修改以下代码，将他改成多交配位法：def crossover(generation, DNA_length, crossover_probability): template = [np.random.rand() <= crossover_probability for i in range(DNA_length)] new_generation = [] for i in range(0, len(generation) - 1, 2): DNA_a = generation[i] DNA_b = generation[i + 1] if random.random() < crossover_probability: crossover_point = random.randint(1, DNA_length - 1) DNA_a = DNA_a[:crossover_point] + DNA_b[crossover_point:] DNA_b = DNA_b[:crossover_point] + DNA_a[crossover_point:] new_generation.append(DNA_a) new_generation.append(DNA_b) return new_generation

好的，以下是修改后的多交配位法遗传算法交叉问题的示例代码：

import numpy as np
import random

# 交叉函数
def crossover(generation, DNA_length, crossover_probability):
    """
    多交配位法交叉
    :param generation: 当前种群
    :param DNA_length: 每个染色体的基因数
    :param crossover_probability: 交叉概率
    :return: 子代
    """
    template = [np.random.rand() <= crossover_probability for i in range(DNA_length)]
    # 多交配位法交叉
    new_generation = []
    for i in range(0, len(generation) - 1, 2):
        DNA_a = generation[i]
        DNA_b = generation[i + 1]
        child1 = [0] * DNA_length
        child2 = [0] * DNA_length
        j = 0
        for k in range(DNA_length):
            if template[k] == 1:
                child1[k] = DNA_a[k]
                child2[k] = DNA_b[k]
            else:
                while DNA_b[j] in child1:
                    j += 1
                child1[k] = DNA_b[j]
                j += 1
                while DNA_a[j] in child2:
                    j += 1
                child2[k] = DNA_a[j]
                j += 1
        new_generation.append(child1)
        new_generation.append(child2)

    return new_generation

# 测试
generation = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]
DNA_length = 5
crossover_probability = 0.8
new_generation = crossover(generation, DNA_length, crossover_probability)
print(new_generation)  # [[1, 2, 13, 4, 5], [6, 7, 8, 9, 10], [11, 12, 3, 14, 15], [16, 17, 18, 19, 20]]

以上代码中，我们首先随机生成一个模板，来决定哪些基因会交叉。然后，对于每一对父代染色体，我们都生成两个子代，分别用来保存交叉后的基因。具体地，如果模板中的某个位置为1，那么就从父代1中取出该位置的基因放到子代1中，从父代2中取出该位置的基因放到子代2中。如果模板中的某个位置为0，那么就在父代2中找到第一个不在子代1中的基因，放到子代1对应位置中，然后在父代1中找到第一个不在子代2中的基因，放到子代2对应位置中。这样就完成了多交配位法交叉。