scripts/opt_tree.py

import numpy as np
from scipy.optimize import minimize

# 参数
p = np.array([0.8, 0.5, 0.3, 0.2, 0.12, 0.07])
q = 1 - p  # 失效概率
N_total = 80

def objective(n):
    """目标函数：Σ n_i * [1 - q_i^{n_i}]"""
    return np.sum(n * (1 - q**n))

# 约束条件
constraints = [
    {'type': 'eq', 'fun': lambda n: np.sum(n) - N_total},
    {'type': 'ineq', 'fun': lambda n: n-1}  # n_i >= 0
]

# 初始猜测（均匀分配）
n0 = np.ones(6) * N_total / 6
n0 = np.maximum(n0, 1)  # 确保初始值 >=1

# 优化（使用连续实数）
res = minimize(lambda n: -objective(n), n0, 
               constraints=constraints,
               bounds=[(0, N_total)]*6,
               method='SLSQP',
               options={'maxiter': 50,  # 修改最大迭代次数为 20（原默认 100）
                        'ftol': 1e-6,  # 函数容差（可调小到 1e-8 以增加迭代）
                        'disp': True})  # 打印迭代日志)
n_opt = res.x
max_value = objective(n_opt)

print("最优节点分配（连续解）:")
for i in range(6):
    print(f"层 {i+1}: {n_opt[i]:.2f} 个节点")
print(f"\n最大值: {max_value:.4f}")

# 检查整数解
from itertools import product
import math

# 搜索附近整数解（简单网格）
def integer_search(center, radius=2):
    best_val = -1
    best_n = None
    
    # 生成附近整数组合
    ranges = [range(max(0, int(center[i])-radius), 
                    int(center[i])+radius+1) for i in range(6)]
    
    # 限制组合数量，实际可更精细
    for combo in product(*ranges):
        if sum(combo) == N_total and all(x >= 0 for x in combo):
            val = objective(np.array(combo))
            if val > best_val:
                best_val = val
                best_n = combo
    return best_n, best_val

int_n, int_val = integer_search(n_opt, radius=3)
print("\n近似最优整数解:")
for i in range(6):
    print(f"层 {i+1}: {int_n[i]} 个节点")
print(f"整数值: {int_val:.4f}")