static void Main()
{
try {
// Sample data
int groundSetSize = 20;
int nSubsets = 4;
int Budget = 12;
double[,] Set = new double[, ]
{
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1 },
{ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0 },
{ 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0 }
};
int[] SetObjPriority = new int[] { 3, 2, 2, 1 };
double[] SetObjWeight = new double[] { 1.0, 0.25, 1.25, 1.0 };
int e, i, status, nSolutions;
// Create environment
GRBEnv env = new GRBEnv("multiobj_cs.log");
// Create initial model
GRBModel model = new GRBModel(env);
model.ModelName = "multiobj_cs";
// Initialize decision variables for ground set:
// x[e] == 1 if element e is chosen for the covering.
GRBVar[] Elem = model.AddVars(groundSetSize, GRB.BINARY);
for (e = 0; e < groundSetSize; e++)
{
string vname = string.Format("El{0}", e);
Elem[e].VarName = vname;
}
// Constraint: limit total number of elements to be picked to be at most
// Budget
GRBLinExpr lhs = new GRBLinExpr();
for (e = 0; e < groundSetSize; e++)
{
lhs.AddTerm(1.0, Elem[e]);
}
model.AddConstr(lhs, GRB.LESS_EQUAL, Budget, "Budget");
// Set global sense for ALL objectives
model.ModelSense = GRB.MAXIMIZE;
// Limit how many solutions to collect
model.Parameters.PoolSolutions = 100;
// Set and configure i-th objective
for (i = 0; i < nSubsets; i++)
{
string vname = string.Format("Set{0}", i);
GRBLinExpr objn = new GRBLinExpr();
for (e = 0; e < groundSetSize; e++)
{
objn.AddTerm(Set[i, e], Elem[e]);
}
model.SetObjectiveN(objn, i, SetObjPriority[i], SetObjWeight[i],
1.0 + i, 0.01, vname);
}
// Save problem
model.Write("multiobj_cs.lp");
// Optimize
model.Optimize();
// Status checking
status = model.Status;
if (status == GRB.Status.INF_OR_UNBD ||
status == GRB.Status.INFEASIBLE ||
status == GRB.Status.UNBOUNDED)
{
Console.WriteLine("The model cannot be solved " +
"because it is infeasible or unbounded");
return;
}
if (status != GRB.Status.OPTIMAL)
{
Console.WriteLine("Optimization was stopped with status {0}", status);
return;
}
// Print best selected set
Console.WriteLine("Selected elements in best solution:");
Console.Write("\t");
for (e = 0; e < groundSetSize; e++)
{
if (Elem[e].X < .9)
{
continue;
}
Console.Write("El{0} ", e);
}
Console.WriteLine();
// Print number of solutions stored
nSolutions = model.SolCount;
Console.WriteLine("Number of solutions found: {0}", nSolutions);
// Print objective values of solutions
if (nSolutions > 10)
{
nSolutions = 10;
}
Console.WriteLine("Objective values for first {0} solutions:", nSolutions);
for (i = 0; i < nSubsets; i++)
{
model.Parameters.ObjNumber = i;
Console.Write("\tSet" + i);
for (e = 0; e < nSolutions; e++)
{
model.Parameters.SolutionNumber = e;
Console.Write("{0,8}", model.ObjNVal);
}
Console.WriteLine();
}
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code = {0}", e);
Console.WriteLine(e.Message);
}
}
static void Main()
{
try {
// Sample data
// Sets of days and workers
string[] Shifts =
new string[] { "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6",
"Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13",
"Sun14" };
string[] Workers =
new string[] { "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu", "Tobi" };
int nShifts = Shifts.Length;
int nWorkers = Workers.Length;
// Number of workers required for each shift
double[] shiftRequirements =
new double[] { 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 };
// Worker availability: 0 if the worker is unavailable for a shift
double[,] availability =
new double[, ] {
{ 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 },
{ 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 },
{ 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 },
{ 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }
};
// Create environment
GRBEnv env = new GRBEnv();
// Create initial model
GRBModel model = new GRBModel(env);
model.ModelName = "workforce5_cs";
// Initialize assignment decision variables:
// x[w][s] == 1 if worker w is assigned to shift s.
// This is no longer a pure assignment model, so we must
// use binary variables.
GRBVar[,] x = new GRBVar[nWorkers, nShifts];
for (int w = 0; w < nWorkers; ++w)
{
for (int s = 0; s < nShifts; ++s)
{
x[w, s] =
model.AddVar(0, availability[w, s], 0, GRB.BINARY,
string.Format("{0}.{1}", Workers[w], Shifts[s]));
}
}
// Slack variables for each shift constraint so that the shifts can
// be satisfied
GRBVar[] slacks = new GRBVar[nShifts];
for (int s = 0; s < nShifts; ++s)
{
slacks[s] =
model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
string.Format("{0}Slack", Shifts[s]));
}
// Variable to represent the total slack
GRBVar totSlack = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
"totSlack");
// Variables to count the total shifts worked by each worker
GRBVar[] totShifts = new GRBVar[nWorkers];
for (int w = 0; w < nWorkers; ++w)
{
totShifts[w] = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
string.Format("{0}TotShifts", Workers[w]));
}
GRBLinExpr lhs;
// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s, plus the slack
for (int s = 0; s < nShifts; ++s)
{
lhs = new GRBLinExpr();
lhs.AddTerm(1.0, slacks[s]);
for (int w = 0; w < nWorkers; ++w)
{
lhs.AddTerm(1.0, x[w, s]);
}
model.AddConstr(lhs, GRB.EQUAL, shiftRequirements[s], Shifts[s]);
}
// Constraint: set totSlack equal to the total slack
lhs = new GRBLinExpr();
lhs.AddTerm(-1.0, totSlack);
for (int s = 0; s < nShifts; ++s)
{
lhs.AddTerm(1.0, slacks[s]);
}
model.AddConstr(lhs, GRB.EQUAL, 0, "totSlack");
// Constraint: compute the total number of shifts for each worker
for (int w = 0; w < nWorkers; ++w)
{
lhs = new GRBLinExpr();
lhs.AddTerm(-1.0, totShifts[w]);
for (int s = 0; s < nShifts; ++s)
{
lhs.AddTerm(1.0, x[w, s]);
}
model.AddConstr(lhs, GRB.EQUAL, 0, string.Format("totShifts{0}", Workers[w]));
}
// Constraint: set minShift/maxShift variable to less <=/>= to the
// number of shifts among all workers
GRBVar minShift = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
"minShift");
GRBVar maxShift = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
"maxShift");
model.AddGenConstrMin(minShift, totShifts, GRB.INFINITY, "minShift");
model.AddGenConstrMax(maxShift, totShifts, -GRB.INFINITY, "maxShift");
// Set global sense for ALL objectives
model.ModelSense = GRB.MINIMIZE;
// Set primary objective
model.SetObjectiveN(totSlack, 0, 2, 1.0, 2.0, 0.1, "TotalSlack");
// Set secondary objective
model.SetObjectiveN(maxShift - minShift, 1, 1, 1.0, 0, 0, "Fairness");
// Save problem
model.Write("workforce5_cs.lp");
// Optimize
int status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts);
if (status != GRB.Status.OPTIMAL)
{
return;
}
// Dispose of model and environment
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: {0}. {1}", e.ErrorCode, e.Message);
}
}