This paper presents a particle swarm optimization algorithm that leverages surrogate modeling to replace the conventional global best solution with the minimum of an n-dimensional quadratic form, providing a better-conditioned dynamic attractor for the swarm. This refined convergence target, informed by the local landscape, enhances global convergence behavior and increases robustness against premature convergence and noise, while incurring only minimal computational overhead. The surrogate-augmented approach is evaluated against the standard algorithm through a numerical study on a set of benchmark optimization functions that exhibit diverse landscapes. To ensure statistical significance, 400 independent runs are conducted for each function and algorithm, and the results are analyzed based on their statistical characteristics and corresponding distributions. The quadratic surrogate attractor consistently outperforms the conventional algorithm across all tested functions. The improvement is particularly pronounced for quasi-convex functions, where the surrogate model can exploit the underlying convex-like structure of the landscape.

翻译：本文提出一种粒子群优化算法，该算法利用代理建模将传统的全局最佳解替换为n维二次型的最小值，为种群提供条件更优的动态吸引子。这一基于局部地形信息优化的收敛目标，在仅增加极小计算开销的同时，增强了全局收敛性能，并提高了对早熟收敛和噪声的鲁棒性。通过在一组具有不同地形的基准优化函数上进行数值实验，将该代理增强方法与标准算法进行了对比评估。为确保统计显著性，对每个函数和算法进行了400次独立运行，并根据其统计特性及相应分布对结果进行分析。二次代理吸引子在所有测试函数上均持续优于传统算法。对于拟凸函数，改进效果尤为显著，因为代理模型能够利用地形中潜在的类凸结构。