mathematical-optimization - 如何使用 Cplex（docplex）输出单纯形乘法器？

Question

我正在使用带有 docplex 库的 python 来解决线性规划问题。我想在最终画面中获得它的单纯形乘数或系数（松弛变量）。

Answer 1

你看过双重价值吗？

 dual_values(cts)

 Returns the dual values of a sequence of linear constraints.

 Note: the model must a pure LP: no integer or binary variable, no piecewise, no SOS. The model must also be solved successfully before
 calling this method.

在http://ibmdecisionoptimization.github.io/docplex-doc/mp/docplex.mp.model.html

让我将 OPL 示例 volsay 翻译成 docplex

from docplex.mp.model import Model

mdl = Model(name='volsay')
Gas = mdl.continuous_var(name='Gas')
Chloride = mdl.continuous_var(name='Cloride')

mdl.add_constraint(Gas + Chloride <= 50, 'ctMaxTotal1')
mdl.add_constraint(3 * Gas + 4 * Chloride <= 180, 'ctMaxTotal2')
mdl.add_constraint(Chloride <= 40, 'ctMaxChloride')

mdl.maximize(40 * Gas + 50 * Chloride)

mdl.solve()



for v in mdl.iter_continuous_vars():
    print(v," = ",v.solution_value)

print("ctMaxTotalDual = ",mdl.dual_values(mdl.find_matching_linear_constraints('ctMaxTotal1'))); 

在 OPL CPLEX 中显示我们将编写的对偶

// --------------------------------------------------------------------------
// Licensed Materials - Property of IBM
//
// 5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55
// Copyright IBM Corporation 1998, 2013. All Rights Reserved.
//
// Note to U.S. Government Users Restricted Rights:
// Use, duplication or disclosure restricted by GSA ADP Schedule
// Contract with IBM Corp.
// --------------------------------------------------------------------------

dvar float+ Gas;
dvar float+ Chloride;


maximize
  40 * Gas + 50 * Chloride;
subject to {
  ctMaxTotal:     
    Gas + Chloride <= 50;
  ctMaxTotal2:    
    3 * Gas + 4 * Chloride <= 180;
  ctMaxChloride:  
    Chloride <= 40;
}

tuple SolutionT{ 
    float Gas; 
    float Chloride; 
};
{SolutionT} Solution = {<Gas,Chloride>};
execute{ 
    writeln(Solution);
}

execute
{
  writeln("ctMaxTotalDual = ",ctMaxTotal.dual);
}