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带差商信息的云有哪些信誉好的足球投注网站优化算法及其收敛性分析 殷 哲1 ，曹 炬1 (华中科技大学大学数学与统计学院，武汉 430074)1 摘要：将云的生成、动态运动、降雨和再生成等自然现象与智能优化算法的思想融合，建立了一种新的智能优化算法-云有哪些信誉好的足球投注网站优化算法（Clouds Search Optimization Algorithm）。云团内部水滴可以产生差商信息指导有哪些信誉好的足球投注网站，差商可以逼近梯度，且负差商与负梯度同样为函数值下降方向，基于此进一步提出带差商信息的云有哪些信誉好的足球投注网站优化算法（Clouds Search Optimization Algorithm with Difference Quotient Information）。依据差商与梯度的近似关系证明了DCSO具有类似经典的基于梯度的优化算法的收敛性，最优水滴可以收敛到极值点。benchmark函数的数值实验表明，CSO与DCSO都具有很强的寻优能力，且差商信息可以指导水滴迅速向极值点移动，大大提高了DCSO的收敛速度。 关键词：云有哪些信誉好的足球投注网站优化算法；智能优化；函数优化；差商信息；梯度 中图法分类号　TP301　　 文献标识码　A Clouds Search Optimization Algorithm with Difference Quotient Information and Its Convergence Analysis YIN Zhe1, CAO Ju1 (School of Mathematics and Statistics, Huazhong University of Science Technology, WuHan 430074)1 Abstract: Clouds have many natural phenomena such as generation, dynamic movement, rainfall and regeneration. A novel intelligent optimization algorithm called clouds search optimization algorithm, or CSO is proposed in this paper by blending these natural phenomena of clouds with the ideas of intelligent optimization algorithms. Droplets inside a cloud can produce difference quotient information to guide the search. Difference quotient information can approximate gradient, and its reverse direction can guide function value’s decline. On the basis of difference quotient’s those properties, clouds search optimization algorithm with difference quotient information (DCSO) is also proposed in this paper. It proved to be convergent by using the relationship between difference quotient and gradient, and the convergence property is similar to classical gradient-based algorithm. Finally, the numerical experiments on benchmark functions showed the excellent performance of the two algorithms and the fast convergence speed of DCSO. Keywords: Clouds Search Optimization Algorithm; Intelligent Optimization; Function Optimization; Difference Quotient Information; Gradient 引言 优化问题广泛存在于工程应用、经济管理、科学研究等领域[1]，对优化算法的研究一直具有重大意义。经典的基于梯度的优化算法（如最速下降法和共轭梯度法）可以成功找到一些简单优化问题的最优解[2]，而且具有完善的收敛性理论。由于