Python如何实现重心法
时间: 2024-05-13 08:11:43 浏览: 16
重心法是一种常用的多目标优化算法,可以用于寻找一组非支配解。在Python中,可以通过如下步骤实现重心法:
1. 随机生成一组初始解,确定每个解的权重;
2. 计算所有解的重心;
3. 将重心作为新的解,重新计算所有解的权重;
4. 判断是否满足停止条件,若满足则输出最终结果,否则回到第2步。
下面是Python的实现示例代码:
```python
import numpy as np
# 定义目标函数
def objective(x):
f1 = x**2 + x**2
f2 = (x-1)**2 + x**2
return np.array([f1, f2])
# 定义重心法函数
def centroid_method(objective, n_objs, n_vars, n_iter, n_pop):
# 随机生成初始解和权重
pop = np.random.rand(n_pop, n_vars)
w = np.random.rand(n_pop, n_objs)
w /= np.sum(w, axis=0)
for i in range(n_iter):
# 计算重心
centroid = np.sum(w[:, None, :] * pop[:, :, None], axis=0) / np.sum(w, axis=0)[:, None]
# 计算所有解的新权重
dist = np.linalg.norm(pop[:, :, None] - centroid[:, None, :], axis=1)
w_new = 1 / dist
w_new /= np.sum(w_new, axis=0)
# 判断是否满足停止条件
if np.allclose(w, w_new):
break
else:
w = w_new
# 返回非支配解和对应的权重
idx = np.arange(n_pop)
non_dom_idx = []
for i in range(n_objs):
non_dom = np.where(np.all(w[:, i][idx, None] <= w[:, i][None, :], axis=1))
idx = np.setdiff1d(idx, non_dom)
non_dom_idx.append(non_dom)
non_dom_sol = pop[non_dom_idx]
non_dom_w = w[non_dom_idx]
return non_dom_sol, non_dom_w
# 设置参数并调用重心法函数
n_objs = 2
n_vars = 2
n_iter = 100
n_pop = 100
non_dom_sol, non_dom_w = centroid_method(objective, n_objs, n_vars, n_iter, n_pop)
# 输出非支配解和对应的权重
print("Non-dominated solutions:")
print(non_dom_sol)
print("Weights:")
print(non_dom_w)
```