人员分配的模拟退火算法代码
时间: 2024-05-27 18:05:57 浏览: 13
人员分配问题是一个经典的组合优化问题,模拟退火算法是一种常用的解决该问题的启发式算法。下面是一个简单的人员分配的模拟退火算法代码示例:
```python
import random
import math
# 初始化人员和任务的分配情况
def initialize(num_persons, num_tasks):
allocation = [random.randint(0, num_tasks-1) for _ in range(num_persons)]
return allocation
# 计算当前分配方案的适应度(目标函数)
def calculate_fitness(allocation, costs):
total_cost = 0
for i in range(len(allocation)):
total_cost += costs[i][allocation[i]]
return total_cost
# 执行模拟退火算法
def simulated_annealing(num_persons, num_tasks, costs, initial_temperature, cooling_rate):
current_allocation = initialize(num_persons, num_tasks)
current_fitness = calculate_fitness(current_allocation, costs)
best_allocation = current_allocation.copy()
best_fitness = current_fitness
temperature = initial_temperature
while temperature > 0.1:
# 随机选择一个人员和一个任务进行交换
new_allocation = current_allocation.copy()
person_index = random.randint(0, num_persons-1)
task_index = random.randint(0, num_tasks-1)
new_allocation[person_index] = task_index
new_fitness = calculate_fitness(new_allocation, costs)
# 根据Metropolis准则决定是否接受新的分配方案
if new_fitness < current_fitness or random.random() < math.exp((current_fitness - new_fitness) / temperature):
current_allocation = new_allocation
current_fitness = new_fitness
# 更新最优解
if current_fitness < best_fitness:
best_allocation = current_allocation.copy()
best_fitness = current_fitness
# 降低温度
temperature *= cooling_rate
return best_allocation, best_fitness
# 示例数据
num_persons = 5
num_tasks = 3
costs = [
[2, 7, 5],
[3, 1, 6],
[4, 9, 8],
[8, 2, 1],
[6, 3, 7]
]
initial_temperature = 100
cooling_rate = 0.95
# 执行模拟退火算法
best_allocation, best_fitness = simulated_annealing(num_persons, num_tasks, costs, initial_temperature, cooling_rate)
print("最优分配方案:", best_allocation)
print("最优适应度:", best_fitness)
```
这段代码实现了一个简单的人员分配的模拟退火算法。首先,通过`initialize`函数初始化人员和任务的分配情况。然后,通过`calculate_fitness`函数计算当前分配方案的适应度(即目标函数值)。接下来,使用模拟退火算法进行迭代优化,直到达到停止条件(温度小于0.1)。在每次迭代中,随机选择一个人员和一个任务进行交换,并根据Metropolis准则决定是否接受新的分配方案。最后,返回最优的分配方案和适应度。