结合梯度下降的自适应混合粒子群优化算法
Adaptive Hybrid Particle Swarm Optimization with Gradient Descent
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中文总结 AI 辅助
该研究提出自适应混合粒子群优化算法（AHPSO），明确了梯度注入在粒子群优化中发挥价值的场景，经实验验证其在特定优化问题上优于对比算法。
中文摘要 AI 辅助
梯度注入仅在粒子群优化（PSO）算法的种群识别出具有平滑局部结构的盆地时才会对其有帮助，并非通用有效。我们提出自适应混合粒子群优化算法（AHPSO），该算法利用种群多样性的Sigmoid函数自动调节梯度影响：探索阶段梯度影响接近零，开发阶段接近最大值，无需手动阶段切换。在预算归一化对比中（PSO与AHPSO获得的总函数评估次数相当），40种配置中PSO获胜占52.5%，AHPSO占20%（Friedman检验p值为7.0e-5）。AHPSO在具有平滑局部盆地的问题（F8、F24-F27）上保持优势，在此类问题中，定向下降即使在成本相同时也优于无定向采样。在29个函数的迭代匹配对比中（42种配置，14700次运行），AHPSO-Adadelta在包括CMA-ES在内的9种方法中排名第一（p值为9.75e-4）。本研究的贡献在于明确了在基于种群的搜索中梯度注入何时具有价值，而非声称其具有通用优越性。
英文摘要
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.
