英文:
Maximize the amount of zeros in continuous matrix (Python, docplex)
问题
我的目标函数不是关于最小化/最大化C的条目，而是要最大化C中的0的数量。
我采用的方法是将C翻译成heaviside(C)，这将使所有非零条目等于1，而所有零条目保持为0。然后，我可以最小化这些矩阵条目的总和，从而得到最大的零条目。
model.set_objective('min', sum(np.heaviside(C[k,j], 0) for k, j in itertools.product(range(M), range(P))))
在这里，我遇到了cplex的错误，因为在这一点上C没有定义的值。将C的值强制转换为整数或浮点数的任何尝试都会失败。
TypeError: ufunc 'heaviside'不支持输入类型，并且根据强制转换规则'safe'，无法安全地将输入强制转换为任何支持的类型。
我不明白为什么会出现这个问题，而例如
model.set_objective('min', sum(C[k,j] for k, j in itertools.product(range(M), range(P))))
可以正常工作。
英文:
I have an optimization problem with a continuous matrix variable (C), but:
My objective function is not about min/max the entries of C, but to maximize the amounts of 0 in C.
My approach to model this, is to translate C to heaviside(C), which would make all non-zero entries equal to 1 and all zero entries stay 0. Then i could minimize the sum of these matrix entries, resulting a maximum of zero entries.
model.set_objective('min', sum(np.heaviside(C[k,j], 0) for k, j in itertools.product(range(M), range(P))))
Here I get errors of cplex, because C does not have defined values at this point. Any kind of casting the values of C to int or float fails as well.
> TypeError: ufunc 'heaviside' not supported for the input types, and
> the inputs could not be safely coerced to any supported types
> according to the casting rule ''safe''
I do not understand, why this is a problem, while e.g.
model.set_objective('min', sum(C[k,j] for k, j in itertools.product(range(M), range(P))))
works fine.
答案1
得分: 0
from docplex.mp.model import Model
mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40*460 + nbbus30*360)
mdl.solve()
for v in mdl.iter_integer_vars():
print(v, " = ", v.solution_value)
print()
print("with the logical constraint")
nbKindOfBuses = mdl.integer_var(name='nbKindOfBuses')
mdl.add(nbKindOfBuses==(nbbus40>=1)+(nbbus30>=1))
mdl.minimize(nbbus40*460 + nbbus30*360+(nbKindOfBuses-1)*(500))
mdl.solve()
for v in mdl.iter_integer_vars():
print(v, " = ", v.solution_value)
Note: I have provided the code portion without translating it, as you requested.
英文:
numpy functions are not allowed you should turn them into functions that are in docplex.
For instance you could rely on logical constraints
from docplex.mp.model import Model
mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40*460 + nbbus30*360)
mdl.solve()
for v in mdl.iter_integer_vars():
print(v," = ",v.solution_value)
print()
print("with the logical constraint")
nbKindOfBuses = mdl.integer_var(name='nbKindOfBuses')
mdl.add(nbKindOfBuses==(nbbus40>=1)+(nbbus30>=1))
mdl.minimize(nbbus40*460 + nbbus30*360+(nbKindOfBuses-1)*(500))
mdl.solve()
for v in mdl.iter_integer_vars():
print(v," = ",v.solution_value)
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