144 lines
4.9 KiB
Python
144 lines
4.9 KiB
Python
"""
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Schreibe einen genetischen Algorithmus, der die Parameter
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(a,b,c,d) der Funktion f (x ) = ax 3 + bx 2 + cx + d so optimiert,
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dass damit die Funktion g(x ) = e x im Bereich [-1..1] möglichst
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gut angenähert wird. Nutze dazu den quadratischen Fehler (oder
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alternativ die Fläche zwischen der e-Funktion und dem Polynom).
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Zeichne die Lösung und vergleiche die Koeffizienten mit denen der
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Taylor-Reihe um 0.
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"""
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import numpy as np
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import random
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import struct
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import time
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import utils
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# import matplotlib.pyplot as plt
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POPULATION_SIZE = 10
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SELECTION_SIZE = (POPULATION_SIZE * 7) // 10 # 70% of population, rounded down for selection
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CROSSOVER_PAIR_SIZE = (POPULATION_SIZE - SELECTION_SIZE) // 2 # pairs needed for crossover
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XOVER_POINT = 3 # 4th position
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MUTATION_BITS = POPULATION_SIZE * 1
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fitness = 0.01
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pop_grey = []
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pop_bin = [] # 32 Bit Binary
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pop_bin_params = []
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pop_new = [] # 32 Bit Grey-Code as String
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e_func = lambda x: np.e**x
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def generate_random_population():
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""" Puts random 32 Bit binary strings into 4 * 8 Bit long params. """
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# Random population array
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for i in range(POPULATION_SIZE):
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pop_grey[i] = format(random.getrandbits(32), '32b')
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pop_bin[i] = utils.grey_to_bin(pop_grey[i])
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pop_bin_params[i] = [pop_bin[i][0:7], pop_bin[i][8:15], pop_bin[i][16:23], pop_bin[i][24:31]]
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return pop_bin_params
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def quadratic_error(original_fn, approx_fn, n):
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error = 0.0
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for i in range(-(n // 2), (n // 2) + 1):
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error += (original_fn(i) - approx_fn(i))**2
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return error
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def eval_fitness(pop_bin_values):
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""" Returns an array with fitness value of every individual in a population. """
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fitness_arr = []
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for params in pop_bin_values:
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# Convert binary string to parameters for bin_values
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a, b, c, d = [utils.bin_to_param(param) for param in params] # assign params to batch of population
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# Create polynomial function with current parameters
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approx = lambda x: a*x**3 + b*x**2 + c*x + d
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fitness = quadratic_error(e_func, approx, 6)
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print(fitness) # debugging
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fitness_arr.append(fitness) # save fitness
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# save params # already saved in pop_grey
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return fitness_arr
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def select(population, fitness_arr):
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sum_of_fitness = sum(fitness_arr)
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while len(population) < SELECTION_SIZE:
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# Roulette logic
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roulette_num = random.random()
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is_chosen = False
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while not is_chosen:
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cumulative_p = 0 # Track cumulative probability
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for i, fitness in enumerate(fitness_arr):
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cumulative_p += fitness / sum_of_fitness
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if roulette_num < cumulative_p:
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# Add the 32 Bit individual in grey code to population
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population.append(pop_grey[i])
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# Calc new sum of fitness
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fitness_arr.pop(i)
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sum_of_fitness = sum(fitness_arr)
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is_chosen = True # break while loop
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break # break for loop
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def xover(population, xover_rate):
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"""Performs crossover on pairs of individuals from population."""
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offspring = []
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# Process pairs while we have enough individuals and haven't reached CROSSOVER_PAIR_SIZE
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pair_count = 0
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i = 0
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while i < len(population) - 1 and pair_count < xover_rate:
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parent_a = population[i]
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parent_b = population[i + 1]
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# Create two new offspring by swapping parts at XOVER_POINT
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offspring_a = parent_a[:XOVER_POINT] + parent_b[XOVER_POINT:]
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offspring_b = parent_b[:XOVER_POINT] + parent_a[XOVER_POINT:]
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offspring.extend([offspring_a, offspring_b])
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pair_count += 1
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i += 2 # Move to next pair
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return offspring
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def mutate(population, mutation_rate):
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"""Mutate random bits in the population with given mutation rate"""
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for _ in range(mutation_rate):
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# Select random individual and convert to list for efficient modification
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random_num = random.randrange(POPULATION_SIZE)
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bits = list(population[random_num])
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# Flip random bit
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bit_pos = random.randrange(32)
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bits[bit_pos] = '1' if bits[bit_pos] == '0' else '0'
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# Convert back to string and update population
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population[random_num] = ''.join(bits)
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def main():
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pop_bin_values = generate_random_population(10)
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while fitness > 0.01:
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# Evaluate fitness
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fitness_arr = eval_fitness(pop_bin_values)
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# Selection
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select(pop_new, fitness_arr) # Alters pop_new
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# Crossover
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offspring = xover(pop_new, CROSSOVER_PAIR_SIZE)
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pop_new.extend(offspring) # .extend needed
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# Mutation
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mutate(pop_new, MUTATION_BITS)
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pop_grey = pop_new
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return 0
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if __name__ == "__main__":
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main() |