考虑一个南北长 2 海里、东西宽 4 海里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。请用遗传算法求解该题给出Python代码和这组测线结果和绘制测线路径

下面是使用遗传算法求解该问题的Python代码：

import random
import numpy as np
import matplotlib.pyplot as plt

# 海域尺寸
length = 2
width = 4

# 海水深度
depth = 110

# 坡度
slope = 1.5

# 开角
beam_angle = 120

# 目标函数：测线长度最短且满足重叠率要求
def objective_function(chromosome):
    lines = decode_chromosome(chromosome)
    total_length = sum([line_length(line) for line in lines])
    overlap_rate = calculate_overlap_rate(lines)
    return total_length + penalty(overlap_rate)

# 解码染色体
def decode_chromosome(chromosome):
    lines = []
    for i in range(len(chromosome)):
        start = i * length / len(chromosome)
        end = (i+1) * length / len(chromosome)
        line = (start, end, chromosome[i])
        lines.append(line)
    return lines

# 计算测线长度
def line_length(line):
    start, end, angle = line
    return np.sqrt((end - start)**2 + (width*np.tan(np.deg2rad(angle)))**2)

# 计算重叠率
def calculate_overlap_rate(lines):
    total_overlap = 0
    for i in range(len(lines)-1):
        overlap = min(lines[i][1], lines[i+1][0]) - max(lines[i][0], lines[i+1][0])
        total_overlap += overlap
    return total_overlap / (length * (len(lines)-1))

# 惩罚函数
def penalty(overlap_rate):
    if overlap_rate < 0.1:
        return 100
    elif overlap_rate > 0.2:
        return 100
    else:
        return 0

# 生成初始种群
def generate_population(population_size, chromosome_length):
    population = []
    for _ in range(population_size):
        chromosome = [random.randint(0, beam_angle) for _ in range(chromosome_length)]
        population.append(chromosome)
    return population

# 选择操作
def selection(population, fitness):
    total_fitness = sum(fitness)
    probabilities = [f/total_fitness for f in fitness]
    selected_indices = np.random.choice(range(len(population)), size=len(population), p=probabilities)
    return [population[i] for i in selected_indices]

# 交叉操作
def crossover(parent1, parent2):
    crossover_point = random.randint(1, len(parent1)-1)
    child1 = parent1[:crossover_point] + parent2[crossover_point:]
    child2 = parent2[:crossover_point] + parent1[crossover_point:]
    return child1, child2

# 变异操作
def mutation(chromosome, mutation_rate):
    for i in range(len(chromosome)):
        if random.random() < mutation_rate:
            chromosome[i] = random.randint(0, beam_angle)
    return chromosome

# 遗传算法主函数
def genetic_algorithm(population_size, chromosome_length, generations, mutation_rate):
    population = generate_population(population_size, chromosome_length)
    best_fitness = float('inf')
    best_solution = None
    fitness_history = []
    for _ in range(generations):
        fitness = [objective_function(chromosome) for chromosome in population]
        best_index = np.argmin(fitness)
        if fitness[best_index] < best_fitness:
            best_fitness = fitness[best_index]
            best_solution = population[best_index]
        fitness_history.append(best_fitness)
        parents = selection(population, fitness)
        new_population = []
        while len(new_population) < population_size:
            parent1 = random.choice(parents)
            parent2 = random.choice(parents)
            child1, child2 = crossover(parent1, parent2)
            child1 = mutation(child1, mutation_rate)
            child2 = mutation(child2, mutation_rate)
            new_population.append(child1)
            new_population.append(child2)
        population = new_population
    return best_solution, best_fitness, fitness_history

# 运行遗传算法
population_size = 100
chromosome_length = 10
generations = 100
mutation_rate = 0.01

best_solution, best_fitness, fitness_history = genetic_algorithm(population_size, chromosome_length, generations, mutation_rate)

# 绘制测线路径
lines = decode_chromosome(best_solution)
x = []
y = []
for line in lines:
    start, end, angle = line
    x.append(start)
    x.append(end)
    y.append(width)
    y.append(width - width*np.tan(np.deg2rad(angle)))

plt.plot(x, y)
plt.xlabel('Length (nm)')
plt.ylabel('Width (nm)')
plt.title('Survey Line Path')
plt.show()

print('Best Solution:', best_solution)
print('Best Fitness:', best_fitness)

运行代码后，会输出最佳解（测线角度序列）、最佳适应度和适应度历史，并绘制测线路径图。