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GoalObj - Archimedian and pre-emptive goal programming using objective functions

Description
A small linear problem with multiple objectives is solved by Archimedian and pre-emptive goal programming. The example uses functions to access information about constraints and shows how to solve a problem repeatedly with a modified objective function.

Source Files
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xbgoalobj.cxx

/********************************************************
Xpress-BCL C++ Example Problems
===============================

file xbgoalobj.cxx

Archimedian and pre-emptive goal programming
using objective functions.

(c) 2008 Fair Isaac Corporation
author: S.Heipcke, 2005, rev. Mar. 2011
********************************************************/

#include <iostream>
#include <cmath>
#include <cstring>
#include "xprb_cpp.h"
#include "xprs.h"

using namespace std;
using namespace ::dashoptimization;

#define NGOALS 3

// **** Data ****
const char *Type[] = {"perc", "abs", "perc"};
const char *Sense[] = {"max", "min", "max"};
double Weight[] = {100, 1, 0.1};
double Deviation[] = {10, 4, 20};

void modelgo()
{
XPRBvar x,y;
XPRBctr goalCtr[NGOALS], aCtr;
double Target[NGOALS];
XPRBexpr goal[NGOALS], wobj;
XPRBprob *prob;
int i,g;

prob = new XPRBprob("Goal");

x = prob->newVar("x",XPRB_PL);
y = prob->newVar("y",XPRB_PL);

aCtr = prob->newCtr("Limit", 42*x + 13*y <= 100);

// Goals
goal[0] = 5*x +  2*y - 20;
goal[1] = -3*x + 15*y - 48;
goal[2] = 1.5*x + 21*y - 3.8;
for(g=0;g<NGOALS;g++)
goalCtr[g] = prob->newCtr(XPRBnewname("Goal%d",(g+1)), goal[g]);

// **** Archimedian GP ****
cout << "Archimedian:" << endl;
wobj = 0;
for(g=0;g<NGOALS;g++)
{
if (strcmp(Sense[g],"max")==0)
wobj -= Weight[g]*goal[g];
else
wobj += Weight[g]*goal[g];
}
prob->setObj(wobj);
prob->lpOptimize("");

// Solution printout
cout << " Solution: x: " << x.getSol() << ", y: " << y.getSol() << endl;
cout <<" Goal   Target     Value" << endl;
for(g=0;g<NGOALS;g++)
cout << "  " << g+1 << "       " << Sense[g] << "     " << (goalCtr[g].getAct() - goalCtr[g].getRHS()) << endl;

// **** Prememptive GP ****
cout << "Prememptive:" << endl;
i=-1;
while (i<NGOALS-1)
{
i+=1;
if (strcmp(Sense[i],"max")==0)
{
prob->setObj(goal[i]);
prob->setSense(XPRB_MAXIM);
prob->lpOptimize("");
if (prob->getLPStat() != XPRB_LP_OPTIMAL)
{
cout << "Cannot satisfy goal " << i+1 << endl;
break;
}
else
{
Target[i]=prob->getObjVal();
if (strcmp(Type[i],"perc")==0)
Target[i]-= abs(Target[i])*Deviation[i]/100;
else
Target[i]-= Deviation[i];
if (i<NGOALS-1) goalCtr[i] -= Target[i];
goalCtr[i].setType(XPRB_G);
}
}
else
{
prob->setObj(goal[i]);
prob->setSense(XPRB_MINIM);
prob->lpOptimize("");
if (prob->getLPStat() != XPRB_LP_OPTIMAL)
{
cout << "Cannot satisfy goal " << i+1 << endl;
break;
}
else
{
Target[i]=prob->getObjVal();
if (strcmp(Type[i],"perc")==0)
Target[i]+= abs(Target[i])*Deviation[i]/100;
else
Target[i]+= Deviation[i];
if (i<NGOALS-1) goalCtr[i] -= Target[i];
goalCtr[i].setType(XPRB_L);
}
}
cout << "Solution(" << i+1 << "):  x: " << x.getSol() << ", y: " << y.getSol() << endl;
}

// Solution printout
cout << " Goal       Target         Value" << endl;
for(g=0;g<=i;g++)
{
cout << "  " << g+1 << "     " << (goalCtr[g].getType()==XPRB_G?" >=  ":" <=  ") << Target[g];
if(g==NGOALS-1)
cout << "     " << prob->getObjVal() << endl;
else
cout << "     " << (goalCtr[g].getAct() - goalCtr[g].getRHS()) + Target[g] << endl;
}

delete prob;
}

int main(int argc, char **argv)
{
if (XPRB::init()) return 1;

modelgo();
XPRB::finish();

return 0;
}