"""
@题目：《圆环区域内传感器节点位置优化建模》---智能方法---GA
@时间：2024年6月26日
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from geneticalgorithm import geneticalgorithm as ga
# 参数
N = 20
R = 1
inner_R = 0.8 * R
# 初始化节点位置
def init_nodes(N, R, inner_R):
nodes = []
while len(nodes) < N:
x, y = np.random.uniform(-R, R, 2)
if inner_R <= np.sqrt(x**2 + y**2) <= R:
nodes.append([x, y])
return np.array(nodes)
# 优化目标函数
def objective(nodes):
nodes = nodes.reshape((N, 2))
min_dist = np.inf
for i in range(N):
for j in range(i + 1, N):
dist = np.linalg.norm(nodes[i] - nodes[j])
if dist < min_dist:
min_dist = dist
return -min_dist
# 约束条件
def constraint1(nodes):
nodes = nodes.reshape((N, 2))
return np.array([np.linalg.norm(node) - inner_R for node in nodes])
def constraint2(nodes):
nodes = nodes.reshape((N, 2))
return np.array([R - np.linalg.norm(node) for node in nodes])
# 遗传算法的约束条件
def constraint_all(nodes):
nodes = nodes.reshape((N, 2))
for node in nodes:
if np.linalg.norm(node) < inner_R or np.linalg.norm(node) > R:
return False
return True
# 遗传算法的定义
varbound = np.array([[-R, R]] * N * 2)
algorithm_param = {'max_num_iteration': 1000, 'population_size': 200, 'mutation_probability': 0.1, 'elit_ratio': 0.01, 'crossover_probability': 0.5, 'parents_portion': 0.3, 'crossover_type': 'uniform', 'max_iteration_without_improv': None}
model = ga(function=objective, dimension=N * 2, variable_type='real', variable_boundaries=varbound, algorithm_parameters=algorithm_param, function_timeout=10, convergence_curve=False, progress_bar=False)
model.run()
# 获取遗传算法优化后的节点
nodes = model.output_dict['variable']
nodes = nodes.reshape((N, 2))
# 使用SLSQP进行局部优化
nodes = nodes.flatten()
cons = [{'type': 'ineq', 'fun': constraint1},
{'type': 'ineq', 'fun': constraint2}]
result = minimize(objective, nodes, constraints=cons, method='SLSQP')
nodes = result.x.reshape(N, 2)
# 计算最小距离
min_dist = np.inf
for i in range(N):
for j in range(i + 1, N):
dist = np.linalg.norm(nodes[i] - nodes[j])
if dist < min_dist:
min_dist = dist
print(f"最小距离: {min_dist}")
# 绘制优化后的节点分布图
fig, ax = plt.subplots()
circle = plt.Circle((0, 0), R, color='b', fill=False)
inner_circle = plt.Circle((0, 0), inner_R, color='r', fill=False)
ax.add_artist(circle)
ax.add_artist(inner_circle)
ax.scatter(nodes[:, 0], nodes[:, 1])
plt.xlim(-R, R)
plt.ylim(-R, R)
plt.gca().set_aspect('equal', adjustable='box')
plt.show()
