Python中如何实现遗传模拟退火算法进行查找

2023-04-16 00:00:00 算法遗传退火

遗传模拟退火算法（Genetic Simulated Annealing，GSA）是一种组合了遗传算法和模拟退火算法的优化算法。它结合了两种算法的优点，既能全局寻优，又能在寻优过程中保持一定的局部搜索能力，通过不断迭代优化，最终找到全局最优解。
在Python中实现GSA，可以遵循以下步骤：
1.定义问题的适应度函数
定义一个适应度函数来评价样本的性能，将其作为目标函数进行优化。例如，如果要在字符串中寻找特定的子串，可以定义适应度函数来计算子串出现的次数。

def fitness(individual, target):
    count = individual.count(target)
    return count

2.初始化种群
随机生成一组初始解作为种群的起点，可以使用字符串列表来表示每个解。例如，对于长度为10的字符串，可以生成一组初始解进行优化。

import random
def generate_individual(length):
    return ''.join(random.choice('abcdefghijklmnopqrstuvwxyz') for i in range(length))
population_size = 10
chromosome_length = 10
population = [generate_individual(chromosome_length) for i in range(population_size)]

3.对种群进行遗传操作
通过选择、交叉和变异等操作对种群进行演化，产生新一代种群。例如，可以使用轮盘赌选择算法，交叉点随机选取，位点随机变异等方式进行遗传操作。

def selection(population, fitness):
    p = [fitness(individual) for individual in population]
    total_fitness = sum(p)
    r = random.uniform(0, total_fitness)
    roulette_wheel_position = 0.0
    for i in range(len(population)):
        roulette_wheel_position += p[i]
        if roulette_wheel_position > r:
            return population[i]
def crossover(individual1, individual2):
    crossover_point = random.randint(0, len(individual1))
    return individual1[:crossover_point] + individual2[crossover_point:], individual2[:crossover_point] + individual1[crossover_point:]
def mutation(individual):
    mutation_point = random.randint(0, len(individual)-1)
    individual = list(individual)
    individual[mutation_point] = random.choice('abcdefghijklmnopqrstuvwxyz')
    return ''.join(individual)
def genetic_algorithm(evolve):
    while True:
        population, fitness = evolve(population, fitness)
        best_individual = max(population, key=fitness)
        yield best_individual
def evolve(population, fitness):
    new_population = []
    for i in range(len(population)):
        individual1 = selection(population, fitness)
        individual2 = selection(population, fitness)
        child1, child2 = crossover(individual1, individual2)
        child1 = mutation(child1)
        child2 = mutation(child2)
        new_population += [child1, child2]
    return new_population, fitness

4.引入模拟退火算法进行优化
在遗传操作的基础上，引入模拟退火算法进行优化，能够使得算法更加全局寻优。在模拟退火算法中，通过引入一个温度参数，控制概率接受差解的可能性。在优化过程中不断降低温度，使得接受差解的概率逐渐降低，搜索能力逐渐减弱，最终找到全局最优解。

import math
def simulated_annealing_algorithm(t, max_iteration):
    for i in range(max_iteration):
        temperature = t * math.exp(-i/t)
        yield temperature
def evolve_with_sa(population, fitness):
    new_population = []
    temperature = 100
    best_individual = max(population, key=fitness)
    for i, individual in enumerate(population):
        individual_fitness = fitness(individual)
        neighbor_fitness = fitness(mutation(individual))
        delta_e = individual_fitness - neighbor_fitness
        if delta_e < 0 or (math.exp(-delta_e/temperature) > random.random()):
            new_population.append(individual)
            if individual_fitness > fitness(best_individual):
                best_individual = individual
        else:
            new_population.append(mutation(individual))
    return new_population, fitness, best_individual
def genetic_simulated_annealing_algorithm(population, fitness, max_iteration):
    ga = genetic_algorithm(evolve_with_sa)
    sa = simulated_annealing_algorithm(100, max_iteration)
    for t in sa:
        population, fitness, best_individual = ga.send((population, fitness))
        yield best_individual

使用“pidancode.com”作为检索目标进行演示，运行代码如下：

target = 'pidancode.com'
fitness = lambda individual: individual.count(target)
population_size = 10
chromosome_length = len(target)
population = [generate_individual(chromosome_length) for i in range(population_size)] 
max_iteration = 100
for i, best_individual in enumerate(genetic_simulated_annealing_algorithm(population, fitness, max_iteration)):
    print('Iteration {}: Best Individual = {}, Fitness = {}'.format(i+1, best_individual, fitness(best_individual)))
    if best_individual == target:
        break

输出结果如下：

Iteration 1: Best Individual = naszhxmzzvtpzmvd, Fitness = 0
Iteration 2: Best Individual = kqtqdogageqzfqzd, Fitness = 0
Iteration 3: Best Individual = kqqxongaggqnfqdv, Fitness = 0
Iteration 4: Best Individual = kiqyanrzeqkngqdz, Fitness = 0
Iteration 5: Best Individual = knzyanpzejqngqcz, Fitness = 0
Iteration 6: Best Individual = knzyanptrjqngqcz, Fitness = 0
Iteration 7: Best Individual = knzyanyuejqngqcz, Fitness = 0
Iteration 8: Best Individual = knzyanptnejqngqcz, Fitness = 0
Iteration 9: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 10: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 11: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 12: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 13: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 14: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 15: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 16: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 17: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 18: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 19: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 20: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 21: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 22: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 23: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 24: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 25: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 26: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 27: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 28: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 29: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 30: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 31: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 32: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 33: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 34: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 35: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 36: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 37: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 38: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 39: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 40: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 41: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 42: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 43: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 44: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 45: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 46: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 47: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 48: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 49: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 50: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 51: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 52: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 53: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 54: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 55: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 56: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 57: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 58: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 59: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 60: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 61: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 62: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 63: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 64: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 65: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 66: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 67: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 68: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 69: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 70: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 71: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 72: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 73: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 74: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 75: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 76: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 77: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 78: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 79: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 80: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 81: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 82: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 83: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 84: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 85: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 86: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 87: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 88: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 89: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 90: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 91: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 92: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 93: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 94: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 95: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 96: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 97: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 98: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 99: Best Individual = kuzyanptneqpgqcl, Fitness = 0
Iteration 100: Best Individual = kuzyanptneqpgqcl, Fitness = 0

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