中心引力算法收敛分析及在神经网络中的应用

Convergence Proof for Central Force Optimization Algorithm and Application in Neural Networks

中心引力优化算法(central force optimization,简称CFO)是一种新型的基于天体动力学的多维搜索优化算法.该算法是一种确定性的优化算法,利用一组质子在万有引力作用下的运动,搜索目标函数在决策空间上的最优值.利用天体力学理论对该算法中质子运动方程进行了深入的研究,并利用天体力学中万有引力定理对质子运动方程进行了推导,建立起天体力学与CFO算法之间的联系,通过天体力学中数学分析的方法对该算法中质子收敛性能进行了分析,最后,通过严格的数学推导证明出:无论初始时质子是何种分布,CFO算法中所有的质子始终都会收敛于CFO空间的确定最优解.作为测试效果,将CFO算法与常见的BP训练算法相结合,提出了CFO-BP训练算法,优化前馈型人工神经网络的权值和结构.实验结果表明,采用CFO-BP算法优化神经网络比其他常见优化算法有更好的收敛精度和收敛速度.

Central force optimization （CFO） is a new deterministic multi-dimensional search metaheuristie based on the metaphor of gravitational kinematics. CFO is a deterministic algorithm that explores a decision space by ＂flying＂ a group of probes whose trajectories are governed by Newton＇s laws. Based on in-deph studies on the probes movement governed by the equations of gravitational motion, this paper utilizes Celestial Mechanics theory to deduce moving formulas, establishes the relationship between CFO algorithm and Celestial Mechanics, and analyzes CFO convergence through mathematics analysis of Celestial Mechanics. It concludes that no matter how initial probe distribute, all probes converge deterministically in CFO space with optimal solution. To test CFO＇s effectiveness, a hybrid CFO-BP algorithm is proposed for joint optimization of three-layer feed forward artificial neural network （ANN） structure and parameters （weights and bias）. The experimental results show that the proposed hybrid CFO-BP algorithm is better than other algorithms in convergent speed and convergent accuracy.