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

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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, ‘
‘, 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, ‘
‘, 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, ‘
‘, 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, ‘
‘, 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, ‘
‘, 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, ‘
‘, 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, ‘
‘, 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

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