我试图从数据帧中选择行的子集，以便在实现目标最大化的同时满足某些约束。这就是我目前所拥有的：
import pandas as pd
import numpy as np
from scipy.optimize import minimize
df = pd.DataFrame({'a': np.random.randint(0, 100, size=100),
'b': np.random.randint(0, 100, size=100),
'c': np.random.randint(0, 10, size=100),
'd': np.random.randint(0, 5, size=100)})
# constraint functions
def a_constraint(x0, df):
return 1000 - df[x0].a.sum()
def c_constraint(x0, df):
return 3 - df[x0].c.value_counts().max()
def d_constraint(x0, df):
return 3 - df[(x0) & (df.d == 1)].shape[0]
def n_constraint(x0, df):
return 15 - df[x0].shape[0]
# objective function
def objective(x0, df):
return -df[x0].b.sum()
# initial guess
x0 = np.full((df.shape[0]), True, dtype=bool)
# optimization connstraints as list of dicts
constraints = [{'type': 'ineq', 'fun': a_constraint, 'args': (df,)},
{'type': 'ineq', 'fun': d_constraint, 'args': (df,)},
{'type': 'eq', 'fun': c_constraint, 'args': (df,)},
{'type': 'eq', 'fun': n_constraint, 'args': (df,)},
]
result = minimize(objective, x0=x0, method='SLSQP', args=(df,), constraints=constraints)
但是，我收到一个KeyError。看起来它把我的布尔数组当作列标签，而不是索引掩码。有人对我哪里出了问题有什么建议吗？
作为对hpaulj以下评论的回应，回溯是：
KeyError Traceback (most recent call last)
d:Usersgithubfplfpl_stackoverflow.py in <module>
38 ]
39
---> 40 result = minimize(objective, x0=x0, method='SLSQP', args=(df,), constraints=constraints)
d:Users.condaenvstest_envlibsite-packagesscipyoptimize_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
626 elif meth == 'slsqp':
627 return _minimize_slsqp(fun, x0, args, jac, bounds,
--> 628 constraints, callback=callback, **options)
629 elif meth == 'trust-constr':
630 return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,
d:Users.condaenvstest_envlibsite-packagesscipyoptimizeslsqp.py in _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, finite_diff_rel_step, **unknown_options)
327 # meq, mieq: number of equality and inequality constraints
328 meq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
--> 329 for c in cons['eq']]))
330 mieq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
331 for c in cons['ineq']]))
d:Users.condaenvstest_envlibsite-packagesscipyoptimizeslsqp.py in <listcomp>(.0)
327 # meq, mieq: number of equality and inequality constraints
328 meq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
--> 329 for c in cons['eq']]))
...
-> 1308 raise KeyError(f"None of [{key}] are in the [{axis_name}]")
1309
1310 ax = self.obj._get_axis(axis)
KeyError: "None of [Float64Index([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,n 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],n dtype='float64')] are in the [columns]"
该错误在目标函数的print(x0)之前抛出。
首先，只有当您能够保证x0始终具有整数或布尔值dtype时，您的公式才有效。由于scipy.optimize.minimize用于连续优化问题，因此它在引擎盖下为当前迭代x使用浮点dtype，因此第一次迭代已经失败。也就是说，你的约束是而不是连续可微的，因此违反了底层算法的数学假设。
长话短说，您尝试使用连续优化问题的求解器来解决离散优化问题。将问题公式化为离散优化问题是一种更方便的方法。python-mip中可能的公式和实现如下所示：
import pandas as pd
import numpy as np
from mip import Model, BINARY, maximize
df = pd.DataFrame({'a': np.random.randint(0, 100, size=100),
'b': np.random.randint(0, 100, size=100),
'c': np.random.randint(0, 10, size=100),
'd': np.random.randint(0, 5, size=100)})
# extract the numpy arrays for easier access
a = df.a.values
b = df.b.values
c = df.c.values
d = df.d.values
N = 100
# Indices at which d[i] == 1
Td = np.argwhere(d == 1).flatten()
# For each unique value k in c we save each index i such that c[i] == k
Tc = {k : np.argwhere(c == k).flatten() for k in np.unique(c)}
# model object
mdl = Model()
# optimization / decision variables
# x[i] == 1 iff we select the i-th element in a,b,c,d and 0 otherwise
x = [mdl.add_var(var_type=BINARY) for i in range(N)]
# objective: maximize the sum of the selected elements in b
mdl.objective = maximize(sum(b[i]*x[i] for i in range(N)))
# constraint (a): the selected elements in a sum up to less-than 1000
mdl.add_constr(sum(a[i]*x[i] for i in range(N)) <= 1000)
# constraint (n): we select at most 15 elements
mdl.add_constr(sum(x[i] for i in range(N)) == 15)
# constraint (d): we select at most 3 elements for which d[i] == 1
mdl.add_constr(sum(x[i] for i in Td) <= 3)
# constraint (c): we select at most 3 elements of c with the same value
for value, Indices in Tc.items():
mdl.add_constr(sum(x[i] for i in Indices) <= 3)
# disable the solver output
mdl.verbose = 0
# solve the optimization problem
mdl.optimize()
# extract the indices of the solution
selected = np.array([i for i in range(N) if x[i].x > 0.99])
print(selected)