带误差余项的基因表达式编程

Gene Expression Programming with Error Remainder

摘要: 基因表达式算法(Gene Expression Programming, GEP)在函数挖掘方面有较大的优越性，但容易过早收敛，且很难跳出局部最优解，导致最后的绝对误差较大，为此提出了一种带有余项误差的方法。该方法在当个体陷入局部最优时，将函数值与目标值的误差作为余项，进一步把该余项数据再进行函数挖掘，由此找到的新函数更接近目标值。反复多次用GEP寻找跟余项数据逼近的函数，再计算新的余项，可让余项的绝对值也就是函数的绝对误差依概率收敛于0。并从理论上证明了这种算法的可行性。通过仿真例，结果表明该方法在降低绝对误差上起到良好的作用。

Abstract: The traditional GEP is superior over other algorithms for function mining, but it gets easily struck at local optimal solution and jump difficultly out of local optimal solution, and result in greater absolute error. A new GEP with remainder is proposed. When the individuality fall in local peak, the error between function value and target value is regarded as remainder term in proposed method. The remainder is considered as a new target value and the algorithm is keeping on working to search the new function. This process is repeated until the error reaches desired target. The absolute value of remainder which means function absolute error has been proved to converge to 0 inprobability. The simulation results show that the algorithm can reduce absolute error efficiently.