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### fixanddive_c++.cpp

/* Copyright 2019, Gurobi Optimization, LLC */

/* Implement a simple MIP heuristic.  Relax the model,
sort variables based on fractionality, and fix the 25% of
the fractional variables that are closest to integer variables.
Repeat until either the relaxation is integer feasible or
linearly infeasible. */

#include "gurobi_c++.h"
#include <algorithm>
#include <cmath>
#include <deque>
using namespace std;

bool vcomp(GRBVar*, GRBVar*) throw(GRBException);

int
main(int argc,
char *argv[])
{
if (argc < 2)
{
cout << "Usage: fixanddive_c++ filename" << endl;
return 1;
}

GRBEnv* env = 0;
GRBVar* x = 0;
try
{
env = new GRBEnv();
GRBModel model = GRBModel(*env, argv[1]);

// Collect integer variables and relax them
// Note that we use GRBVar* to copy variables
deque<GRBVar*> intvars;
x = model.getVars();
for (int j = 0; j < model.get(GRB_IntAttr_NumVars); ++j)
{
if (x[j].get(GRB_CharAttr_VType) != GRB_CONTINUOUS)
{
intvars.push_back(&x[j]);
x[j].set(GRB_CharAttr_VType, GRB_CONTINUOUS);
}
}

model.set(GRB_IntParam_OutputFlag, 0);
model.optimize();

// Perform multiple iterations. In each iteration, identify the first
// quartile of integer variables that are closest to an integer value
// in the relaxation, fix them to the nearest integer, and repeat.

for (int iter = 0; iter < 1000; ++iter)
{

// create a list of fractional variables, sorted in order of
// increasing distance from the relaxation solution to the nearest
// integer value

deque<GRBVar*> fractional;
for (size_t j = 0; j < intvars.size(); ++j)
{
double sol = fabs(intvars[j]->get(GRB_DoubleAttr_X));
if (fabs(sol - floor(sol + 0.5)) > 1e-5)
{
fractional.push_back(intvars[j]);
}
}

cout << "Iteration " << iter << ", obj " <<
model.get(GRB_DoubleAttr_ObjVal) << ", fractional " <<
fractional.size() << endl;

if (fractional.size() == 0)
{
cout << "Found feasible solution - objective " <<
model.get(GRB_DoubleAttr_ObjVal) << endl;
break;
}

// Fix the first quartile to the nearest integer value
sort(fractional.begin(), fractional.end(), vcomp);
int nfix = fractional.size() / 4;
nfix = (nfix > 1) ? nfix : 1;
for (int i = 0; i < nfix; ++i)
{
GRBVar* v = fractional[i];
double fixval = floor(v->get(GRB_DoubleAttr_X) + 0.5);
v->set(GRB_DoubleAttr_LB, fixval);
v->set(GRB_DoubleAttr_UB, fixval);
cout << "  Fix " << v->get(GRB_StringAttr_VarName) << " to " <<
fixval << " ( rel " << v->get(GRB_DoubleAttr_X) << " )" <<
endl;
}

model.optimize();

// Check optimization result

if (model.get(GRB_IntAttr_Status) != GRB_OPTIMAL)
{
cout << "Relaxation is infeasible" << endl;
break;
}
}

}
catch (GRBException e)
{
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
}
catch (...)
{
cout << "Error during optimization" << endl;
}

delete[] x;
delete env;
return 0;
}

bool vcomp(GRBVar* v1,
GRBVar* v2) throw(GRBException)
{
double sol1 = fabs(v1->get(GRB_DoubleAttr_X));
double sol2 = fabs(v2->get(GRB_DoubleAttr_X));
double frac1 = fabs(sol1 - floor(sol1 + 0.5));
double frac2 = fabs(sol2 - floor(sol2 + 0.5));
return (frac1 < frac2);
}


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