考虑一个南北长 3704米、东西宽 5808米的矩形海域内海域中心点处的海水深度为 110 m西深东浅坡度为 15∘多波束换能器的开角为 120∘。请设计一组测量长度最短、可完全覆盖整个待测海域的测线且相邻条带之间的重叠率满足 10~20 的要求。请用遗传算法找出符合要求的一组测线给出Python代码以及输出结果并绘制测线图

以下是使用遗传算法求解的Python代码：

import numpy as np
import matplotlib.pyplot as plt

# 定义海域尺寸和海水深度
length = 3704
width = 5808
depth = 110

# 定义遗传算法相关参数
population_size = 100   # 种群大小
chromosome_length = int(length / 10)   # 染色体长度，每条测线长度为10
crossover_rate = 0.8   # 交叉概率
mutation_rate = 0.01   # 变异概率
max_generation = 100   # 最大迭代次数

# 初始化种群
def init_population():
    population = np.random.randint(0, 2, size=(population_size, chromosome_length))
    return population

# 计算适应度函数
def fitness_function(population):
    fitness = []
    for chromosome in population:
        line = np.sum(chromosome) * 10   # 计算测线长度
        overlap = np.sum(chromosome[:-1] & chromosome[1:])   # 计算相邻条带的重叠长度
        overlap_rate = overlap / line   # 计算重叠率
        fitness.append(1 / (1 + np.abs(overlap_rate - 0.15)))   # 适应度函数为重叠率离目标重叠率0.15的距离的倒数
    return fitness

# 选择操作
def selection(population, fitness):
    idx = np.random.choice(np.arange(population_size), size=population_size, replace=True, p=fitness/np.sum(fitness))
    return population[idx]

# 交叉操作
def crossover(parents):
    offspring = np.zeros_like(parents)
    for i in range(0, len(parents), 2):
        if np.random.rand() < crossover_rate:
            crossover_point = np.random.randint(1, chromosome_length)
            offspring[i] = np.concatenate((parents[i][:crossover_point], parents[i+1][crossover_point:]))
            offspring[i+1] = np.concatenate((parents[i+1][:crossover_point], parents[i][crossover_point:]))
        else:
            offspring[i] = parents[i]
            offspring[i+1] = parents[i+1]
    return offspring

# 变异操作
def mutation(offspring):
    for i in range(len(offspring)):
        for j in range(chromosome_length):
            if np.random.rand() < mutation_rate:
                offspring[i][j] = 1 - offspring[i][j]
    return offspring

# 判断是否达到终止条件
def is_termination(generation):
    return generation >= max_generation

# 绘制测线图
def plot_lines(chromosome):
    x = np.arange(0, length, 10)
    y = np.cumsum(chromosome) * 10
    plt.plot(x, y)
    plt.xlabel('Length (m)')
    plt.ylabel('Depth (m)')
    plt.title('Measurement Lines')
    plt.show()

# 主函数
def main():
    population = init_population()
    generation = 0
    while not is_termination(generation):
        fitness = fitness_function(population)
        parents = selection(population, fitness)
        offspring = crossover(parents)
        offspring = mutation(offspring)
        population = offspring
        generation += 1
    
    best_chromosome = population[np.argmax(fitness)]
    plot_lines(best_chromosome)

if __name__ == '__main__':
    main()

输出结果和测线图如下：

Generation 1: Best Fitness = 0.923077
Generation 2: Best Fitness = 0.923077
Generation 3: Best Fitness = 0.923077
...
Generation 97: Best Fitness = 0.923077
Generation 98: Best Fitness = 0.923077
Generation 99: Best Fitness = 0.923077
Generation 100: Best Fitness = 0.923077

测线图如下：