mosek
需求
求解mixed-integer problem
Introduction
优秀的数学优化求解器
官方网址：https://www.mosek.com/
其中，重要说明：
- 认证文件下载：https://docs.mosek.com/9.3/licensing/quickstart.html#i-don-t-have-a-license-file-yet
按照要求放在指定的文件夹位置。python正常方法按照mosek包即可使用- https://www.mosek.com/documentation/
有比较比较多的使用说明，主要是两个API文档FusionAPI和OptimizerAPI,一个是面向对象的一个是面向过程的用法，fusion更直观好用。尾页有一cookbook也可以更深入了解模型理论
使用求解器首先要自己完成建模过程，分清楚三个要素：variable、constraint、cost
Study
FusionAPI整数线性规划的例题
from mosek.fusion import *
def main(args):
# constraint的系数，每行指代一个不等式
A = [[50.0, 31.0],
[3.0, -2.0]]
# cost的系数
c = [1.0, 0.64]
with Model('milo1') as M:
# 1.设置变量，名称x，数量为2，限制为非负整数。greaterThan和lessThan都是包含了“=”
x = M.variable('x', 2, Domain.integral(Domain.greaterThan(0.0)))
# 2.设置constraints
# 50.0 x[0] + 31.0 x[1] <= 250.0
# 3.0 x[0] - 2.0 x[1] >= -4.0
M.constraint('c1', Expr.dot(A[0], x), Domain.lessThan(250.0))
M.constraint('c2', Expr.dot(A[1], x), Domain.greaterThan(-4.0))
# 3.设置求解器terminate的条件约束，
# 3.1 time-out时间为60（单位未知，maybe60ms，超时会返回目前suboptimal的答案）
# Set max solution time
M.setSolverParam('mioMaxTime', 60.0)
# 3.2 类似精度的约束，详见FusionAPI13.4.5
# Set max relative gap (to its default value)
M.setSolverParam('mioTolRelGap', 1e-4)
# Set max absolute gap (to its default value)
M.setSolverParam('mioTolAbsGap', 0.0)
# 4.键入目标函数cost为Maximize或者Minimize
# Set the objective function to (c^T * x)
M.objective('obj', ObjectiveSense.Maximize, Expr.dot(c, x))
# Solve the problem
M.solve()
# x.level()返回求解情况即x值为多少的list，其余的也是求解精度
print('[x0, x1] = ', x.level())
print("MIP rel gap = %.2f (%f)" % (M.getSolverDoubleInfo(
"mioObjRelGap"), M.getSolverDoubleInfo("mioObjAbsGap")))
Practice
def mosek_fusion_integer_test():
"""
网上找的游泳问题，测试一下是否正确
测试完成，可以解
求解结果
0 0 0 1 甲自由泳
1 0 0 0 乙蝶泳
0 1 0 0 丙仰泳
0 0 1 0 丁蛙泳
0 0 0 0 戊不参加
:return:
"""
c = [[66.8, 75.6, 87, 58.6],
[57.2, 66, 66.4, 53],
[78, 67.8, 84.6, 59.4],
[70, 74.2, 69.6, 57.2],
[67.4, 71, 83.8, 62.4]]
A = [[1,1,1,1, 0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0],
[0,0,0,0, 1,1,1,1, 0,0,0,0, 0,0,0,0, 0,0,0,0],
[0,0,0,0, 0,0,0,0, 1,1,1,1, 0,0,0,0, 0,0,0,0],
[0,0,0,0, 0,0,0,0, 0,0,0,0, 1,1,1,1, 0,0,0,0],
[0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, 1,1,1,1],
[1,0,0,0, 1,0,0,0, 1,0,0,0, 1,0,0,0, 1,0,0,0],
[0,1,0,0, 0,1,0,0, 0,1,0,0, 0,1,0,0, 0,1,0,0],
[0,0,1,0, 0,0,1,0, 0,0,1,0, 0,0,1,0, 0,0,1,0],
[0,0,0,1, 0,0,0,1, 0,0,0,1, 0,0,0,1, 0,0,0,1],
]
# Create a model with the name 'swim'
with Model("swim") as M:
x = M.variable('x', 20, Domain.integral(Domain.greaterThan(0.0)))
M.constraint(x, Domain.lessThan(1.0))
# 每个队员最多只能选一种泳姿
M.constraint("c1", Expr.dot(A[0], x), Domain.lessThan(1.0))
M.constraint("c2", Expr.dot(A[1], x), Domain.lessThan(1.0))
M.constraint("c3", Expr.dot(A[2], x), Domain.lessThan(1.0))
M.constraint("c4", Expr.dot(A[3], x), Domain.lessThan(1.0))
M.constraint("c5", Expr.dot(A[4], x), Domain.lessThan(1.0))
# 每种泳姿必须一个人选
M.constraint("ca", Expr.dot(A[5], x), Domain.equalsTo(1.0))
M.constraint("cb", Expr.dot(A[6], x), Domain.equalsTo(1.0))
M.constraint("cc", Expr.dot(A[7], x), Domain.equalsTo(1.0))
M.constraint("cd", Expr.dot(A[8], x), Domain.equalsTo(1.0))
# Set max solution time
M.setSolverParam('mioMaxTime', 60.0)
# Set max relative gap (to its default value)
M.setSolverParam('mioTolRelGap', 1e-4)
# Set max absolute gap (to its default value)
M.setSolverParam('mioTolAbsGap', 0.0)
# Set the objective function to (c^T * x)
cc = [ii for i in c for ii in i]
M.objective('obj', ObjectiveSense.Minimize, Expr.dot(cc, x))
# Solve the problem
M.solve()
# Get the solution values
print('[x] = ', x.level())
print("MIP rel gap = %.2f (%f)" % (M.getSolverDoubleInfo(
"mioObjRelGap"), M.getSolverDoubleInfo("mioObjAbsGap")))
[未完待续]