個問題勝過 5 個近期的大規模多目標演化演算法。

Large-scale multi-objective optimization problems (LSMOPs) present a signif-icant challenge for classical evolutionary algorithms due to the curse of dimension-ality inherent in high-dimensional decision spaces, making it difficult to achieve both rapid convergence and rich solution diversity. To address these issues, we pro-pose LVIDE-DGR, a dynamic variable-grouping evolutionary algorithm built upon the LVIDE framework. First, we quantify each decision variable’s importance and use this to form global importance-based variable groups (IVG) and objective-based IVG (OIVG), alongside a simple linear grouping (LG). During evolution, the algo-rithm periodically switches between LG and IVG/OIVG—emphasizing IVG in early stages and OIVG in later stages—to focus the search on the most relevant subspaces at each phase.Second, we introduce a two-stage VIDE offspring generation mechanism guided by decision-variable bounds for fine-grained convergence within subspaces, and we insert Differential Evolution (DE) operators at a low probability to maintain global diversity. The population is also split by objectives with periodic information ex-change across subpopulations, ensuring both accelerated convergence and uniform Pareto-front coverage. Experimental results on nine LSMOP benchmark problems demonstrate that LVIDE-DGR outperforms five state-of-the-art large-scale multi-objective evolutionary algorithms in eight out of nine cases, validating its effective-ness in balancing convergence speed and solution diversity.