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3、主要操作介绍 9 W- L9 n: Y8 s( W1 }, A3.1 种群初始化 3 @$ q- V. i& t. ]! T种群的初始化和具体的问题有关。比如一个问题有n个决策变量{x1,x2,…,xn}。每个决策变量有取值范围:下界{L1,L2,…,Ln}和上界{U1,U2,…,Un},则种群中个体的初始化即随机地在决策变量的取值范围内生成各个决策变量的值:Xj={x1,x2,...,xn},其中xi属于范围(Li,Ui)内。所有的个体即构成种群。当每个个体都初始化后,即种群完成初始化。) G. D' @! k" y( v# [2 Q& d g4 V
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3.2 评价种群 ( p! a t6 l, X4 U- j% l! S种群的评价即计算种群中个体的适应度值。假设种群population有popsize个个体。依次计算每个个体的适应度值及评价种群。, \( h7 y A) A# ]$ x
- \5 E$ {! }: u4 n! x3 q1 V2 D3.3 选择操作0 P- `3 J. a4 X8 a) _7 b
GA算法中常见的选择操作有轮盘赌方式:种群中适应度值更优的个体被选择的概率越大。假设popsize=4,按照如下表达式计算各个个体的被选择概率的大小,然后用圆饼图表示如下。7 t9 L! y8 b. L: Q2 n! m1 w
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P(Xj) = fit(Xj)/(fit(X1)+fit(X2)+fit(X3)+fit(X4)),j=1,2,3,4" ^" X- }) o: u8 Z2 t6 }, m9 b
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4、Python代码 % x1 I7 Y7 W8 D9 @1 d* q#-*- coding:utf-8 -*- ; m4 n7 G: `' J+ b* o# p 6 F" s( E$ ?0 Gimport random 7 G1 Q3 \) z" z Ximport math8 M/ h0 W6 E. B6 k) l( U2 H5 B
from operator import itemgetter " D2 v4 N' i' x( t1 g$ \* ] a% M% O; M- t- }/ g
class Gene:8 x V2 c+ A q- Z* i/ p! E
''' 9 I: z3 \6 P# x' Y3 Y% S$ N This is a class to represent individual(Gene) in GA algorithom% s" N, P* h) E8 U+ G" J/ ~
each object of this class have two attribute: data, size1 L3 o4 M& P( c+ K* Q
'''3 o# R! F" n- ] V" `; u
def __init__(self,**data): , \; y* _1 b+ _, q: ` self.__dict__.update(data) - W( s8 i6 b8 d6 g; e
self.size = len(data['data'])#length of gene6 c) R2 t" A5 O* e$ e
" E7 q. W V8 T2 F! K% w - n% n; G0 e( ^- C' nclass GA:& H; p/ {2 K, r6 ]+ X) S1 f
'''8 X) T* H O1 X+ g7 a' ^. a7 a
This is a class of GA algorithm. ( }7 R9 J n3 y* g2 y; `
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def __init__(self,parameter): + x4 g" A9 B. ]; g2 b) V ''' . C7 ~( ?7 m8 O8 V. J+ f Initialize the pop of GA algorithom and evaluate the pop by computing its' fitness value .4 k: S' A# v) d4 J& k. t
The data structure of pop is composed of several individuals which has the form like that:+ h6 I( \7 x! C- O! q$ n+ e m
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{'Gene':a object of class Gene, 'fitness': 1.02(for example)} 4 V# Z+ S+ D, F( m: ]1 U Representation of Gene is a list: [b s0 u0 sita0 s1 u1 sita1 s2 u2 sita2]+ F; Z; |5 j# [ w
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'''' i8 E: i: N6 J" W, d- T" z+ C
#parameter = [CXPB, MUTPB, NGEN, popsize, low, up]: S1 z4 q2 ` M" Y/ W
self.parameter = parameter 5 h8 Q. c) S" l5 ^3 y0 T# ]! k 5 X5 T2 {, s; h2 R2 V* N low = self.parameter[4] 9 n- H% R( ]6 J' c' ~ up = self.parameter[5] ! ]- h. G$ n9 Y) O$ \+ f$ O. ]7 B) C6 M0 f* N; d
self.bound = [] + K1 b5 K% ?0 y( B1 x9 {. f self.bound.append(low) ' _" ~: P* _( w3 G) d0 a self.bound.append(up) % P8 c5 i' G3 K# W1 `, L' n+ l r" p' @7 k
pop = [] 4 x. I) h* h) R! l for i in range(self.parameter[3]): 1 t6 P# c; ~& X" i: Q geneinfo = [] 7 S# O. o: [# G0 l9 p6 y+ o for pos in range(len(low)):+ \$ W% b, L1 _. m* ^$ p
geneinfo.append(random.uniform(self.bound[0][pos], self.bound[1][pos]))#initialise popluation' K8 d% U) E) F5 w' g( o
, H/ \3 g5 n: n* u& E9 I fitness = evaluate(geneinfo)#evaluate each chromosome / v( [3 u* K* g2 L2 E Q pop.append({'Gene':Gene(data = geneinfo), 'fitness':fitness})#store the chromosome and its fitness# t! X: _8 ?' ?7 p/ H
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self.pop = pop% {' s$ J6 K; T: O- n
self.bestindividual = self.selectBest(self.pop)#store the best chromosome in the population' l! P7 ~; [( _3 u2 n b
% ?0 G' C: @7 |! X2 `, e8 V! D def selectBest(self, pop): 5 Q! D& i9 a% j3 s9 J ''' 2 m4 [: I5 g# {5 R* i. O/ a select the best individual from pop$ _# B: y% B# z1 f/ o# `
''' # l. t5 @$ W* R F* G$ R, u s_inds = sorted(pop, key = itemgetter("fitness"), reverse = False) " k- a' X8 x/ F1 Q3 Z3 w8 t return s_inds[0]% N. a' x+ ^8 @3 R6 ~
0 [1 D3 G" \/ x) Z8 Q) B def selection(self, individuals, k):" h9 `* _3 g7 r- P1 ]9 J
''' n# z1 S2 p4 a! k/ l O select two individuals from pop6 e9 {% m2 E# Z+ n0 Q( [
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s_inds = sorted(individuals, key = itemgetter("fitness"), reverse=True)#sort the pop by the reference of 1/fitness 8 g, l7 S7 ]; _% \, q- K
sum_fits = sum(1/ind['fitness'] for ind in individuals) #sum up the 1/fitness of the whole pop 0 P! s8 x$ S; ]) P 3 ^: X! P) I7 H, p o4 v chosen = []( j; u/ `8 o% |& O, X
for i in xrange(k): 3 G3 G' c4 H1 C9 m- w/ M2 _/ D2 E* Z u = random.random() * sum_fits#randomly produce a num in the range of [0, sum_fits] " }6 R1 P, P0 k( l$ R2 }/ B sum_ = 0: v. I5 q7 b: Y6 l* D# P
for ind in s_inds:: g/ ?4 R& x3 ]9 R% }. {$ ?
sum_ += 1/ind['fitness']#sum up the 1/fitness * q: L/ d4 p {7 s; a if sum_ > u: ! N9 I/ A" q! ~4 z7 p7 z2 y: N #when the sum of 1/fitness is bigger than u, choose the one, which means u is in the range of [sum(1,2,...,n-1),sum(1,2,...,n)] and is time to choose the one ,namely n-th individual in the pop& w- C3 b+ ^' C) g
chosen.append(ind) ) x I j- l. w- l# j0 {* ^ break % L: d; N( i/ L% p . _# t/ h% H6 n1 x' @ return chosen , o0 E6 _ T+ y" t
. g2 j+ e8 Q# s, u X 3 n$ [9 S9 X2 x def crossoperate(self, offspring): , V ~1 p3 x0 x0 m '''$ B v6 K" D& E, ]0 d
cross operation * c# M4 L. a, H ~3 \0 @' s& |0 e ''' ) t. J+ k" S/ w% e8 ? dim = len(offspring[0]['Gene'].data)" M3 r6 ?5 c* ?- Y& e
. M1 o5 U5 {; Q* c geninfo1 = offspring[0]['Gene'].data#Gene's data of first offspring chosen from the selected pop 3 n6 w) \- C* D! M1 \- K9 T geninfo2 = offspring[1]['Gene'].data#Gene's data of second offspring chosen from the selected pop9 ]; d4 f$ @% v4 X
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pos1 = random.randrange(1,dim)#select a position in the range from 0 to dim-1, a: n9 D% @, H$ s! {; H! L3 V pos2 = random.randrange(1,dim) : }, I5 g+ Y/ r" k. V u8 g+ Q o* W8 z
newoff = Gene(data = [])#offspring produced by cross operation' P' K/ U1 A& L! \ s. c
temp = []% B* R# N* U2 M2 A
for i in range(dim): 0 H7 T+ E9 t" b; V* i, O7 n% r1 E if (i >= min(pos1,pos2) and i <= max(pos1,pos2)):$ Y) O8 @2 t# D0 b3 {
temp.append(geninfo2) . s/ O$ a; l& Z3 {2 O #the gene data of offspring produced by cross operation is from the second offspring in the range [min(pos1,pos2),max(pos1,pos2)]% u$ ?' N3 d: m: k2 B
else: 9 D" M$ g: Z+ X" i2 Q$ T) @6 w$ \% W temp.append(geninfo1) / o8 E; G: t9 m: ^- h7 q #the gene data of offspring produced by cross operation is from the frist offspring in the range [min(pos1,pos2),max(pos1,pos2)]' R* H; u! K# M# N8 G4 W/ K
newoff.data = temp : C: b, Y7 a' i8 ^ 2 y7 Q& Y. `5 C9 } return newoff 2 l2 O: [* ^& p1 x5 [6 s8 ^) v! G+ N0 S' S0 S5 {
; r0 s' E* F% Z pos = random.randrange(1,dim)#chose a position in crossoff to perform mutation. + p3 y1 Q _; G4 K# [ N) E ) b0 E/ b) S" T' e/ ?+ U7 @% | crossoff.data[pos] = random.uniform(bound[0][pos],bound[1][pos])& }) J" r/ |7 g6 q
return crossoff * P/ m! O; t7 J& L( q) o3 _1 _, } V8 R7 a: F2 m( T, `+ l
def GA_main(self): 4 M8 e5 n, h' I# t, @# R, k- a ''' + o! a1 U4 L& ~5 x main frame work of GA) ]9 M! }8 d+ j7 }# r
''' 9 P7 [1 @/ `+ Q% V q& B0 L8 E7 F0 E& K7 }
popsize = self.parameter[3]5 P6 \9 A# _ Y8 o7 ?
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print("Start of evolution") 1 Y5 [5 f% [3 {* h- N; i5 ?+ o5 _8 a7 `+ E$ W* @$ i! p5 Q
# Begin the evolution! [$ E3 u G+ ^5 ?: E3 q
for g in range(NGEN):! m7 e& j4 v/ ~! i; K' n
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print("-- Generation %i --" % g) # P+ Q0 Z8 f0 Q, O
W2 q- l0 F2 l" ]0 b #Apply selection based on their converted fitness ) X R3 u3 I8 {0 o selectpop = self.selection(self.pop, popsize) ' ]5 i3 O4 V$ r( d3 K, ~ 3 q. f1 N* {3 h3 B) ] nextoff = [] 2 ~6 V* c$ G9 L$ C6 l
while len(nextoff) != popsize: 7 C+ ?4 ^$ }# C& D0 H" c
# Apply crossover and mutation on the offspring $ y6 E( u# v% @/ p0 c b6 _
+ u3 Z) s# h: |! C. j: l
# Select two individuals) p# W7 a T/ B/ N- p/ T5 f9 J
offspring = [random.choice(selectpop) for i in xrange(2)] # s0 X+ K6 f9 K/ o( `5 p" Y8 z ( P) b N$ y) R4 k2 N2 r if random.random() < CXPB: # cross two individuals with probability CXPB 2 Q- |! e Q: A. Y, J% r crossoff = self.crossoperate(offspring)5 r4 o6 j2 p- ^" W$ P! t# E
fit_crossoff = evaluate(self.xydata, crossoff.data)# Evaluate the individuals " B( Q$ a$ A3 u/ H( ?7 V/ P- v& t
! p0 O p; b2 i4 a7 X7 Y0 L if random.random() < MUTPB: # mutate an individual with probability MUTPB1 p ^' b4 c. C' K' b# X. S2 Y
muteoff = self.mutation(crossoff,self.bound) % M/ C1 c& n: H, j2 Z; k7 j fit_muteoff = evaluate(self.xydata, muteoff.data)# Evaluate the individuals" h/ I8 ~. f0 |# R4 i
nextoff.append({'Gene':muteoff,'fitness':fit_muteoff}) 4 B! t3 H; H, G3 p- p- l/ N, E1 m' u0 Z2 m' W1 J- X1 K: n+ s
# The population is entirely replaced by the offspring/ W* v1 _8 O' A% E$ M, z; z9 K$ c8 C
self.pop = nextoff % Z4 c" u4 T& ^ % l8 [- E- X" U. s. B+ a # Gather all the fitnesses in one list and print the stats4 K4 @/ I# `! m5 o1 s. L; M! L
fits = [ind['fitness'] for ind in self.pop]' e$ n, Z( j7 m5 J/ S6 d( ~
+ {. A; V6 R3 m) e! J) p* I% f5 M
length = len(self.pop)2 @" e4 w; b. K1 ]/ c( V
mean = sum(fits) / length& X( i9 Z0 b/ D! K5 Z" `3 W$ s
sum2 = sum(x*x for x in fits)' E! T9 S" A9 R4 h% D
std = abs(sum2 / length - mean**2)**0.5 , n M Y# M% S) H1 \" i, ^- L best_ind = self.selectBest(self.pop)6 [4 N6 a* ]! f! I2 Q' P, @& M1 ]
: b) C/ R7 z1 j. S if best_ind['fitness'] < self.bestindividual['fitness']:6 _/ f' C) B8 S+ X$ N9 f
self.bestindividual = best_ind* M" Q& w% z! |$ q% `
- a1 ~+ j/ C& c8 y print("Best individual found is %s, %s" % (self.bestindividual['Gene'].data,self.bestindividual['fitness'])) 6 K, j3 @. F. r/ I7 j9 Q+ o; U print(" Min fitness of current pop: %s" % min(fits))$ L; x2 M) S2 K& c
print(" Max fitness of current pop: %s" % max(fits)) A7 Z @; W! `7 H( g2 d' d
print(" Avg fitness of current pop: %s" % mean)# R9 u6 b0 n5 H* ~$ w
print(" Std of currrent pop: %s" % std) - d' ~: t! `9 Q: q* `4 F 8 s# m' S0 j4 S% g4 P print("-- End of (successful) evolution --") # G7 Q0 J7 |& M. G5 H E2 i 6 [$ L- q# Z$ S @if __name__ == "__main__":1 U1 n6 E1 X4 Q4 L; ?8 s
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CXPB, MUTPB, NGEN, popsize = 0.8, 0.3, 50, 100#control parameters ; o7 E2 u( v! g+ [$ U$ [ * M# a7 Q* \. l8 u+ E) G up = [64, 64, 64, 64, 64, 64, 64, 64, 64, 64]#upper range for variables 4 |( G, _: I ~# M3 F low = [-64, -64, -64, -64, -64, -64, -64, -64, -64, -64]#lower range for variables+ h! s. m$ n( i% \3 [9 c
parameter = [CXPB, MUTPB, NGEN, popsize, low, up]8 z- w, I% f4 d7 }+ S/ u' w
" T1 A7 ` { G, f+ y& d1 I) z& Z run = GA(parameter) ! y! a% H' [* ~8 v2 R0 G4 Y" n run.GA_main() 6 Z ]! O9 I' m————————————————) W" O4 l& x# O- }3 o
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原文链接:https://blog.csdn.net/bible_reader/article/details/72782675 $ Q: R+ T2 K8 [ w2 F# n3 ^7 E5 a Q
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