自适应融合梯度下降的粒子群优化，提升搜索效率。
Adaptive Hybrid Particle Swarm Optimization with Gradient Descent
- 根据种群多样性自动调节梯度影响，无需手动切换探索与利用阶段。
- 在平滑局部区域问题上表现更优，优于传统粒子群优化方法。
- 适合需要高效全局搜索的复杂优化任务，尤其擅长平滑目标函数。
梯度注入仅在粒子群识别出平滑局部结构时有效，并非普遍适用。本文提出自适应混合粒子群优化（AHPSO），通过在种群多样性上使用Sigmoid函数自动调节梯度影响：探索阶段接近零，利用阶段接近最大值，无需人工设定阶段切换。在预算归一化对比中（给定相同总函数评估次数），传统PSO在40组配置中胜出52.5%，而AHPSO仅20%（p = 7.0e-5，Friedman检验）。但AHPSO在具有平滑局部盆地的问题（如F8, F24-F27）上保持优势，即使成本相等，定向下降也优于无向采样。在迭代匹配对比中，跨29个函数（42组配置，14,700次运行），AHPSO-Adadelta在9种方法中排名第一，包括CMA-ES（p = 9.75e-4）。核心贡献是明确界定梯度注入在群体搜索中起效的条件，而非宣称普适优越性。
原文摘要 · Abstract (English)
Gradient injection helps Particle Swarm Optimization (PSO) only when the swarm has identified a basin with smooth local structure, not universally. We propose Adaptive Hybrid PSO (AHPSO), which uses a sigmoid function on swarm diversity to automatically modulate gradient influence: near-zero during exploration, near-maximum during exploitation, with no manual phase-switching. Under budget-normalized comparison (PSO given equivalent total function evaluations), PSO wins 52.5% of 40 configurations versus AHPSO's 20% (p = 7.0e-5, Friedman). AHPSO retains advantage specifically on problems with smooth local basins (F8, F24-F27) where directed descent outperforms undirected sampling even at equal cost. Under iteration-matched comparison across 29 functions (42 configurations, 14,700 runs), AHPSO-Adadelta ranks first of 9 methods including CMA-ES (p = 9.75e-4). The contribution is a principled characterization of when gradient injection provides value in swarm-based search, not a claim of universal superiority.
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