python 遗传编程_【python(deap库)实现】GEAP 遗传算法/遗传编程 genetic programming +

前言

本文不介绍原理的东西，主要是实现进化算法的python实现。

原理介绍可以看这里，能学习要很多，我也在这里写了一些感受心得：

遗传算法/遗传编程 进化算法基于python DEAP库深度解析讲解

1.优化问题的定义

单目标优化

creator.create('FitnessMin', base.Fitness, weights=(-1.0, ))

在创建单目标优化问题时，weights用来指示最大化和最小化。此处-1.0即代表问题是一个最小化问题，对于最大化，应将weights改为正数，如1.0。

另外即使是单目标优化，weights也需要是一个tuple，以保证单目标和多目标优化时数据结构的统一。

对于单目标优化问题，weights 的绝对值没有意义，只要符号选择正确即可。

多目标优化

creator.create('FitnessMulti', base.Fitness, weights=(-1.0, 1.0))

对于多目标优化问题，weights用来指示多个优化目标之间的相对重要程度以及最大化最小化。如示例中给出的(-1.0, 1.0)代表对第一个目标函数取最小值，对第二个目标函数取最大值。

2.个体编码

实数编码(Value encoding)：直接用实数对变量进行编码。优点是不用解码，基因表达非常简洁，而且能对应连续区间。但是实数编码后搜索区间连续，因此容易陷入局部最优。

实数编码

from deap import base, creator, tools

import random

IND_SIZE = 5

creator.create('FitnessMin', base.Fitness, weights=(-1.0,)) #优化目标：单变量，求最小值

creator.create('Individual', list, fitness = creator.FitnessMin) #创建Individual类，继承list

toolbox = base.Toolbox()

toolbox.register('Attr_float', random.random)

toolbox.register('Individual', tools.initRepeat, creator.Individual, toolbox.Attr_float, n=IND_SIZE)

ind1 = toolbox.Individual()

print(ind1)

# 结果：[0.8579615693371493, 0.05774821674048369, 0.8812411734389638, 0.5854279538236896, 0.12908399219828248]

二进制编码

from deap import base, creator, tools

from scipy.stats import bernoulli

creator.create('FitnessMin', base.Fitness, weights=(-1.0,)) #优化目标：单变量，求最小值

creator.create('Individual', list, fitness = creator.FitnessMin) #创建Individual类，继承list

GENE_LENGTH = 10

toolbox = base.Toolbox()

toolbox.register('Binary', bernoulli.rvs, 0.5) #注册一个Binary的alias，指向scipy.stats中的bernoulli.rvs，概率为0.5

toolbox.register('Individual', tools.initRepeat, creator.Individual, toolbox.Binary, n = GENE_LENGTH) #用tools.initRepeat生成长度为GENE_LENGTH的Individual

ind1 = toolbox.Individual()

print(ind1)

# 结果：[1, 0, 0, 0, 0, 1, 0, 1, 1, 0]

序列编码(Permutation encoding)

from deap import base, creator, tools

import random

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))

creator.create("Individual", list, fitness=creator.FitnessMin)

IND_SIZE=10

toolbox = base.Toolbox()

toolbox.register("Indices", random.sample, range(IND_SIZE), IND_SIZE)

toolbox.register("Individual", tools.initIterate, creator.Individual,toolbox.Indices)

ind1 = toolbox.Individual()

print(ind1)

#结果：[0, 1, 5, 8, 2, 3, 6, 7, 9, 4]

粒子(Particles)

import random

from deap import base, creator, tools

creator.create("FitnessMax", base.Fitness, weights=(1.0, 1.0))

creator.create("Particle", list, fitness=creator.FitnessMax, speed=None,

smin=None, smax=None, best=None)

# 自定义的粒子初始化函数

def initParticle(pcls, size, pmin, pmax, smin, smax):

part = pcls(random.uniform(pmin, pmax) for _ in range(size))

part.speed = [random.uniform(smin, smax) for _ in range(size)]

part.smin = smin

part.smax = smax

return part

toolbox = base.Toolbox()

toolbox.register("Particle", initParticle, creator.Particle, size=2, pmin=-6, pmax=6, smin=-3, smax=3) #为自己编写的initParticle函数注册一个alias "Particle"，调用时生成一个2维粒子，放在容器creator.Particle中，粒子的位置落在(-6,6)中，速度限制为(-3，3)

ind1 = toolbox.Particle()

print(ind1)

print(ind1.speed)

print(ind1.smin, ind1.smax)

# 结果：[-2.176528549934324, -3.0796558214905]

#[-2.9943676285620104, -0.3222138308543414]

#-3 3

print(ind1.fitness.valid)

# 结果：False

# 因为当前还没有计算适应度函数，所以粒子的最优适应度值还是invalid

3 初始种群建立

一般族群

这是最常用的族群类型，族群中没有特别的顺序或者子族群。

from deap import base, creator, tools

from scipy.stats import bernoulli

# 定义问题

creator.create('FitnessMin', base.Fitness, weights=(-1.0,)) # 单目标，最小化

creator.create('Individual', list, fitness = creator.FitnessMin)

# 生成个体

GENE_LENGTH = 5

toolbox = base.Toolbox() #实例化一个Toolbox

toolbox.register('Binary', bernoulli.rvs, 0.5)

toolbox.register('Individual', tools.initRepeat, creator.Individual, toolbox.Binary, n=GENE_LENGTH)

# 生成初始族群

N_POP = 10

toolbox.register('Population', tools.initRepeat, list, toolbox.Individual)

toolbox.Population(n = N_POP)

# 结果：

# [[1, 0, 1, 1, 0],

# [0, 1, 1, 0, 0],

# [0, 1, 0, 0, 0],

# [1, 1, 0, 1, 0],

# [0, 1, 1, 1, 1],

# [0, 1, 1, 1, 1],

# [1, 0, 0, 0, 1],

# [1, 1, 0, 1, 0],

# [0, 1, 1, 0, 1],

# [1, 0, 0, 0, 0]]

同类群

同类群即一个族群中包含几个子族群。在有些算法中，会使用本地选择(Local selection)挑选育种个体，这种情况下个体仅与同一邻域的个体相互作用。

toolbox.register("deme", tools.initRepeat, list, toolbox.individual)

DEME_SIZES = 10, 50, 100

population = [toolbox.deme(n=i) for i in DEME_SIZES]

粒子群

粒子群中的所有粒子共享全局最优。在实现时需要额外传入全局最优位置与全局最优适应度给族群。

creator.create("Swarm", list, gbest=None, gbestfit=creator.FitnessMax)

toolbox.register("swarm", tools.initRepeat, creator.Swarm, toolbox.particle)

4 评价

评价部分是根据任务的特性高度定制的，DEAP库中并没有预置的评价函数模版。

在使用DEAP时，需要注意的是，无论是单目标还是多目标优化，评价函数的返回值必须是一个tuple类型。

from deap import base, creator, tools

import numpy as np

# 定义问题

creator.create('FitnessMin', base.Fitness, weights=(-1.0,)) #优化目标：单变量，求最小值

creator.create('Individual', list, fitness = creator.FitnessMin) #创建Individual类，继承list

# 生成个体

IND_SIZE = 5

toolbox = base.Toolbox()

toolbox.register('Attr_float', np.random.rand)

toolbox.register('Individual', tools.initRepeat, creator.Individual, toolbox.Attr_float, n=IND_SIZE)

# 生成初始族群

N_POP = 10

toolbox.register('Population', tools.initRepeat, list, toolbox.Individual)

pop = toolbox.Population(n = N_POP)

# 定义评价函数

def evaluate(individual):

return sum(individual), #注意这个逗号，即使是单变量优化问题，也需要返回tuple

# 评价初始族群

toolbox.register('Evaluate', evaluate)

fitnesses = map(toolbox.Evaluate, pop)

for ind, fit in zip(pop, fitnesses):

ind.fitness.values = fit

print(ind.fitness.values)

# 结果：

# (2.593989197511478,)

# (1.1287944225903104,)

# (2.6030877077096717,)

# (3.304964061515382,)

# (2.534627558467466,)

# (2.4697149450205536,)

# (2.344837782191844,)

# (1.8959030773060852,)

# (2.5192475334239,)

# (3.5069764929866585,)

5 配种选择

selTournament()锦标赛选择

selRoulette()轮盘赌选择(不能用于最小化或者适应度会小于等于0的问题)

selNSGA2()NSGA-II选择，适用于多目标遗传算法

selSPEA2()SPEA2选择，目前版本(ver 1.2.2)的该函数实现有误，没有为个体分配距离，不建议使用。

selRandom()有放回的随机选择

selBest()选择最佳

selWorst()选择最差

selTournamentDCD()Dominance/Crowding distance锦标赛选择，目前版本的实现也有些问题

selDoubleTournament()Size+Fitness双锦标赛选择

selStochasticUniversalSampling()随机抽样选择

selLexicase()词典选择，参考这篇文章

selEpsilonLexicase()词典选择在连续值域上的扩展

from deap import base, creator, tools

import numpy as np

# 定义问题

creator.create('FitnessMin', base.Fitness, weights=(-1.0,)) #优化目标：单变量，求最小值

creator.create('Individual', list, fitness = creator.FitnessMin) #创建Individual类，继承list

# 生成个体

IND_SIZE = 5

toolbox = base.Toolbox()

toolbox.register('Attr_float', np.random.rand)

toolbox.register('Individual', tools.initRepeat, creator.Individual, toolbox.Attr_float, n=IND_SIZE)

# 生成初始族群

N_POP = 10

toolbox.register('Population', tools.initRepeat, list, toolbox.Individual)

pop = toolbox.Population(n = N_POP)

# 定义评价函数

def evaluate(individual):

return sum(individual), #注意这个逗号，即使是单变量优化问题，也需要返回tuple

# 评价初始族群

toolbox.register('Evaluate', evaluate)

fitnesses = map(toolbox.Evaluate, pop)

for ind, fit in zip(pop, fitnesses):

ind.fitness.values = fit

# 选择方式1：锦标赛选择

toolbox.register('TourSel', tools.selTournament, tournsize = 2) # 注册Tournsize为2的锦标赛选择

selectedTour = toolbox.TourSel(pop, 5) # 选择5个个体

print('锦标赛选择结果：')

for ind in selectedTour:

print(ind)

print(ind.fitness.values)

# 选择方式2: 轮盘赌选择

toolbox.register('RoulSel', tools.selRoulette)

selectedRoul = toolbox.RoulSel(pop, 5)

print('轮盘赌选择结果：')

for ind in selectedRoul:

print(ind)

print(ind.fitness.values)

# 选择方式3: 随机普遍抽样选择

toolbox.register('StoSel', tools.selStochasticUniversalSampling)

selectedSto = toolbox.StoSel(pop, 5)

print('随机普遍抽样选择结果：')

for ind in selectedSto:

print(ind)

print(ind.fitness.values)

#结果：

#锦标赛选择结果：

#[0.2673058115582905, 0.8131397980144155, 0.13627430737326807, 0.10792026110464248, 0.4166962522797264]

#(1.741336430330343,)

#[0.5448284697291571, 0.9702727117158071, 0.03349947770537576, 0.7018813286570782, 0.3244029157717422]

#(2.5748849035791603,)

#[0.8525836387058023, 0.28064482205939634, 0.9235436615033125, 0.6429467684175085, 0.5965523553349544]

#(3.296271246020974,)

#[0.5243293164960845, 0.37883291328325286, 0.28423194217619596, 0.5005947374376103, 0.3017896612109636]

#(1.9897785706041071,)

#[0.4038211036464676, 0.841374996509095, 0.3555644512425019, 0.5849111474726337, 0.058759891556433574]

#(2.2444315904271317,)

#轮盘赌选择结果：

#[0.42469039733882064, 0.8411201950346711, 0.6322812691061555, 0.7566549973076343, 0.9352307652371067]

#(3.5899776240243884,)

#[0.42469039733882064, 0.8411201950346711, 0.6322812691061555, 0.7566549973076343, 0.9352307652371067]

#(3.5899776240243884,)

#[0.5448284697291571, 0.9702727117158071, 0.03349947770537576, 0.7018813286570782, 0.3244029157717422]

#(2.5748849035791603,)

#[0.630305953330188, 0.09565983206218687, 0.890691659939096, 0.8706091807317707, 0.19708949882847437]

#(2.684356124891716,)

#[0.5961060867498598, 0.4300051776616509, 0.4512760237511251, 0.047731561819711055, 0.009892120639829804]

#(1.5350109706221766,)

#随机普遍抽样选择结果：

#[0.2673058115582905, 0.8131397980144155, 0.13627430737326807, 0.10792026110464248, 0.4166962522797264]

#(1.741336430330343,)

#[0.4038211036464676, 0.841374996509095, 0.3555644512425019, 0.5849111474726337, 0.058759891556433574]

#(2.2444315904271317,)

#[0.630305953330188, 0.09565983206218687, 0.890691659939096, 0.8706091807317707, 0.19708949882847437]

#(2.684356124891716,)

#[0.40659881466060876, 0.8387139101647804, 0.28504735705240236, 0.46171554118627334, 0.7843353275244066]

#(2.7764109505884718,)

#[0.42469039733882064, 0.8411201950346711, 0.6322812691061555, 0.7566549973076343, 0.9352307652371067]

#(3.5899776240243884,)

6 变异

cxOnePoint()单点交叉实数、二进制

cxTwoPoint()两点交叉实数、二进制

cxUniform()均匀交叉实数、二进制

cxPartialyMatched()部分匹配交叉PMX序列

cxUniformPartialyMatched()PMX变种，改两点为均匀交叉序列

cxOrdered()有序交叉序列

cxBlend()混合交叉实数

cxESBlend()带进化策略的混合交叉

cxESTwoPoint()带进化策略的两点交叉

cxSimulatedBinary()模拟二值交叉实数

cxSimulatedBinaryBounded()有界模拟二值交叉实数

cxMessyOnePoint()混乱单点交叉实数、二进制

from deap import base, creator, tools

import random

# 创建两个序列编码个体

random.seed(42) # 保证结果可复现

IND_SIZE = 8

creator.create('FitnessMin', base.Fitness, weights=(-1.0, ))

creator.create('Individual', list, fitness = creator.FitnessMin)

toolbox = base.Toolbox()

toolbox.register('Indices', random.sample, range(IND_SIZE), IND_SIZE)

toolbox.register('Individual', tools.initIterate, creator.Individual, toolbox.Indices)

ind1, ind2 = [toolbox.Individual() for _ in range(2)]

print(ind1, '\n', ind2)

# 结果：[1, 0, 5, 2, 7, 6, 4, 3]

# [1, 4, 3, 0, 6, 5, 2, 7]

# 单点交叉

child1, child2 = [toolbox.clone(ind) for ind in (ind1, ind2)]

tools.cxOnePoint(child1, child2)

print(child1, '\n', child2)

#结果：[1, 4, 3, 0, 6, 5, 2, 7]

# [1, 0, 5, 2, 7, 6, 4, 3]

# 可以看到从第四位开始被切开并交换了

# 两点交叉

child1, child2 = [toolbox.clone(ind) for ind in (ind1, ind2)]

tools.cxTwoPoint(child1, child2)

print(child1, '\n', child2)

# 结果：[1, 0, 5, 2, 6, 5, 2, 3]

# [1, 4, 3, 0, 7, 6, 4, 7]

# 基因段[6, 5, 2]与[7, 6, 4]互换了

# 均匀交叉

child1, child2 = [toolbox.clone(ind) for ind in (ind1, ind2)]

tools.cxUniform(child1, child2, 0.5)

print(child1, '\n', child2)

# 结果：[1, 0, 3, 2, 7, 5, 4, 3]

# [1, 4, 5, 0, 6, 6, 2, 7]

# 部分匹配交叉

child1, child2 = [toolbox.clone(ind) for ind in (ind1, ind2)]

tools.cxPartialyMatched(child1, child2)

print(child1, '\n', child2)

# 结果：[1, 0, 5, 2, 6, 7, 4, 3]

# [1, 4, 3, 0, 7, 5, 2, 6]

# 可以看到与之前交叉算子的明显不同，这里的每个序列都没有冲突

# 有序交叉

child1, child2 = [toolbox.clone(ind) for ind in (ind1, ind2)]

tools.cxOrdered(child1, child2)

print(child1, '\n', child2)

# 结果：[5, 4, 3, 2, 7, 6, 1, 0]

# [3, 0, 5, 6, 2, 7, 1, 4]

# 混乱单点交叉

child1, child2 = [toolbox.clone(ind) for ind in (ind1, ind2)]

tools.cxMessyOnePoint(child1, child2)

print(child1, '\n', child2)

# 结果：[1, 0, 5, 2, 7, 4, 3, 0, 6, 5, 2, 7]

# [1, 6, 4, 3]

# 注意个体序列长度的改变

7 突变

from deap import base, creator, tools

import random

# 创建一个实数编码个体

random.seed(42) # 保证结果可复现

IND_SIZE = 5

creator.create('FitnessMin', base.Fitness, weights=(-1.0, ))

creator.create('Individual', list, fitness = creator.FitnessMin)

toolbox = base.Toolbox()

toolbox.register('Attr_float', random.random)

toolbox.register('Individual', tools.initRepeat, creator.Individual, toolbox.Attr_float, IND_SIZE)

ind1 = toolbox.Individual()

print(ind1)

# 结果：[0.6394267984578837, 0.025010755222666936, 0.27502931836911926, 0.22321073814882275, 0.7364712141640124]

# 高斯突变

mutant = toolbox.clone(ind1)

tools.mutGaussian(mutant, 3, 0.1, 1)

print(mutant)

# 结果：[3.672658632864655, 2.99827700737295, 3.2982590920597916, 3.339566606808737, 3.6626390539295306]

# 可以看到当均值给到3之后，变异形成的个体均值从0.5也增大到了3附近

# 乱序突变

mutant = toolbox.clone(ind1)

tools.mutShuffleIndexes(mutant, 0.5)

print(mutant)

# 结果：[0.22321073814882275, 0.7364712141640124, 0.025010755222666936, 0.6394267984578837, 0.27502931836911926]

# 有界多项式突变

mutant = toolbox.clone(ind1)

tools.mutPolynomialBounded(mutant, 20, 0, 1, 0.5)

print(mutant)

# 结果：[0.674443861742489, 0.020055418656044655, 0.2573977358171454, 0.11555018832942898, 0.6725269223692601]

# 均匀整数突变

mutant = toolbox.clone(ind1)

tools.mutUniformInt(mutant, 1, 5, 0.5)

print(mutant)

# 结果：[0.6394267984578837, 3, 0.27502931836911926, 0.22321073814882275, 0.7364712141640124]

# 可以看到在第二个位置生成了整数3

8 环境选择

DEAP中没有设定专门的reinsertion操作。可以简单的用python的list操作来完成选择