如何使用 Python 在 Cplex 中表述线性规划问题

Question

我正在尝试使用IBM的Cplex解决线性规划问题，同时从Python调用它。

问题是最小化 a+c，

受制于 Ax'=m' 的约束，

其中 x=[a，b，c]

A = [[20,0,0]，[0,20,30]]

m = [20,30]

a，b，c 介于 0 和 1 之间。

该问题的一个正确解决方案是 a=1、b=0 和 c=1。但是 Cplex 给出了解决方案，a=1、b=1 和 c=0。在表述问题时存在错误，但我无法弄清楚在哪里。下面的代码

import cplex
from cplex.exceptions import CplexError
import sys

my_obj      = [1.0, 0.0, 1.0]
my_ub       = [1.0] * len(my_obj)
my_lb       = [0.0] * len(my_obj)
my_colnames = ["a", "b", "c"]
my_rhs      = [20.0, 30.0]
my_rownames = ["c1", "c2"]
my_sense    = "E" * len(my_rownames)

def populatebynonzero(prob):
prob.objective.set_sense(prob.objective.sense.minimize)
prob.linear_constraints.add(rhs = my_rhs, senses = my_sense,names = my_rownames)
prob.variables.add(obj = my_obj, ub = my_ub, lb = my_lb ,names = my_colnames)

rows = [0,1]
cols = [0,1]
vals = [20.0,30.0]
prob.linear_constraints.set_coefficients(zip(rows, cols, vals))

def lpex1():
try:
my_prob = cplex.Cplex()
handle = populatebynonzero(my_prob)
my_prob.solve()
except CplexError, exc:
print exc
return
numrows = my_prob.linear_constraints.get_num()
numcols = my_prob.variables.get_num()
print
# solution.get_status() returns an integer code
print "Solution status = " , my_prob.solution.get_status(), ":",
# the following line prints the corresponding string
print my_prob.solution.status[my_prob.solution.get_status()]
print "Solution value  = ", my_prob.solution.get_objective_value()
slack = my_prob.solution.get_linear_slacks()
pi    = my_prob.solution.get_dual_values()
x     = my_prob.solution.get_values()
dj    = my_prob.solution.get_reduced_costs()
for i in range(numrows):
print "Row %d:  Slack = %10f  Pi = %10f" % (i, slack[i], pi[i])
for j in range(numcols):
print "Column %d:  Value = %10f Reduced cost = %10f" % (j, x[j], dj[j])
my_prob.write("lpex1.lp")


print x, "SOLUTIONS"
lpex1()

Answer 1

约束的行和列的定义有误，更正如下，现在有效

rows = [0,1,1] 
cols = [0,1,2]
vals = [20.0,20.0,30.0]