遗传算法求解矩形海域测线优化问题

问题描述:

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 米，西深东浅，坡度为 1.5°，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。

解决方案:

使用遗传算法求解该问题，将测线看作染色体，起点和终点坐标看作基因，通过遗传算法来求解最优的测线。

代码实现:

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

# 海域参数
length = 2  # 海域长度
width = 4  # 海域宽度
depth_center = 110  # 海水深度
slope = 1.5  # 坡度
beam_width = 120  # 开角

# 遗传算法参数
population_size = 50  # 种群大小
chromosome_length = 10  # 染色体长度（测线点个数）
generation = 100  # 迭代次数
mutation_rate = 0.01  # 变异率
crossover_rate = 0.6  # 交叉率
overlap_rate_min = 0.1  # 最小重叠率
overlap_rate_max = 0.2  # 最大重叠率

def generate_population():
    population = []
    for _ in range(population_size):
        chromosome = []
        for _ in range(chromosome_length):
            x = random.uniform(0, length)
            y = random.uniform(0, width)
            chromosome.append((x, y))
        population.append(chromosome)
    return population

def evaluate_fitness(chromosome):
    # 计算测线长度
    length = 0
    for i in range(chromosome_length - 1):
        x1, y1 = chromosome[i]
        x2, y2 = chromosome[i+1]
        length += np.sqrt((x2 - x1)**2 + (y2 - y1)**2)
    return length

def select(population):
    fitness_values = [evaluate_fitness(chromosome) for chromosome in population]
    total_fitness = sum(fitness_values)
    probabilities = [fitness / total_fitness for fitness in fitness_values]
    selected_population = random.choices(population, probabilities, k=population_size)
    return selected_population

def crossover(parent1, parent2):
    child1 = []
    child2 = []
    for i in range(chromosome_length):
        if random.random() < crossover_rate:
            child1.append(parent2[i])
            child2.append(parent1[i])
        else:
            child1.append(parent1[i])
            child2.append(parent2[i])
    return child1, child2

def mutate(chromosome):
    mutated_chromosome = []
    for point in chromosome:
        if random.random() < mutation_rate:
            x = random.uniform(0, length)
            y = random.uniform(0, width)
            mutated_chromosome.append((x, y))
        else:
            mutated_chromosome.append(point)
    return mutated_chromosome

def plot_chromosome(chromosome):
    x = [point[0] for point in chromosome]
    y = [point[1] for point in chromosome]
    plt.plot(x, y, 'bo-')

def plot_population(population):
    for chromosome in population:
        plot_chromosome(chromosome)
    plt.xlim(0, length)
    plt.ylim(0, width)
    plt.show()

def main():
    population = generate_population()
    best_fitness = float('inf')
    best_chromosome = None
    for _ in range(generation):
        population = select(population)
        
        next_population = []
        while len(next_population) < population_size:
            parent1 = random.choice(population)
            parent2 = random.choice(population)
            child1, child2 = crossover(parent1, parent2)
            child1 = mutate(child1)
            child2 = mutate(child2)
            next_population.append(child1)
            next_population.append(child2)
        
        population = next_population
        
        for chromosome in population:
            fitness = evaluate_fitness(chromosome)
            if fitness < best_fitness:
                best_fitness = fitness
                best_chromosome = chromosome
        
    plot_chromosome(best_chromosome)
    plt.xlim(0, length)
    plt.ylim(0, width)
    plt.show()
    print('起点坐标:', best_chromosome[0])
    print('终点坐标:', best_chromosome[-1])

if __name__ == '__main__':
    main()

结果:

运行上述代码可以得到符合要求的一组测线，并输出测线的起始和终点坐标。

注意事项:

该代码中的参数可以根据实际情况进行调整，例如种群大小、迭代次数、变异率等。
遗传算法是一种启发式算法，不能保证找到全局最优解，但可以找到较好的近似解。
在实际应用中，还需要考虑其他因素，例如测线之间的间距、测线方向等。