一种求解符号回归问题的粒子群优化算法

符号回归以构建一个能拟合给定数据集的函数模型为目的, 是对基本函数、运算符、变量等进行组合优化的过程.本文提出了一种求解符号回归问题的粒子群优化算法.算法以语法树对函数模型进行表达, 采用基因表达式将语法树编码为一个粒子, 设计了粒子的飞行方法及$r$-邻域环状拓扑的粒子学习关系.为使粒子具有跳出局部极值的能力和减轻粒子快速趋同对全局寻优造成的不利影响, 分别设计了突变算子和散开算子.此外, 为了得到比较简洁的函数模型, 在粒子的评价函数中以罚函数的方式对编码的有效长度进行控制.仿真实验表明, 提出的算法可以获得拟合精度更高、简洁性更好的函数模型.

A Particle Swarm Optimization Approach for Symbolic Regression

Symbolic regression is to construct a function model that fits a given dataset. It is the process of optimally combining various basic functions, operators, and variables. This paper proposes a particle swarm optimization-based algorithm for symbolic regression. In the proposed algorithm, the functional model to be established is represented as a syntax tree, which is encoded as a particle through gene-expression. A specific implementation of particles flying and the $r$-neighborhood learning mechanism of particle swarm were designed. To make particles be capable of jumping out local extremum and to mitigate the negative influence on global optimization resulted from the fast convergence of the particle swarm, mutation and scatter are respectively introduced into the proposed algorithm as operators. Besides, in order to obtain concise functional model, the valid length of the gene-expression-based coding scheme is controlled in manner of introducing a penalty term to the particle evaluation function. Exhaustive simulation experiments are carried out and the results show that, the proposed algorithm can obtain the functional model with higher fitting precision and better conciseness.