// If the solution space is very large, this method will not return.
// The most likely result is that it will exceed memory capacity
// and then fail. As a result, we shouldn't use this method in
// any production optimization.
public IEnumerable <ProductionTarget> GetFeasibleTargets(double claySupply, double glazeSupply)
{
List <ProductionTarget> targets = new List <ProductionTarget>();
// Setup the Gurobi environment & Model
GRBEnv env = new GRBEnv();
GRBModel model = new GRBModel(env);
// Setup the decision variables
GRBVar xS = CreateSmallVasesVariable(claySupply, model);
GRBVar xL = CreateLargeVasesVariable(glazeSupply, model);
model.Update();
// Create Constraints
CreateConstraints(model, xS, xL, claySupply, glazeSupply);
// Find the greatest number of small vases we can make
var maxSmall = System.Math.Min(claySupply, glazeSupply);
// Find the greatest number of large vases we can make
var maxLarge = System.Math.Min(claySupply / 4.0, glazeSupply / 2.0);
// Find all feasible combinations of small and large vases
// Note: There are probably several better ways of doing this
// that are more efficient and organic. For example, we could make
// a tree that represents all of the possible decisions and let the
// optimizer find the solutions from within that tree.
var results = new List <ProductionTarget>();
for (int nSmall = 0; nSmall <= maxSmall; nSmall++)
{
for (int nLarge = 0; nLarge <= maxLarge; nLarge++)
{
// Force the solution to the target set of values
var c1 = model.AddConstr(xS == nSmall, $"xS_Equals_{nSmall}");
var c2 = model.AddConstr(xL == nLarge, $"xL_Equals_{nLarge}");
model.Update();
// See if the solution is feasible with those values
model.Optimize();
if (model.IsFeasible())
{
results.Add(new ProductionTarget()
{
Small = nSmall, Large = nLarge
});
}
model.Remove(c1);
model.Remove(c2);
model.Update();
}
}
return(results);
}
public static void Remove(this GRBModel model, IEnumerable <GRBSOS> constraints)
{
foreach (var constraint in constraints)
{
model.Remove(constraint);
}
}
public static void Remove(this GRBModel model, IEnumerable <GRBVar> variables)
{
foreach (var variable in variables)
{
model.Remove(variable);
}
}
/// <summary>
/// Basicly the same as DesiredOverlap but with unavailable
/// </summary>
/// <param name="model"></param>
/// <param name="numberOfRoutes"></param>
/// <param name="v"></param>
/// <param name="w"></param>
/// <param name="c"></param>
/// <param name="unavailableDuration"></param>
private void UnavailableOverlap(GRBModel model, int numberOfRoutes, GRBVar[][] v, GRBVar[][] w, GRBVar[][] c, GRBVar[][][] unavailableDuration, bool hardConstraint = false)
{
for (int s = 0; s < numberOfRoutes; s++)
{
var day = s / input.Santas.Length;
var(dayStart, dayEnd) = input.Days[day];
var dayDuration = dayEnd - dayStart;
for (int i = 1; i < visitDurations.Length; i++)
{
var visit = input.Visits[i - 1];
for (int d = 0; d < visit.Unavailable.Length; d++)
{
// check if unavailable is on this day
var(unavailableFrom, unavailableTo) = visit.Unavailable[d];
if (unavailableTo < dayStart || unavailableFrom > dayEnd)
{
model.Remove(unavailableDuration[s][i][d]);
unavailableDuration[s][i][d] = null;
//model.AddConstr(unavailableDuration[s][i][d] == 0, GurobiVarName($"unavailalbe[{s}][{i}][{d}] == 0, outside of day"));
continue;
}
// temp
if (hardConstraint)
{
model.AddConstr(unavailableDuration[s][i][d] == 0, GurobiVarName($"unavailalbe[{s}][{i}][{d}] == 0, hard constraint"));
}
var maxUnavailableDuration = Math.Min(visit.Duration, unavailableTo - unavailableFrom);
model.AddConstr(unavailableDuration[s][i][d] <= maxUnavailableDuration * v[s][i], GurobiVarName($"unavailable[{s}][{i}][{d}] only possible if v[{s}][{i}]"));
var unavailableStart = model.AddVar(unavailableFrom - dayStart, dayDuration, 0, GRB.CONTINUOUS, GurobiVarName($"unavailableStart[{s}][{i}][{d}]"));
var binHelperStart = model.AddVar(0, 1, 0, GRB.BINARY, GurobiVarName($"binHelperUnavailableStart[{s}][{i}][{d}]"));
var visitStart = c[s][i];
model.AddConstr(unavailableStart >= visitStart, null);
model.AddGenConstrIndicator(binHelperStart, 0, unavailableStart <= unavailableFrom - dayStart, null);
model.AddGenConstrIndicator(binHelperStart, 1, unavailableStart <= visitStart, null);
var unavailableEnd = model.AddVar(0, unavailableTo - dayStart, 0, GRB.CONTINUOUS, GurobiVarName($"unavailableEnd[{s}][{i}][{d}]"));
var binHelperEnd = model.AddVar(0, 1, 0, GRB.BINARY, GurobiVarName($"binHelperUnavailableEnd[{s}][{i}][{d}]"));
var visitEnd = visitStart + visit.Duration * v[s][i];
model.AddConstr(unavailableEnd <= visitEnd, GurobiVarName($"unavailableEnd[{s}[{i}][{d}] <= visitEnd"));
model.AddGenConstrIndicator(binHelperEnd, 0, unavailableEnd >= unavailableTo - dayStart, null);
model.AddGenConstrIndicator(binHelperEnd, 1, unavailableEnd >= visitEnd, null);
model.AddConstr(
unavailableDuration[s][i][d] >= unavailableEnd - unavailableStart,
GurobiVarName($"unavailable overlap[{s}][{i}][{d}]"));
}
}
}
}
public override bool DelConstraint(object solver, int row)
{
GRBModel model = solver as GRBModel;
if (model == null)
{
return(false);
}
model.Remove(model.GetConstrs()[row]);
model.Update();
return(true);
}
public override bool DelColumn(object solver, int column)
{
GRBModel model = solver as GRBModel;
if (model == null)
{
return(false);
}
model.Remove(model.GetVars()[column]);
model.Update();
return(true);
}
private void ChangeNBreaksGurobi(GRBModel pModel, GRBLinExpr pTotalStepsConst, GRBVar[] pDecVar, int intNClasses, int intNFeatures)
{
try
{
Cs = new double[intNClasses + 1];
cbIdx = new int[intNClasses + 1]; // For Graph
int intNDecVar = (intNFeatures * (intNFeatures + 1)) / 2; // Add L0_0
pModel.Remove(pModel.GetConstrByName("Nsteps"));
pModel.AddConstr(pTotalStepsConst, GRB.EQUAL, intNClasses, "Nsteps");
//Solving
pModel.Optimize();
//Add Results to CS array
Cs[0] = arrEst[0]; //Estimate Array was sorted
int intIdxCs = 0;
if (pModel.Get(GRB.IntAttr.Status) == GRB.Status.OPTIMAL)
{
for (int i = 0; i < intNDecVar; i++)
{
if (pDecVar[i].Get(GRB.DoubleAttr.X) == 1)
{
intIdxCs++;
string strName = pDecVar[i].Get(GRB.StringAttr.VarName);
int intIndexUBar = strName.IndexOf("_");
string strTo = strName.Substring(intIndexUBar + 1);
int intToValue = Convert.ToInt16(strTo);
Cs[intIdxCs] = arrEst[intToValue - 1]; //Closed
cbIdx[intIdxCs] = intToValue - 1;
}
}
}
txtObjValue.Text = pModel.Get(GRB.DoubleAttr.ObjVal).ToString("N5");
}
catch (Exception ex)
{
MessageBox.Show(this.Handle.ToString() + " Error:" + ex.Message);
return;
}
}
private void DesiredOverlap(GRBModel model, int numberOfRoutes, GRBVar[][] v, GRBVar[][] w, GRBVar[][] c, GRBVar[][][] desiredDuration)
{
for (int s = 0; s < numberOfRoutes; s++)
{
var day = s / input.Santas.Length;
var(dayStart, dayEnd) = input.Days[day];
var dayDuration = dayEnd - dayStart;
for (int i = 1; i < visitDurations.Length; i++)
{
var visit = input.Visits[i - 1];
for (int d = 0; d < visit.Desired.Length; d++)
{
var(desiredFrom, desiredTo) = visit.Desired[d];
// check if desired on day
if (desiredTo < dayStart || desiredFrom > dayEnd)
{
model.Remove(desiredDuration[s][i][d]);
desiredDuration[s][i][d] = null; //free up memory
//model.AddConstr(desiredDuration[s][i][d] == 0, GurobiVarName($"desiredDuration[{s}][{i}][{d}] == 0, outside of day"));
continue;
}
var maxDesiredDuration = Math.Min(visit.Duration, desiredTo - desiredFrom);
model.AddConstr(desiredDuration[s][i][d] <= maxDesiredDuration * v[s][i], GurobiVarName($"desired[{s}][{i}][{d}] only possible if v[{s}][{i}]"));
var desiredStart = model.AddVar(Math.Max(desiredFrom - dayStart, 0), dayDuration, 0, GRB.CONTINUOUS, GurobiVarName($"desiredStart[{s}][{i}][{d}]"));
model.AddConstr(desiredStart >= c[s][i], GurobiVarName($"desiredStart[{s}[{i}][{d}] >= visitStart"));
var desiredEnd = model.AddVar(0, desiredTo - dayStart, 0, GRB.CONTINUOUS, GurobiVarName($"desiredEnd[{s}][{i}][{d}]"));
model.AddConstr(desiredEnd <= c[s][i] + visit.Duration * v[s][i], GurobiVarName($"desiredEnd[{s}[{i}][{d}] <= visitEnd"));
var binDecisionVariable = model.AddVar(0, 1, 0, GRB.BINARY, GurobiVarName($"binDesiredDecisionVar[{s}][{i}][{d}]"));
// if positive, duration = end -start
model.AddGenConstrIndicator(binDecisionVariable, 0, desiredEnd - desiredStart >= 0, null);
model.AddGenConstrIndicator(binDecisionVariable, 0, desiredDuration[s][i][d] == desiredEnd - desiredStart, null);
// if negative, duration = 0
model.AddGenConstrIndicator(binDecisionVariable, 1, desiredEnd - desiredStart <= 0, null);
model.AddGenConstrIndicator(binDecisionVariable, 1, desiredDuration[s][i][d] == 0, null);
}
}
}
}
static void Main()
{
try {
// Create environment
GRBEnv env = new GRBEnv();
// Create a new m
GRBModel m = new GRBModel(env);
double lb = 0.0, ub = GRB.INFINITY;
GRBVar x = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "x");
GRBVar y = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "y");
GRBVar u = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "u");
GRBVar v = m.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "v");
// Set objective
m.SetObjective(2 * x + y, GRB.MAXIMIZE);
// Add linear constraint
m.AddConstr(u + 4 * v <= 9, "l1");
// Approach 1) PWL constraint approach
double intv = 1e-3;
double xmax = Math.Log(9.0);
int len = (int)Math.Ceiling(xmax / intv) + 1;
double[] xpts = new double[len];
double[] upts = new double[len];
for (int i = 0; i < len; i++)
{
xpts[i] = i * intv;
upts[i] = f(i * intv);
}
GRBGenConstr gc1 = m.AddGenConstrPWL(x, u, xpts, upts, "gc1");
double ymax = (9.0 / 4.0) * (9.0 / 4.0);
len = (int)Math.Ceiling(ymax / intv) + 1;
double[] ypts = new double[len];
double[] vpts = new double[len];
for (int i = 0; i < len; i++)
{
ypts[i] = i * intv;
vpts[i] = g(i * intv);
}
GRBGenConstr gc2 = m.AddGenConstrPWL(y, v, ypts, vpts, "gc2");
// Optimize the model and print solution
m.Optimize();
printsol(m, x, y, u, v);
// Approach 2) General function constraint approach with auto PWL
// translation by Gurobi
// restore unsolved state and get rid of PWL constraints
m.Reset();
m.Remove(gc1);
m.Remove(gc2);
m.Update();
GRBGenConstr gcf1 = m.AddGenConstrExp(x, u, "gcf1", "");
GRBGenConstr gcf2 = m.AddGenConstrPow(y, v, 0.5, "gcf2", "");
m.Parameters.FuncPieceLength = 1e-3;
// Optimize the model and print solution
m.Optimize();
printsol(m, x, y, u, v);
// Zoom in, use optimal solution to reduce the ranges and use a smaller
// pclen=1e-5 to solve it
x.LB = Math.Max(x.LB, x.X - 0.01);
x.UB = Math.Min(x.UB, x.X + 0.01);
y.LB = Math.Max(y.LB, y.X - 0.01);
y.UB = Math.Min(y.UB, y.X + 0.01);
m.Update();
m.Reset();
m.Parameters.FuncPieceLength = 1e-5;
// Optimize the model and print solution
m.Optimize();
printsol(m, x, y, u, v);
// Dispose of model and environment
m.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " + 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" };
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 };
// Amount each worker is paid to work one shift
double[] pay = new double[] { 10, 12, 10, 8, 8, 9, 11 };
// 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 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }
};
// Model
GRBEnv env = new GRBEnv();
GRBModel model = new GRBModel(env);
model.ModelName = "assignment";
// Assignment variables: x[w][s] == 1 if worker w is assigned
// to shift s. Since an assignment model always produces integer
// solutions, we use continuous variables and solve as an LP.
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], pay[w], GRB.CONTINUOUS,
Workers[w] + "." + Shifts[s]);
}
}
// The objective is to minimize the total pay costs
model.ModelSense = GRB.MINIMIZE;
// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s
for (int s = 0; s < nShifts; ++s)
{
GRBLinExpr lhs = 0.0;
for (int w = 0; w < nWorkers; ++w)
{
lhs.AddTerm(1.0, x[w, s]);
}
model.AddConstr(lhs == shiftRequirements[s], Shifts[s]);
}
// Optimize
model.Optimize();
int status = model.Status;
if (status == GRB.Status.UNBOUNDED)
{
Console.WriteLine("The model cannot be solved "
+ "because it is unbounded");
return;
}
if (status == GRB.Status.OPTIMAL)
{
Console.WriteLine("The optimal objective is " + model.ObjVal);
return;
}
if ((status != GRB.Status.INF_OR_UNBD) &&
(status != GRB.Status.INFEASIBLE))
{
Console.WriteLine("Optimization was stopped with status " + status);
return;
}
// Do IIS
Console.WriteLine("The model is infeasible; computing IIS");
LinkedList <string> removed = new LinkedList <string>();
// Loop until we reduce to a model that can be solved
while (true)
{
model.ComputeIIS();
Console.WriteLine("\nThe following constraint cannot be satisfied:");
foreach (GRBConstr c in model.GetConstrs())
{
if (c.IISConstr == 1)
{
Console.WriteLine(c.ConstrName);
// Remove a single constraint from the model
removed.AddFirst(c.ConstrName);
model.Remove(c);
break;
}
}
Console.WriteLine();
model.Optimize();
status = model.Status;
if (status == GRB.Status.UNBOUNDED)
{
Console.WriteLine("The model cannot be solved "
+ "because it is unbounded");
return;
}
if (status == GRB.Status.OPTIMAL)
{
break;
}
if ((status != GRB.Status.INF_OR_UNBD) &&
(status != GRB.Status.INFEASIBLE))
{
Console.WriteLine("Optimization was stopped with status " +
status);
return;
}
}
Console.WriteLine("\nThe following constraints were removed "
+ "to get a feasible LP:");
foreach (string s in removed)
{
Console.Write(s + " ");
}
Console.WriteLine();
// Dispose of model and env
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " +
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" };
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 };
// Amount each worker is paid to work one shift
double[] pay = new double[] { 10, 12, 10, 8, 8, 9, 11 };
// 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 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
// Model
GRBEnv env = new GRBEnv();
GRBModel model = new GRBModel(env);
model.Set(GRB.StringAttr.ModelName, "assignment");
// Assignment variables: x[w][s] == 1 if worker w is assigned
// to shift s. Since an assignment model always produces integer
// solutions, we use continuous variables and solve as an LP.
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], pay[w], GRB.CONTINUOUS,
Workers[w] + "." + Shifts[s]);
}
}
// The objective is to minimize the total pay costs
model.Set(GRB.IntAttr.ModelSense, 1);
// Update model to integrate new variables
model.Update();
// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s
for (int s = 0; s < nShifts; ++s) {
GRBLinExpr lhs = 0.0;
for (int w = 0; w < nWorkers; ++w)
lhs += x[w, s];
model.AddConstr(lhs == shiftRequirements[s], Shifts[s]);
}
// Optimize
model.Optimize();
int status = model.Get(GRB.IntAttr.Status);
if (status == GRB.Status.UNBOUNDED) {
Console.WriteLine("The model cannot be solved "
+ "because it is unbounded");
return;
}
if (status == GRB.Status.OPTIMAL) {
Console.WriteLine("The optimal objective is " +
model.Get(GRB.DoubleAttr.ObjVal));
return;
}
if ((status != GRB.Status.INF_OR_UNBD) &&
(status != GRB.Status.INFEASIBLE)) {
Console.WriteLine("Optimization was stopped with status " + status);
return;
}
// Do IIS
Console.WriteLine("The model is infeasible; computing IIS");
LinkedList<string> removed = new LinkedList<string>();
// Loop until we reduce to a model that can be solved
while (true) {
model.ComputeIIS();
Console.WriteLine("\nThe following constraint cannot be satisfied:");
foreach (GRBConstr c in model.GetConstrs()) {
if (c.Get(GRB.IntAttr.IISConstr) == 1) {
Console.WriteLine(c.Get(GRB.StringAttr.ConstrName));
// Remove a single constraint from the model
removed.AddFirst(c.Get(GRB.StringAttr.ConstrName));
model.Remove(c);
break;
}
}
Console.WriteLine();
model.Optimize();
status = model.Get(GRB.IntAttr.Status);
if (status == GRB.Status.UNBOUNDED) {
Console.WriteLine("The model cannot be solved "
+ "because it is unbounded");
return;
}
if (status == GRB.Status.OPTIMAL) {
break;
}
if ((status != GRB.Status.INF_OR_UNBD) &&
(status != GRB.Status.INFEASIBLE)) {
Console.WriteLine("Optimization was stopped with status " +
status);
return;
}
}
Console.WriteLine("\nThe following constraints were removed "
+ "to get a feasible LP:");
foreach (string s in removed) {
Console.Write(s + " ");
}
Console.WriteLine();
// Dispose of model and env
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " +
e.Message);
}
}
