基于多目标人工鱼群算法的符号回归

Symbolic regression via a multi-objective artificial fish school algorithm

针对现有符号回归方法仅关注拟合误差而忽略模型简化的问题,提出了一种基于多目标的人工鱼群算法,将拟合误差与模型复杂度同时作为目标函数进行优化.以二叉堆对语法树编码,优良分支得以稳定地遗传和继承,也更易解码.在引入蒙版、邻域、小生境、拥挤度等概念的基础上,设计和定义了适用于二叉堆编码的随机游动、觅食、追尾、逃脱等人工鱼行为算子.详尽的实验表明,提出算法在符号回归过程中能获取高质量的Pareto解.此外,对从Pareto前沿上选取折衷解及降低算法内存开销的方法也进行了讨论.

Aiming at the issue that the existing methods for symbolic regression focus on minimizing the fitting error merely while ignore the model simplification,a multi-objective artificial fish school algorithm is proposed for minimizing the fitting error and the model complexity simultaneously during symbolic regression.The parse tree is encoded as the form of binary heap,such that fine branches of the parse tree could be stably inherited,and suchlike binary heap-based representation is easier to decode.By introducing the conceptions such as mask,neighborhood,niche,and crowding degree,several behavior operators performed by the artificial fish,including randomly moving,foraging,following,and escaping,are defined.Exhaustive simulation results show that the proposed algorithm is capable of obtaining high-quality Pareto solutions during symbolic regression.Besides,the method of determining a trade-off solution from the obtained Pareto front and that of reducing the memory overhead are also discussed.