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Apply a binary fixing heuristic to an unpresolved MIP problem

Description

We take a production plan model and solve its LP relaxation.

Next we fix those binary variables that are very near zero to 0.0, and those that are almost one to 1.0, by changing their respective upper and lower bounds. Finally, we solve the modified problem as a MIP.

This heuristic will speed up solution - though may fail to optimse the problem.

The results are displayed on screen and the problem statistics stored in a log file.

Source Files
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Data Files

FixBV.cs

/***********************************************************************
Xpress Optimizer Examples
=========================

file FixBV.cs

Apply a binary fixing heuristic to an unpresolved MIP problem.

We take a production plan model and solve its LP relaxation.
Next we fix those binary variables that are very
near zero to 0.0, and those that are almost one to 1.0, by changing
their respective upper and lower bounds. Finally, we solve the
modified problem as a MIP.
This heuristic will speed up solution - though may fail to optimise
the problem.
The results are displayed on screen and the problem statistics
stored in a log file.

(c) 2021 Fair Isaac Corporation
***********************************************************************/

using System;
using System.IO;
using Optimizer;

namespace XPRSExamples
{
class FixBV
{
public static void Main(string[] args)
{
FixBV example = new FixBV();
example.Run();
}

private const double TOL=0.0005;            // Tolerance on binary variables

private void Run()
{
try
{
string sProblem="coco";      // Problem name
string sLogFile="fixbv.log"; // Log file name

int nCol;                    // Number of columns

// Global problem information
int nGlEnt;                  // Number of global entities: binary, integer, semi-continuous and partial integer variables
int nSet;                    // Number of S1 and S2 sets
int[] pGlInd;                 // Column indices of the global entities
char[] pGlType;               // Global entity types

// Bound changes
int[] pBndInd;                // Column indices of the bounds to be changed
char[] pBndType;              // New bound type
double[] pBndVal;             // New bound values
int nBnd;                    // Bound counter
int i;                       // Loop counter
int j;                       // Holder for the bound indices

// Solution information
double[] x;                  // LP solution values
int nGlStatus;               // Global status
int nNodes;                  // Number of nodes solved so far in the global search
double dObjVal;              // Objective value of the best integer solution

// Initialise Optimizer
XPRS.Init("");

prob = new XPRSprob();

// Delete and define log file
// Delete the file if it exists.
if (File.Exists(sLogFile))
{
File.Delete(sLogFile);
}
prob.SetLogFile(sLogFile);

// Tell Optimizer to call optimizermsg whenever a message is output
prob.MessageCallbacks += new MessageCallback(this.OptimizerMsg);

// Turn off presolve and permit no cuts - to slow down solution and allow
// the effect of the heuristic to be be seen
prob.Presolve = 0;
prob.CutStrategy = 0;

prob.MPSFormat = -1;

// Solve the LP relaxation

// Get the number of columns
nCol = prob.Cols;

// Allocate memory for solution array and check for memory shortage
x= new double[nCol];

// Solve the LP
prob.Maxim("");

// Get LP solution values
prob.GetSol(x,null,null,null);

// Fix the binary variables that are at their bounds

// Allocate memory for global entity arrays
pGlInd = new int[nCol];
pGlType = new char[nCol];

// Get global entity information

prob.GetGlobal(out nGlEnt, out nSet, pGlType, pGlInd, null, null, (int[])null, null, null);

// Allocate memory for bound arrays
pBndInd = new int[nGlEnt];
pBndVal = new double[nGlEnt];
pBndType = new char[nGlEnt];

// Initialise bound counter
nBnd=0;

// Go through the global entities
for(i=0; i<nGlEnt; i++)
{
// Test whether each is a binary variable
if (pGlType[i] == 'B')
{
// Hold the index of the BV
j=pGlInd[i];

// If the value of the BV is within TOL of zero, store its index,
//   set its upper bound to 0, and increment the bound counter
if (x[j]<=TOL)
{
pBndInd[nBnd]=j;
pBndType[nBnd]='U';
pBndVal[nBnd]=0.0;
nBnd++;

// If the value of the BV is within TOL of one,store its index,
//   set its lower bound to 1, and increment the bound counter
}
else if ((1-x[j])<=TOL)
{
pBndInd[nBnd]=j;
pBndType[nBnd]='L';
pBndVal[nBnd]=1.0;
nBnd++;
}
}
}
// Instruct Optimizer to change the bounds of the appropriate BVs,
//   and tell the user how many have been fixed
prob.ChgBounds(nBnd,pBndInd,pBndType,pBndVal);

Console.WriteLine("Solving problem {0} with a binary fixing heuristic:\n\n",sProblem);
Console.WriteLine("   After the LP optimisation {0} binary variables were fixed\n\n",nBnd);

// Solve the modified problem as a MIP

// Search for an integer solution
prob.Global();

// Get the number of nodes solved in the global search
nNodes = prob.Nodes;

// Get the objective value of the best integer solution
dObjVal = prob.MIPObjVal;

// Check the global status and display the results of the global search
nGlStatus = (int)prob.MIPStatus;

switch (nGlStatus)
{
case 0:
Console.WriteLine("   Problem has not been loaded");
break;
case 1:
Console.WriteLine("   Search has not begun - LP has not been optimised");
break;
case 2:
Console.WriteLine("   Search has not begun - LP has been optimised");
break;
case 3:
Console.WriteLine("   Search interrupted - No integer solution was found");
break;
case 4:
Console.WriteLine("   Search interrupted - Integer solution found: %g",dObjVal);
break;
case 5:
Console.WriteLine("   No integer solution was found");
break;
case 6:
Console.WriteLine("   Integer solution found: {0}",dObjVal);
break;
}
Console.WriteLine("\n\n   The MIP optimisation took {0} nodes\n\n",nNodes);

}
catch (XPRSException e)
{
Console.WriteLine(e.ToString());
throw e;
}
finally
{
prob.Destroy();
XPRS.Free();
}
}

public void OptimizerMsg (XPRSprob prob, object data, string message, int len, int msglvl)
{
switch(msglvl)
{
case 3:
case 4:
Console.WriteLine ("{0}" + message, data);
break;
}
}

private XPRSprob prob;
}
}

`