251 lines
8.1 KiB
Python
251 lines
8.1 KiB
Python
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import numpy as np
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import random
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import math
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import matplotlib.pyplot as plt
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import time
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class MTSP_GA:
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def __init__(self, cities, vehicle_num, population_size=200, max_iterations=1500):
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"""
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初始化遗传算法求解器
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Args:
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cities: 城市坐标数组，第一个城市为起始点
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vehicle_num: 车辆数量
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population_size: 种群大小
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max_iterations: 最大迭代次数
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"""
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self.cities = np.array(cities)
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self.city_count = len(cities)
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self.vehicle_num = vehicle_num
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self.origin = 0 # 起始点
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# GA参数
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self.population_size = population_size
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self.max_iterations = max_iterations
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self.retain_rate = 0.3 # 强者存活率
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self.random_rate = 0.5 # 弱者存活概率
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self.mutation_rate = 0.3 # 变异率
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# 计算距离矩阵
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self.distance_matrix = self._compute_distance_matrix()
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# 记录收敛过程
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self.distance_history = []
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self.best_path_history = []
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def _compute_distance_matrix(self):
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"""计算城市间距离矩阵"""
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distance = np.zeros((self.city_count, self.city_count))
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for i in range(self.city_count):
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for j in range(self.city_count):
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distance[i][j] = math.sqrt(
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(self.cities[i][0] - self.cities[j][0]) ** 2 +
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(self.cities[i][1] - self.cities[j][1]) ** 2
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)
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return distance
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def _create_individual(self):
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"""生成初始个体"""
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index = [i for i in range(self.city_count)]
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index.remove(self.origin)
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a = int(np.floor(len(index)/self.vehicle_num))
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X = []
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for i in range(self.vehicle_num):
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if i < self.vehicle_num-1:
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x = index[a*i:a*(i+1)]
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else:
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x = index[a*i:]
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X.append(x)
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return X
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def _get_total_distance(self, X):
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"""计算路径总距离"""
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distance = 0
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distance_list = []
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for x in X:
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d = self.distance_matrix[self.origin][x[0]] # 从起点到第一个城市
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d += self.distance_matrix[self.origin][x[-1]] # 从最后一个城市返回起点
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for i in range(len(x)-1):
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d += self.distance_matrix[x[i]][x[i+1]]
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distance += d
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distance_list.append(d)
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return distance, distance_list
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def _selection(self, population):
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"""选择操作"""
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graded = [[self._get_total_distance(x)[0], x] for x in population]
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graded = [x[1] for x in sorted(graded)]
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retain_length = int(len(graded) * self.retain_rate)
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parents = graded[:retain_length]
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for chromosome in graded[retain_length:]:
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if random.random() < self.random_rate:
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parents.append(chromosome)
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return parents
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def _crossover(self, parents):
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"""交叉操作"""
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target_count = self.population_size - len(parents)
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children = []
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while len(children) < target_count:
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male_index = random.randint(0, len(parents) - 1)
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female_index = random.randint(0, len(parents) - 1)
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if male_index != female_index:
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male = parents[male_index]
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female = parents[female_index]
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gene1 = []
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gene2 = []
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for i in range(len(male)):
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gene1 += male[i]
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gene2 += female[i]
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left = random.randint(0, len(gene1)//2)
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right = random.randint(left + 1, len(gene1))
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cut = gene1[left:right]
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copy = gene2.copy()
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for j in cut:
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copy.remove(j)
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child = copy + cut
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a = int(np.floor(len(child)/self.vehicle_num))
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child_c = []
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for i in range(self.vehicle_num):
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if i < self.vehicle_num - 1:
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x = child[a * i:a * (i + 1)]
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else:
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x = child[a * i:]
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child_c.append(x)
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children.append(child_c)
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return children
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def _mutation(self, children):
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"""变异操作"""
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for i in range(len(children)):
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if random.random() < self.mutation_rate:
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child = children[i]
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for j in range(int(np.floor(len(child)/2))):
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a = 2*j
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u = random.randint(1, len(child[a]) - 1)
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w = random.randint(1, len(child[a+1]) - 1)
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child_1 = child[a][:u].copy()
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child_2 = child[a][u:].copy()
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child_3 = child[a+1][:w].copy()
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child_4 = child[a+1][w:].copy()
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child_a = child_1+child_3
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child_b = child_2+child_4
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child[a] = child_a
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child[a+1] = child_b
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children[i] = child.copy()
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return children
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def _get_best_solution(self, population):
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"""获取最优解"""
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graded = [[self._get_total_distance(x)[0], x] for x in population]
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graded = sorted(graded, key=lambda x: x[0])
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return graded[0][0], graded[0][1]
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def solve(self):
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"""
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求解MTSP，加入早停机制
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当连续50轮没有更好的解时停止迭代
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"""
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# 初始化种群
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population = [self._create_individual() for _ in range(self.population_size)]
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# 初始化早停相关变量
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best_distance = float('inf')
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early_stop_counter = 0
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early_stop_threshold = 100
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# 迭代优化
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for i in range(self.max_iterations):
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parents = self._selection(population)
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children = self._crossover(parents)
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children = self._mutation(children)
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population = parents + children
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# 记录当前最优解
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current_distance, current_path = self._get_best_solution(population)
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self.distance_history.append(current_distance)
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self.best_path_history.append(current_path)
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# 早停判断
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if current_distance < best_distance:
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best_distance = current_distance
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best_path = current_path
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early_stop_counter = 0 # 重置计数器
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else:
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early_stop_counter += 1
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# 如果连续50轮没有更好的解，则停止迭代
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if early_stop_counter >= early_stop_threshold:
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print(f"Early stopping at iteration {i} due to no improvement in {early_stop_threshold} iterations")
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break
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# 返回最优解
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return best_distance, best_path
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def plot_convergence(self):
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"""绘制收敛曲线"""
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plt.plot(range(len(self.distance_history)), self.distance_history)
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plt.xlabel('Iteration')
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plt.ylabel('Total Distance')
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plt.title('Convergence Curve')
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plt.show()
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def main():
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# 城市坐标
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cities = np.array([
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(456, 320), # 起点（基地）
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(228, 0),
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(912, 0),
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(0, 80),
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(114, 80),
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(570, 160),
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(798, 160),
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(342, 240),
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(684, 240),
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(570, 400),
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(912, 400),
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(114, 480),
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(228, 480),
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(342, 560),
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(684, 560),
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(0, 640),
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(798, 640)
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])
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# 设置随机种子
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np.random.seed(42)
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random.seed(42)
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# 创建求解器实例
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solver = MTSP_GA(
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cities=cities,
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vehicle_num=4,
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population_size=200,
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max_iterations=1500
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)
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# 求解
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start_time = time.time()
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best_distance, best_path = solver.solve()
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end_time = time.time()
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# 输出结果
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print(f"最优总距离: {best_distance:.2f}")
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print("最优路径方案:")
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for i, path in enumerate(best_path):
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print(f"车辆{i+1}的路径: {path}")
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print(f"求解时间: {end_time - start_time:.2f}秒")
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# 绘制收敛曲线
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solver.plot_convergence()
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if __name__ == "__main__":
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main()
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