如何修复PuLP python中分配优化的约束

Question

背景：

我正在尝试将客户Ci分配给财务顾问Pj。每个客户都有一个策略值xi。我假设分配给每个顾问的客户数量（n）是相同的，并且不能将同一客户分配给多个顾问。因此，每个合作伙伴都将分配如下策略值：

P1 = [x1，x2，x3]，P2 = [x4，x5，x6]，P3 = [x7，x8，x9]

我正在尝试寻找最佳分配方案，以最大程度地减少顾问之间的基金价值分散。我将分散度定义为最高资金值（z_max）和最低资金值（z_min）的顾问之间的差额。

因此，此问题的公式为：

如果将客户Ci分配给顾问Pj，则yij = 1，否则为0

第一个约束条件要求zmax必须大于或等于每个策略值；由于目标函数鼓励使用较小的zmax值，因此这意味着zmax将等于最大策略值。类似地，第二约束将zmin设置为等于最小策略值。第三个约束条件是，必须将每个客户分配给一个顾问。第四条说，每个顾问必须分配n名客户。信用：@ LarrySnyder610

问题：

当在PulP中实现此问题时，我希望根据约束3和4在173个顾问中分配1740（n x p）个客户。但是，没有获得72036的最优分配。

import random 
import pandas as pd
import pulp 


=============================================================================
# SAMPLE DATA 
=============================================================================

n = 10 # number of customers for each financial adviser
c = 414 #number of customers 
p = 174 #number of financial adviser
policy_values = random.sample(range(1, 1000000), c)


set_I = range(c)
set_J = range(p)
set_N = range(n)
x = {i: policy_values[i] for i in set_I} #customer policy values
y = {(i,j): random.randint(0, 1) for i in set_I for j in set_J} # allocation dummies 


model = pulp.LpProblem("Allocation Model", pulp.LpMinimize)

# =============================================================================
# DECISION VARIABLES
# =============================================================================

y_vars  = {(i,j): pulp.LpVariable(cat=pulp.LpBinary, name="y_{0}_{1}".format(i,j)) for i in set_I for j in set_J}
z_max = pulp.LpVariable("Max Policy Value", 0)
z_min = pulp.LpVariable("Min Policy Value", 0)

# =============================================================================
# OBJECTIVE FUNCTION
# =============================================================================

model += z_max - z_min

# =============================================================================
# CONSTRAINTS
# =============================================================================
model += {j: pulp.lpSum(y_vars[i,j] * x[i] for i in set_I) for j in set_J} <= z_max # constraint 1
model += {j: pulp.lpSum(y_vars[i,j] * x[i] for i in set_I) for j in set_J} >= z_min # constraint 2
model += {i: pulp.lpSum(y_vars[i,j] for j in set_J) for i in set_I} == 1 # constraint 3
model += {j: pulp.lpSum(y_vars[i,j] for i in set_I) for j in set_J} == n #constraint 4

# =============================================================================
# SOLVE MODEL
# =============================================================================

model.solve()
print('Optimised model status: '+str(pulp.LpStatus[model.status]))

count=0
for v in model.variables():
    if v.varValue == 1.0:
        count+=1
        #print(v.name, "=", v.varValue)
print(count)
#>>> 72036 # expecting 1740

print('Optimal difference between highest and lowest summed policy_value: ' + str(pulp.value(model.objective)))

我是否需要更改目标函数/约束以实现上述方程式？

Answer 1

一些提示：

1. 通过total调试
2. 从一个小的数据集开始

3. 没有正确制定约束条件。应该是这样的

   text

   1. 如果 public class ExampleAuthenticator implements Authenticator<BasicCredentials, User> { @Override public Optional<User> authenticate(BasicCredentials credentials) throws AuthenticationException { if ("secret".equals(credentials.getPassword())) { return Optional.of(new User(credentials.getUsername())); } return Optional.absent(); } }
   ，该模型将不可行
   2. 详细信息：我们可能应该重写约束1和2。重复长的求和将创建大量非零元素。

Answer 2

我认为您不能使用该格式添加约束。尝试使用以下格式：

for j in set_J:
    model += pulp.lpSum([y_vars[i,j] * x[i] for i in set_I]) <= z_max

等

还要注意[...]内的lpSum(...)。

最后，我认为您不能像以前那样声明变量。我通常使用LpVariable.dicts()，如下所示：

y_vars = pulp.lpVariable.dicts('y_vars', set_I, 0, 1, pulp.LpInteger)