基于粒子群优化算法的广义累加灰色模型

Indirect generating grey model based on particle swarm optimization algorithm

探讨定性分析与定量计算相结合的广义累加生成技术,讨论基于粒子群优化算法(particl swarm optimization algorithm,PSOA)的累加矩阵求解方法和间接灰色模型的优化算法。首先分析和总结4类典型序列的累加生成矩阵模式与参数结构,然后根据实际问题选择合适的累加生成矩阵模式,并用模式中的参数与背景值修正向量共同构成待求粒子。借助粒子群优化算法,以间接灰色模型的平均相对误差为适应度函数,以其最小为目标,通过迭代求解累加生成矩阵和背景值修正向量。实例计算表明,该优化模型不仅具有较高的模拟和预测精度,而且能够较好地跟踪波动序列和高增长序列的变化趋势。

This paper discusses the extended accumulated generating technology combined qualitative analysis with quantitative evaluation,and researches the solving method of extended accumulated generating matrix and the optimized algorithm of the extended accumulated generating grey model.Firstly,the accumulated generating modes and its structures of parameters are summed up for four classical sequences.Then,an appropriate generating mode should be chosen according to actual problem,and a particle including parameters of the mode and the modified vector of background value is constructed.Furthermore,the particle swarm optimization algorithm（PSOA） is adopted to solve the generating matrix and the modified vector of background value.The fitness function of PSOA is the absolute of mean relative error,and objective function is the minimization of the fitness.The practical examples show that the optimized model not only improves the simulation and prediction accuracy,but also can track the trend of fluctuate and fast increase sequences.