arXiv:2511.13843math.OCcs.LG2025-11

QUASAR算法通过自适应机制加速高维优化,显著提升求解速度与精度。

QUASAR: An Evolutionary Algorithm to Accelerate High-Dimensional Numerical Optimization

  • 融合量子启发机制,动态调节探索与利用平衡
  • 在CEC2017测试集上平均性能优于DE和L-SHADE,速度提升达5.16倍
  • 适合高维非可微复杂优化问题,无需调参,易用性强

高维数值优化在计算科学中长期面临挑战。本文提出准自适应渐近重初始化搜索(QUASAR),一种进化算法,用于加速复杂、不可微问题的收敛,克服维度诅咒。该算法基于差分进化(DE)核心思想,引入准自适应机制,动态平衡探索与利用。受量子粒子行为启发,采用三种高度随机机制:1)概率化变异策略与缩放因子;2)基于排名的交叉率;3)渐近衰减的协方差重初始化。在著名的CEC2017基准测试套件(29个测试函数)上,QUASAR以最低总体秩和(367)胜出,优于DE(735)和L-SHADE(452)。几何均值比较显示,相比DE和L-SHADE,最终解质量分别提升3.85倍和2.07倍(p≪0.001),平均优化速度分别快1.40倍和5.16倍。结果表明,QUASAR是一种高效、有效且用户友好的高维复杂优化算法。

原文摘要 · Abstract (English)

High-dimensional numerical optimization presents a persistent challenge in computational science. This paper introduces Quasi-Adaptive Search with Asymptotic Reinitialization (QUASAR), an evolutionary algorithm to accelerate convergence in complex, non-differentiable problems afflicted by the curse of dimensionality. QUASAR expands upon the core principles of Differential Evolution (DE), introducing quasi-adaptive mechanisms to dynamically balance exploration and exploitation in its search. Inspired by the behavior of quantum particles, the algorithm utilizes three highly stochastic mechanisms that augment standard DE: 1) probabilistic mutation strategies and scaling factors; 2) rank-based crossover rates; 3) asymptotically decaying covariance reinitializations. Evaluated on the notoriously difficult CEC2017 benchmark suite of 29 test functions, QUASAR achieved the lowest overall rank sum (367) using the Friedman test, outperforming DE (735) and L-SHADE (452). Geometric mean comparisons show average final solution quality improvements of $3.85 \times$ and $2.07 \times$ compared to DE and L-SHADE, respectively ($p \ll 0.001$), with average optimization speed averaging $1.40 \times$ and $5.16 \times$ faster. QUASAR's performance establishes it as an effective, efficient, and user-friendly evolutionary algorithm for complex high-dimensional problems.

进化算法高维优化差分进化数值优化

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