A Two-Stage Many-Objective Evolutionary Algorithm with Survival-Ratio-Based Switching

Many-objective optimization problems (MaOPs) suffer from weakened selection pressure as the number of objectives increases, making it difficult to balance convergence and diversity. Existing two-stage and multi-stage many-objective evolutionary algorithms (MaOEAs) often determine stage transitions using preset schedules or indirect population criteria that may not reflect changes in search productivity. This paper proposes TSEA-SR, a two-stage MaOEA with survival-ratio-based switching, in which the stage transition is determined by offspring survival after environmental selection. Candidate solutions are first pre-screened according to the hyper-dominance degree. The first stage uses the Euclidean norm to promote centripetal convergence, whereas the second uses the harmonic mean to expand coverage of boundary and extreme regions. Pre-screening and competition organized by reference vectors are retained throughout the search, and the transition is triggered only when low offspring survival persists across generations. Experiments on 80 benchmark instances and 12 real-world combinatorial optimization instances compare TSEA-SR with six state-of-the-art MaOEAs. The results demonstrate the competitive performance of TSEA-SR across the evaluated problems, while ablation studies further support the complementary roles of the two stages and the effectiveness of determining the transition from offspring survival.