如何使用 scipy.optimize.linprog 获得整数解?

问题描述

当我解决线性规划问题时，就像下面的公式，我希望x的结果都是int类型

考虑以下问题:

最小化:f = -1*x[0] + 4*x[1]

受制于:

-3*x[0] + 1*x[1] = -3

其中:-inf

接下来是python编码器

>>>c = [-1, 4]>>>A = [[-3, 1], [1, 2]]>>>b = [6, 4]>>>x0_bounds =(无，无)>>>x1_bounds = (-3, 无)>>>res = linprog(c, A_ub=A, b_ub=b, bounds=(x0_bounds, x1_bounds),... options="disp": True})>>>打印(资源)优化已成功终止.当前函数值:-11.428571迭代次数:2状态:0成功:正确乐趣:-11.428571428571429x: 数组([-1.14285714, 2.57142857])消息:'优化成功终止.'尼特:2

解决方案

来自 文档:

method : str，可选求解器类型.此时只有单纯"是支持.

Simplex 无法处理完整性约束，因此您还无法使用 scipy.optimize.linprog 解决整数规划问题.您可以尝试其他库，例如 PuLP、Pyomo 或 CVXOPT.

When I solve the problem of Linear Programming, like in the following formula, I want the result of x all to be int type

Consider the following problem:

Minimize: f = -1*x[0] + 4*x[1]

Subject to:

-3*x[0] + 1*x[1] <= 6    
1*x[0] + 2*x[1] <= 4    
x[1] >= -3

where: -inf <= x[0] <= inf

next is the python coder

>>> c = [-1, 4]
>>> A = [[-3, 1], [1, 2]]
>>> b = [6, 4]
>>> x0_bounds = (None, None)
>>> x1_bounds = (-3, None)
>>> res = linprog(c, A_ub=A, b_ub=b, bounds=(x0_bounds, x1_bounds),
...               options={"disp": True})
>>> print(res)
Optimization terminated successfully.
Current function value: -11.428571
Iterations: 2
status: 0
success: True
fun: -11.428571428571429
x: array([-1.14285714,  2.57142857])
message: 'Optimization terminated successfully.'
nit: 2

解决方案

From the docs:

Simplex cannot handle integrality constraints so you cannot solve integer programming problems with scipy.optimize.linprog yet. You can try other libraries like PuLP, Pyomo or CVXOPT.

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