手术排程问题:已知各手术术式平均用时,每日有140台手术需要安排到20个手术间,最大化手术室黄金时间利用率并且最小化医院20个手术间用时标准差的启发式算法python具体代码
时间: 2024-01-24 21:17:47 浏览: 26
这是一个NP难问题,可以采用启发式算法来逼近最优解。以下是一个基于模拟退火的启发式算法的Python代码:
```python
import random
import math
import copy
# 手术间数量
ROOM_NUM = 20
# 每天手术数量
DAILY_OP_NUM = 140
# 每个手术室每天最大使用时间
MAX_TIME_PER_ROOM = 480
# 每个手术的平均用时
OP_TIME = [60, 90, 120, 150, 180]
# 初始温度
INIT_TEMP = 100
# 降温速率
COOL_RATE = 0.99
# 终止温度
END_TEMP = 1
# 迭代次数
ITER_NUM = 500
# 模拟退火算法
def simulated_annealing():
# 随机生成初始解
solution = [[[] for j in range(ROOM_NUM)] for i in range(DAILY_OP_NUM)]
for i in range(DAILY_OP_NUM):
for j in range(ROOM_NUM):
op_time = random.choice(OP_TIME)
solution[i][j] = op_time
# 计算初始解的黄金时间利用率和用时标准差
max_time_per_day = MAX_TIME_PER_ROOM * ROOM_NUM
time_used = [0 for i in range(DAILY_OP_NUM)]
for i in range(DAILY_OP_NUM):
for j in range(ROOM_NUM):
time_used[i] += solution[i][j]
time_used.sort()
gold_time_used = sum(time_used[-DAILY_OP_NUM//2:])
time_std = math.sqrt(sum([(t - gold_time_used)**2 for t in time_used]) / DAILY_OP_NUM)
# 初始化温度
temp = INIT_TEMP
# 迭代降温
for i in range(ITER_NUM):
# 随机选择一个手术进行调整
op_idx = random.randint(0, DAILY_OP_NUM-1)
from_room_idx = random.randint(0, ROOM_NUM-1)
to_room_idx = random.randint(0, ROOM_NUM-1)
while from_room_idx == to_room_idx:
to_room_idx = random.randint(0, ROOM_NUM-1)
# 复制当前解
new_solution = copy.deepcopy(solution)
# 调整手术
new_solution[op_idx][from_room_idx], new_solution[op_idx][to_room_idx] = new_solution[op_idx][to_room_idx], new_solution[op_idx][from_room_idx]
# 计算新解的黄金时间利用率和用时标准差
new_time_used = [0 for i in range(DAILY_OP_NUM)]
for i in range(DAILY_OP_NUM):
for j in range(ROOM_NUM):
new_time_used[i] += new_solution[i][j]
new_time_used.sort()
new_gold_time_used = sum(new_time_used[-DAILY_OP_NUM//2:])
new_time_std = math.sqrt(sum([(t - new_gold_time_used)**2 for t in new_time_used]) / DAILY_OP_NUM)
# 计算能量差
delta_e = new_gold_time_used - gold_time_used + (time_std - new_time_std) / 10
# 判断是否接受新解
if delta_e < 0 or math.exp(-delta_e/temp) > random.random():
solution = new_solution
gold_time_used = new_gold_time_used
time_std = new_time_std
# 降温
temp *= COOL_RATE
if temp < END_TEMP:
break
return solution, gold_time_used, time_std
# 测试
solution, gold_time_used, time_std = simulated_annealing()
print('黄金时间利用率:', gold_time_used / (MAX_TIME_PER_ROOM * ROOM_NUM * DAILY_OP_NUM))
print('用时标准差:', time_std)
print('手术安排方案:')
for i in range(DAILY_OP_NUM):
print(solution[i])
```
其中,黄金时间利用率是指每天手术间使用时间的中位数占总时间的比例,用时标准差是用来衡量手术间使用时间分布的均匀性的指标。模拟退火算法的基本思路是随机生成初始解,然后迭代地在解空间进行随机搜索,通过接受劣解的概率逐渐降低温度,最终得到一个相对较优的解。