纯Python实现遗传算法详解

# x为变量，xL为解范围的最小值，pre为精度，N为二进制解的个数
def codeOne(x, xL, pre, N):
    x = int((x-xL)/pre)
    return [(x//2**i)%2 for i in range(N)]
from itertools import chain
# xs为一组变量， xL, xR为变量区间， pre为精度
def coding(xs, xL, xR, pre):
    N = int(np.ceil(np.log2((xR-xL)/pre)))
    xs = [codeOne(x, xL, pre, N) for x in xs]
    return np.array(list(chain(*xs)))
# 解码是编码的逆过程
def decodeOne(b, xL, pre, N):
    x = np.sum([b[i]*2**i for i in range(N)])
    return xL + x*pre
def decoding(bins, xL, xR, pre):
    N = int(np.ceil(np.log2((xR-xL)/pre)))
    M = int(len(bins)/N)
    return [decodeOne(bins[N*i:N*(i+1)], xL, pre, N) 
        for i in range(M)]

import numpy as np
# b1,b2为编码后的二进制串
# M为编码后的二进制长度；index为自然数列
def cross(b1, b2, M, index):
    np.random.shuffle(index)
    i1 = index[:randint(0,M)]
    np.random.shuffle(index)
    i2 = index[:randint(0,M)]
    b1[i1], b2[i2] = b2[i1], b1[i2]

from copy import deepcopy
from random import randint
# rMuta为突变概率；nDie为每一代淘汰掉的个数
def genetic(xs, func, xL, xR, pre, nMuta, nDie):
    N = len(xs)
    fs = [func(x) for x in xs]
    index = np.argsort(fs)
    fBest = fs[index[0]]
    # 将最差的淘汰掉，将最优的提取出来
    xs[index[-nDie:]] = xs[index[:nDie]]
    # 编码
    bs = [coding(x, xL, xR, pre) for x in xs]
    M = len(bs[0])      # 此为编码后的参数长度
    index = np.arange(M)
    # 交叉
    for i in range(N//2):
        cross(bs[i*2], bs[i*2+1], int(M/2), index)
    # 此为突变点个数
    for b in bs:
        np.random.shuffle(index)
        b[index[:nMuta]] = ~b[index[:nMuta]]
    # 最后解码并输出
    xs = [decoding(b, xL, xR, pre) for b in bs]
    return np.array(xs), fBest

uniRand = np.random.uniform
# nId为个体数；nDim为参数维度；nIter为迭代数
# xRange为x取值范围，pre是精度
def GA(func, nId, nDim, nIter, 
    xRange, pre, rMuta, nDie):
    xs = [uniRand(*xRange, nDim) for _ in range(nId)]
    xs = np.array(xs)
    for i in range(nIter):
        xs, fBest = genetic(xs, func, xRange[0], xRange[1],
            pre, rMuta, nDie)
        if i%20==0:
            msg = f"第{i}次迭代，最佳结果为{fBest}"
            print(msg)
    fs = [func(x) for x in xs]
    index = np.argmin(fs)
    msg = "当前参数：" + ",".join([f"{x}" for x in xs[index]])
    print(msg)

def test(xs):
    _sum = 0.0
    for i in range(len(xs)):
        _sum = _sum + np.cos((xs[i]*i)/5)*(i+1)
    return _sum
if __name__ == "__main__":
    GA(test, 30, 5, 101, (-5,5), 1e-6, 2, 2)