我正在尝试使用simulated annealing实现n-queens问题。我已经查看了所有存在的问题，但它并没有解决我的问题。我想出的代码就是这个
#Generate random state for Simulated Annealing
def generateRandomState(n):
rand = [0] * n
for num in range(0, n):
pos = random.randint(0, n-1)
rand[num] = pos
return rand
#Cost function for Simulated Annealing
def costFunction(solution):
cost = 0
for position in range(0, len(solution)):
for next_position in range(position+1, len(solution)):
if (solution[position] == solution[next_position]) or abs(position - next_position) == abs(solution[position] - solution[next_position]):
cost = cost + 1
return cost
def generateNextState(state):
for i in range(0, len(state)):
state[i] = random.randint(0,len(state)-1)
return state
def simulatedAnnealing(solution, temperature, alpha):
max_iter = 170000
size= len(solution)
current_state = generateRandomState(size)
for iteration in range(max_iter):
temperature = temperature * alpha
next_state = generateNextState(current_state)
delta_E = costFunction(next_state) - costFunction(current_state)
exp = decimal.Decimal(decimal.Decimal(math.e) ** (decimal.Decimal(-delta_E) * decimal.Decimal(temperature)))
if (delta_E>0) or (exp > random.uniform(0,1)):
current_state = next_state[:]
if(costFunction(current_state) == 0):
return current_state
我知道我的个人模块costFunction正常运行。但是，没有生成解决方案。我的代码基于此link。当我为n=4运行我的代码时，所有迭代都会结束，并且不会生成任何解决方案。
任何帮助将不胜感激
答案 0 :(得分：0)
您的代码存在一些问题。首先，您的generateNextState功能从根本上被打破。它有设计和实施问题。
让我们先处理实施问题。在还返回之前，该函数会修改state。这是不好的，因为你正在传递当前状态，然后将新状态与旧状态进行比较（如果它们是同一个对象则不是很有用）。该函数应该可以复制输入。
设计问题是它创建了一个完全随机的新状态。新州与以前的州没有关系。这很糟糕，因为这意味着您的搜索只是随机选择值并查看您是否最终猜出了解决方案。你应该选择一个与旧状态密切相关的新状态。例如，您可以尝试将随机女王移动到随机行：
def generateNextState(state):
new_state = state[:] # copy the state, so we don't modify the original
new_state[random.randint(0, len(state)-1)] = random.randint(0,len(state)-1)
return new_state
还有很多其他方法可以产生新状态，这只是我想到的一个想法。其他选项可能是将部分或全部女王移动到邻近位置。或者，如果您从range创建初始状态（因此每个值只出现一次），您可以在两列之间交换行，生成随机排列。这种方法可能更有效，因为排列的状态空间小于允许重复值的状态空间。
其他问题与您如何选择是否使用您生成的新状态有关。你当前的逻辑有很多东西倒退。我想你想改变这些界限：
exp = decimal.Decimal(decimal.Decimal(math.e) ** (decimal.Decimal(-delta_E) * decimal.Decimal(temperature)))
if (delta_E>0) or (exp > random.uniform(0,1)):
更像这样的事情：
exp = math.exp(-delta_E / temperature) # divide by temp, no need for decimals
if delta_E < 0 or exp > random.uniform(0,1): # first condition needs the operator flipped
这是我一直在玩的代码的完整版本。我已经更改了一些工作代码不必要的东西，但它们使诊断问题更容易：
import random
import math
#Generate random state for Simulated Annealing
def generateRandomState(n):
return list(range(n)) # in python 2 you don't need the `list` call here
#Cost function for Simulated Annealing
def costFunction(solution):
cost = 0
for position in range(0, len(solution)):
for next_position in range(position+1, len(solution)):
if (solution[position] == solution[next_position]) or abs(position - next_position) == abs(solution[position] - solution[next_position]):
cost = cost + 1
return cost
def generateNextState(state): # randomly swap two values
state = state[:]
i, j = random.sample(range(len(state)), 2)
state[i], state[j] = state[j], state[i]
return state
def simulatedAnnealing(size, temperature, alpha):
max_iter = 170000
current_state = generateRandomState(size)
current_cost = costFunction(current_state)
for iteration in range(max_iter):
print(current_state, current_cost, temperature)
temperature = temperature * alpha
next_state = generateNextState(current_state)
next_cost = costFunction(next_state)
delta_E = next_cost - current_cost
if delta_E<0 or math.exp(-delta_E / temperature) > random.uniform(0,1):
current_state = next_state
current_cost = next_cost
if current_cost == 0:
return current_state
return None
示例运行：
In [342]: simulatedAnnealing(8, 2, 0.99)
[0, 1, 2, 3, 4, 5, 6, 7] 28 2
[6, 1, 2, 3, 4, 5, 0, 7] 18 1.98
[6, 1, 2, 4, 3, 5, 0, 7] 8 1.9602
[6, 1, 2, 5, 3, 4, 0, 7] 5 1.9405979999999998
[6, 4, 2, 5, 3, 1, 0, 7] 4 1.92119202
[6, 4, 2, 5, 3, 1, 0, 7] 4 1.9019800997999998
[3, 4, 2, 5, 6, 1, 0, 7] 4 1.8829602988019998
[3, 4, 2, 5, 6, 1, 0, 7] 4 1.8641306958139798
[6, 4, 2, 5, 3, 1, 0, 7] 4 1.84548938885584
[6, 4, 2, 5, 1, 3, 0, 7] 4 1.8270344949672814
[6, 4, 3, 5, 1, 2, 0, 7] 5 1.8087641500176086
[6, 4, 3, 5, 1, 2, 0, 7] 5 1.7906765085174325
[6, 4, 3, 5, 1, 2, 0, 7] 5 1.7727697434322582
[6, 4, 3, 5, 1, 2, 7, 0] 6 1.7550420459979357
[6, 7, 3, 5, 1, 2, 4, 0] 5 1.7374916255379562
[3, 7, 6, 5, 1, 2, 4, 0] 5 1.7201167092825767
[3, 7, 6, 5, 1, 2, 4, 0] 5 1.7029155421897508
[3, 7, 0, 5, 1, 2, 4, 6] 3 1.6858863867678533
[3, 7, 0, 1, 5, 2, 4, 6] 3 1.6690275229001748
[3, 5, 0, 1, 7, 2, 4, 6] 4 1.652337247671173
[3, 5, 0, 1, 7, 2, 4, 6] 4 1.6358138751944613
[1, 5, 0, 3, 7, 2, 4, 6] 2 1.6194557364425166
[1, 5, 0, 3, 7, 2, 4, 6] 2 1.6032611790780915
[1, 5, 0, 3, 7, 4, 2, 6] 2 1.5872285672873105
[1, 5, 0, 3, 7, 4, 2, 6] 2 1.5713562816144375
[1, 5, 0, 2, 7, 4, 3, 6] 4 1.555642718798293
[1, 5, 0, 2, 7, 4, 3, 6] 4 1.5400862916103102
[1, 5, 2, 0, 7, 4, 3, 6] 3 1.524685428694207
[4, 5, 2, 0, 7, 1, 3, 6] 4 1.509438574407265
[4, 5, 2, 0, 7, 1, 3, 6] 4 1.4943441886631923
[7, 5, 2, 0, 4, 1, 3, 6] 3 1.4794007467765604
[7, 5, 2, 0, 4, 6, 3, 1] 3 1.4646067393087947
[7, 5, 2, 4, 0, 6, 3, 1] 3 1.4499606719157068
[7, 5, 2, 4, 0, 6, 3, 1] 3 1.4354610651965496
[7, 5, 2, 4, 0, 6, 3, 1] 3 1.4211064545445842
[7, 5, 2, 4, 6, 0, 3, 1] 1 1.4068953899991383
[7, 5, 2, 4, 6, 0, 3, 1] 1 1.392826436099147
[7, 5, 2, 4, 6, 0, 3, 1] 1 1.3788981717381554
[7, 5, 2, 4, 6, 0, 3, 1] 1 1.365109190020774
[6, 5, 2, 4, 7, 0, 3, 1] 1 1.3514580981205662
[6, 1, 2, 4, 7, 0, 3, 5] 1 1.3379435171393605
[6, 1, 2, 4, 7, 0, 3, 5] 1 1.324564081967967
[6, 1, 2, 4, 7, 0, 3, 5] 1 1.3113184411482872
[6, 1, 2, 4, 7, 0, 3, 5] 1 1.2982052567368043
[4, 1, 2, 6, 7, 0, 3, 5] 4 1.2852232041694363
[3, 1, 2, 6, 7, 0, 4, 5] 5 1.2723709721277419
[3, 1, 2, 6, 0, 7, 4, 5] 5 1.2596472624064645
[3, 1, 2, 5, 0, 7, 4, 6] 3 1.2470507897824
[3, 1, 2, 5, 0, 7, 4, 6] 3 1.234580281884576
[3, 1, 4, 5, 0, 7, 2, 6] 5 1.2222344790657302
[3, 1, 4, 5, 7, 0, 2, 6] 3 1.210012134275073
[3, 2, 4, 5, 7, 0, 1, 6] 4 1.1979120129323222
[2, 3, 4, 5, 7, 0, 1, 6] 7 1.1859328928029989
[2, 6, 4, 5, 7, 0, 1, 3] 5 1.1740735638749689
[2, 6, 4, 5, 7, 0, 1, 3] 5 1.162332828236219
[2, 6, 4, 5, 7, 0, 1, 3] 5 1.150709499953857
[4, 6, 2, 5, 7, 0, 1, 3] 3 1.1392024049543183
[4, 6, 2, 5, 1, 0, 7, 3] 2 1.1278103809047753
[4, 6, 2, 5, 1, 0, 7, 3] 2 1.1165322770957276
[0, 6, 2, 5, 1, 4, 7, 3] 1 1.1053669543247702
[0, 4, 2, 5, 1, 6, 7, 3] 3 1.0943132847815225
[0, 4, 2, 5, 1, 6, 7, 3] 3 1.0833701519337071
[0, 4, 2, 5, 7, 6, 1, 3] 3 1.07253645041437
[6, 4, 2, 5, 7, 0, 1, 3] 3 1.0618110859102263
[1, 4, 2, 5, 7, 0, 6, 3] 3 1.051192975051124
[1, 4, 2, 5, 7, 6, 0, 3] 3 1.0406810453006128
[6, 4, 2, 5, 7, 1, 0, 3] 5 1.0302742348476066
[6, 1, 2, 5, 7, 4, 0, 3] 2 1.0199714924991305
[6, 1, 2, 5, 7, 4, 0, 3] 2 1.0097717775741393
[6, 1, 2, 5, 7, 4, 0, 3] 2 0.9996740597983979
[6, 1, 2, 5, 7, 4, 0, 3] 2 0.9896773192004139
[6, 1, 2, 5, 7, 4, 0, 3] 2 0.9797805460084098
[6, 1, 2, 5, 7, 4, 0, 3] 2 0.9699827405483257
[6, 1, 2, 5, 7, 4, 3, 0] 2 0.9602829131428424
[6, 1, 2, 5, 7, 4, 3, 0] 2 0.950680084011414
[6, 1, 2, 5, 7, 4, 3, 0] 2 0.9411732831712999
[6, 1, 3, 5, 7, 4, 2, 0] 1 0.9317615503395869
[6, 1, 3, 5, 7, 4, 2, 0] 1 0.922443934836191
[6, 1, 3, 5, 7, 4, 2, 0] 1 0.9132194954878291
[6, 1, 3, 5, 7, 4, 2, 0] 1 0.9040873005329508
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8950464275276213
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8860959632523451
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8772350036198217
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8684626535836234
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8597780270477872
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8511802467773093
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8426684443095362
[6, 5, 3, 1, 7, 4, 2, 0] 1 0.8342417598664409
[6, 1, 3, 5, 7, 4, 2, 0] 1 0.8258993422677765
[6, 1, 3, 5, 7, 2, 4, 0] 1 0.8176403488450987
[6, 0, 3, 5, 7, 2, 4, 1] 1 0.8094639453566478
[6, 0, 3, 5, 7, 1, 4, 2] 1 0.8013693059030813
[6, 0, 3, 5, 7, 1, 4, 2] 1 0.7933556128440505
[6, 0, 3, 5, 7, 1, 4, 2] 1 0.78542205671561
[6, 0, 3, 5, 7, 1, 4, 2] 1 0.7775678361484539
[6, 0, 3, 5, 7, 1, 4, 2] 1 0.7697921577869694
Out[342]: [4, 0, 3, 5, 7, 1, 6, 2]