Abstract: Gene Expression Programming（GEP） is a powerful evolutionary algorithm widely used in function mining. and how to determine numeric constants has important influence to the performance of GEP. A novel approach of optimizing numeric constants based on co-evolutionary Gene Expression Programming（GEP-DE） is proposed in this paper. The main improvement in GEP-DE is to give a novel numeric constants optimization method, where the evolutionary process is divided into 2 phases in each generation：in the first phase, GEP focuses on optimizing the structure of function expression, and in the second one, DE focuses on optimizing the constant parameters. The experimental result on function mining problems shows that the performance of GEP-DE is better than that of the state-of-the-art GEP variants.

Key words: evolution computing, function mining, constant optimization, differential evolution, co-evolution

摘要： 基因表达式编程（GEP）算法是一种具有强大函数发现能力的新型进化算法。GEP在函数发现时如何确定合适的数值常量对算法的性能具有很大影响。提出了一种基于协同进化基因表达式编程的函数发现算法（GEP-DE），该算法的最大改进在于一种新的常量优化方法：在每一代中将函数发现的过程分为两个阶段：第一阶段，由标准GEP算法结合固定常量集确定函数结构；第二阶段，使用差分进化算法（DE）对第一阶段得出的函数结构的常量进行优化。实验结果表明，GEP-DE算法比重要文献中的常量处理方法其效果有较大提升，并且算法的综合性能也优于最新重要文献提出的GEP算法。

关键词: 进化计算, 函数发现, 常量优化, 差分进化, 协同进化