MLE/03_euler_gen_alg.py

83 lines
2.6 KiB
Python

"""
Schreibe einen genetischen Algorithmus, der die Parameter
(a,b,c,d) der Funktion f (x ) = ax 3 + bx 2 + cx + d so optimiert,
dass damit die Funktion g(x ) = e x im Bereich [-1..1] möglichst
gut angenähert wird. Nutze dazu den quadratischen Fehler (oder
alternativ die Fläche zwischen der e-Funktion und dem Polynom).
Zeichne die Lösung und vergleiche die Koeffizienten mit denen der
Taylor-Reihe um 0.
"""
import numpy as np
import random
import struct
import time
# import matplotlib.pyplot as plt
def generate_random_population():
pop_grey = [format(random.getrandbits(32), '32b') for i in range(10)]
pop_bin = grey_to_bin(pop_grey)
a, b, c, d = pop_bin[0:7], pop_bin[8:15], pop_bin[16:23], pop_bin[24:31]
return [a, b, c, d]
def grey_to_bin(gray):
"""Convert Gray code to binary, operating on the integer value directly"""
num = int(gray, 2) # Convert string to integer
mask = num
while mask != 0:
mask >>= 1
num ^= mask
return format(num, f'0{len(gray)}b') # Convert back to binary string with same length
def bin_to_grey(binary):
"""Convert binary to Gray code using XOR with right shift"""
num = int(binary, 2) # Convert string to integer
gray = num ^ (num >> 1) # Gray code formula: G = B ^ (B >> 1)
return format(gray, f'0{len(binary)}b') # Convert back to binary string with same length
def bin_to_param(binary, q_min = 0.0, q_max = 10.0):
"""Convert binary string to float parameter in range [q_min, q_max]"""
val = int(binary, 2) / 25.5 * 10 # conversion to 0.0 - 10.0 float
# Scale to range [q_min, q_max]
q = q_min + ((q_max - q_min) / (2**len(binary))) * val
return q
def quadratic_error(original_fn, approx_fn, n):
error = 0.0
for i in range(-(n // 2), (n // 2) + 1):
error += (original_fn(i) - approx_fn(i))**2
return error
def e_fn_approx(a, b, c, d, x = 1):
return a*x**3 + b*x**2 + c*x + d
def fuck_that_shit_up():
bin_values = generate_random_population()
# Convert binary string to parameters for bin_values
a, b, c, d = [bin_to_param(bin) for bin in bin_values]
e_func = lambda x: np.e**x
fixed_approx = lambda x: e_fn_approx(a, b, c, d, x)
fitness = quadratic_error(e_func, fixed_approx, 6)
while fitness > 0.01:
# calc fitness
fitness = quadratic_error(e_func, fixed_approx, 6)
print(fitness)
time.sleep(1)
# selection
# crossover
# mutation
# neue population
return 0
fuck_that_shit_up()
# b = format(random.getrandbits(32), '32b')
# print(quadratic_error(e_func, fixed_approx, 6)) # hopefully works