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ackley.py
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ackley.py
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#File ackley.py
#Algoritmo para obtener minimo de la funcion de ackley
#Miguel Angel Maya Hernandez
#Last change: 14 de Septiembre 2016
import math
import random
def random_chromosome():
chromosome=[]
for i in range(0,L_chromosome):
if random.random()<0.1:
chromosome.append(0)
else:
chromosome.append(1)
return chromosome
#binary codification
def decode_chromosome(chromosome):
global L_chromosome,N_chains,a,b
v1=0
v2=0
for p in range(L_chromosome):
if(p<L_chromosome/2):
v2+=(2**p)*chromosome[-1-p]
else:
v1+=(2**(p-L_chromosome/2))*chromosome[-1-p]
return (a+(b-a)*float(v1)/(N_chains-1) , a+(b-a)*float(v2)/(N_chains-1))
def f (x1, x2):
res = 0
a1 = 20.0
b1 = 0.2
c1 = 2.0 * math.pi
res = (-a1)*math.exp((-b1)*math.sqrt((0.5)*(x1**2 + x2**2)))
res-= math.exp((0.5)*( math.cos(c1*x1) + math.cos(c1*x2))) + a1 + math.exp(1.0)
return res
def evaluate_chromosomes():
global F0
for p in range(N_chromosomes):
(v,v1)=decode_chromosome(F0[p])
fitness_values[p]=f(v, v1)
def compare_chromosomes(chromosome1,chromosome2):
(vc11,vc12)=decode_chromosome(chromosome1)
(vc21,vc22)=decode_chromosome(chromosome2)
fvc1=f(vc11, vc12)
fvc2=f(vc21, vc22)
if fvc1 > fvc2:
return 0
elif fvc1 == fvc2:
return 1
else: #fvg1<fvg2
return -1
def create_wheel():
global F0,fitness_values
maxv=max(fitness_values)
acc=0
for p in range(N_chromosomes):
acc+=maxv-fitness_values[p]
fraction=[]
for p in range(N_chromosomes):
fraction.append( float(maxv-fitness_values[p])/acc)
if fraction[-1]<=1.0/Lwheel:
fraction[-1]=1.0/Lwheel
## print fraction
fraction[0]-=(sum(fraction)-1.0)/2
fraction[1]-=(sum(fraction)-1.0)/2
## print fraction
wheel=[]
pc=0
for f in fraction:
Np=int(f*Lwheel)
for i in range(Np):
wheel.append(pc)
pc+=1
return wheel
def nextgeneration():
global n_generation
F0.sort(cmp=compare_chromosomes)
n_generation+=1
print "Generation: ",n_generation
print "Best solution so far:"
(v1,v2)=decode_chromosome(F0[0])
print "f(",decode_chromosome(F0[0]),")= ", f(v1,v2)
#elitism, the two best chromosomes go directly to the next generation
F1[0]=F0[0]
F1[1]=F0[1]
for i in range(0,(N_chromosomes-2)/2):
roulette=create_wheel()
#Two parents are selected
p1=random.choice(roulette)
p2=random.choice(roulette)
#Two descendants are generated
o1=F0[p1][0:crossover_point]
o1.extend(F0[p2][crossover_point:L_chromosome])
o2=F0[p2][0:crossover_point]
o2.extend(F0[p1][crossover_point:L_chromosome])
#Each descendant is mutated with probability prob_m
if random.random() < prob_m:
o1[int(round(random.random()*(L_chromosome-1)))]^=1
if random.random() < prob_m:
o2[int(round(random.random()*(L_chromosome-1)))]^=1
#The descendants are added to F1
F1[2+2*i]=o1
F1[3+2*i]=o2
#The generation replaces the old one
F0[:]=F1[:]
a=-32.768
b= 32.768
L_chromosome=2
print "Ackley \n\n"
for j in range (0, 6):
L_chromosome*=2;
prob_m=-0.1
for k in range (0,5):
prob_m+=0.2
N_chains=2**(L_chromosome/2)
crossover_point=L_chromosome/2
#Number of chromosomes
N_chromosomes=10
#probability of mutation
#Nomenclatura de primera poblacion
F0=[]
F1=[]
fitness_values=[]
for i in range(0,N_chromosomes):
F0.append(random_chromosome())
fitness_values.append(0)
suma=float(N_chromosomes*(N_chromosomes+1))/2.
Lwheel=N_chromosomes*10
F1=F0[:]
F0.sort(cmp=compare_chromosomes)
evaluate_chromosomes()
n_generation=0
print "Chromosomes "
print L_chromosome
print " mutation "
print prob_m
print "\n\n"
for i in range(0,100):
nextgeneration()
print "\n\n"