private void BreakHandling(GRBModel model, int numberOfRoutes, GRBVar[][] v)
{
for (int i = 1; i < visitDurations.Length; i++)
{
if (!input.Visits[i - 1].IsBreak)
{
continue;
}
var visit = input.Visits[i - 1];
var breakRoutes = new List <int>();
for (var day = 0; day < input.Days.Length; day++)
{
var s = visit.SantaId + day * input.Santas.Length;
model.AddGenConstrOr(v[s][i], v[s].Take(i - 1).Skip(1).ToArray(), null); // assignment if used
breakRoutes.Add(s);
}
// break cannot be visited by another santa
foreach (var nonBreakRoute in Enumerable.Range(0, numberOfRoutes).Except(breakRoutes))
{
model.AddConstr(v[nonBreakRoute][i] == 0, null);
}
}
}
//linearize a condition f. For example, f=k1+k2*k3+k4, it would return f=u1+u2+u3, where u1=k1, u2=k2*k3, u3=k4
//Furthermore, this function could identify if f has a constant term. If so, it would mark out that f has a constant term in the array consflag.
static public List <GRBVar> LinearConstrain(GRBModel m, GRBVar[] Uvar, GRBVar[] UFvar, UInt32[, ,] ConS, int[] conlen, int ind, GRBVar[] keyvar, GRBVar[] ivvar, int[] loc1, GRBVar[] kvf, GRBVar[] vvf, GRBVar[] Wvar, int[] locw, List <GRBVar> LinFlagRes)
{
List <GRBVar> LinVar = new List <GRBVar>()
{
};
List <GRBVar> LinVarFlag = new List <GRBVar>()
{
};
List <GRBVar> TempVarFlag = new List <GRBVar>()
{
}; //store the flag variables of the variables appearing in a monimial
List <GRBVar> TempVar = new List <GRBVar>()
{
}; //store the assignment variables of the variables appearing in a monimial
int weight = 0;
int i, j, k;
int t;
int loc = 0;
int locf = 0;
int loc_w = locw[0];
loc = loc1[0];
locf = loc1[1];
for (j = 0; j < conlen[ind]; j++)
{
//for the j-th monomial
//Cons[ind,j,0-2]stores the iv variable appearing in the monimial
//Cons[ind,j,3-5]stores the key variable appearing in the monimial
weight = 0;
TempVar.Clear();
TempVarFlag.Clear();
for (i = 0; i < 96; i++)
{
t = (int)((ConS[ind, j, (i >> 5)] >> (i & 0x1f)) & 0x01);
weight = weight + t;
if (t == 1)
{
TempVar.Add(ivvar[i]);
TempVarFlag.Add(vvf[i]);
}
}
for (i = 0; i < 96; i++)
{
t = (int)((ConS[ind, j, (i >> 5) + 3] >> (i & 0x1f)) & 0x01);
weight = weight + t;
if (t == 1)
{
TempVar.Add(keyvar[i]);
TempVarFlag.Add(kvf[i]);
}
}
//if weight ==1, it is a monomial of degree one, then we only replace it with a new variable
if (weight == 1)
{
m.AddConstr(Uvar[loc] == TempVar[0], "SingleBit" + loc.ToString());
m.AddConstr(UFvar[locf] == TempVarFlag[0], "SingleBit" + loc.ToString());
LinVar.Add(Uvar[loc]);
LinFlagRes.Add(UFvar[locf]);
loc++;
locf++;
}
//if weight>1, then it is a nonlinear monomial and we should linearize it accroding to the rule of AND in our paper.
if (weight > 1)
{
GRBVar[] PickVars = new GRBVar[TempVar.Count];
for (i = 0; i < TempVar.Count; i++)
{
PickVars[i] = TempVar[i];
//Wvar[loc_w+i]= TempVar[i]^TempVarFlag[i]
GRBVar[] tempor = new GRBVar[2] {
TempVar[i], TempVarFlag[i]
};
m.AddGenConstrOr(Wvar[loc_w + i], tempor, "tempor" + i.ToString());//变元与变元的标志相或
}
GRBVar[] tempm = new GRBVar[TempVar.Count];
//Wvar[loc_w+l]=min(Wvar[loc_w],Wvar[loc_w+1],...,Wvar[loc_w+l-1]), where l is the number variables appearing in the monomial
for (i = 0; i < TempVar.Count; i++)
{
tempm[i] = Wvar[loc_w + i];
}
loc_w = loc_w + TempVar.Count;
m.AddGenConstrMin(Wvar[loc_w], tempm, 1, "linmin" + loc_w.ToString());
loc_w++;
for (i = 0; i < TempVar.Count; i++)
{
tempm[i] = TempVarFlag[i];
}
//Wvar[loc_w]=max(TempVarFlag[0],TempVarFlag[1],...,TempVarFlag[l-1]), where l is the number variables appearing in the monomial
m.AddGenConstrMax(Wvar[loc_w], tempm, 0, "linmaxFlag" + loc_w.ToString());
loc_w++;
GRBVar[] tempminFlag = new GRBVar[2] {
Wvar[loc_w - 1], Wvar[loc_w - 2]
};
//UFvar[loc] is the final flag variable of the monomial
m.AddGenConstrMin(UFvar[locf], tempminFlag, 1, "minFlag" + loc.ToString());
//Uvar[loc] is the final assignment variable of the monomial
m.AddGenConstrMin(Uvar[loc], PickVars, 0, "Linearity" + loc.ToString());
LinVar.Add(Uvar[loc]);
LinFlagRes.Add(UFvar[locf]);
loc++;
locf++;
}
}
loc1[0] = loc;
loc1[1] = locf;
locw[0] = loc_w;
return(LinVar);
}
static void Main()
{
try {
// Example data:
// e.g. {0, n+1, 2} means clause (x0 or ~x1 or x2)
int[,] Clauses = new int[, ]
{
{ 0, n + 1, 2 }, { 1, n + 2, 3 },
{ 2, n + 3, 0 }, { 3, n + 0, 1 },
{ n + 0, n + 1, 2 }, { n + 1, n + 2, 3 },
{ n + 2, n + 3, 0 }, { n + 3, n + 0, 1 }
};
int i, status;
// Create environment
GRBEnv env = new GRBEnv("genconstr_cs.log");
// Create initial model
GRBModel model = new GRBModel(env);
model.ModelName = "genconstr_cs";
// Initialize decision variables and objective
GRBVar[] Lit = new GRBVar[NLITERALS];
GRBVar[] NotLit = new GRBVar[NLITERALS];
for (i = 0; i < NLITERALS; i++)
{
Lit[i] = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, string.Format("X{0}", i));
NotLit[i] = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, string.Format("notX{0}", i));
}
GRBVar[] Cla = new GRBVar[NCLAUSES];
for (i = 0; i < NCLAUSES; i++)
{
Cla[i] = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, string.Format("Clause{0}", i));
}
GRBVar[] Obj = new GRBVar[NOBJ];
for (i = 0; i < NOBJ; i++)
{
Obj[i] = model.AddVar(0.0, 1.0, 1.0, GRB.BINARY, string.Format("Obj{0}", i));
}
// Link Xi and notXi
GRBLinExpr lhs;
for (i = 0; i < NLITERALS; i++)
{
lhs = new GRBLinExpr();
lhs.AddTerm(1.0, Lit[i]);
lhs.AddTerm(1.0, NotLit[i]);
model.AddConstr(lhs, GRB.EQUAL, 1.0, string.Format("CNSTR_X{0}", i));
}
// Link clauses and literals
for (i = 0; i < NCLAUSES; i++)
{
GRBVar[] clause = new GRBVar[3];
for (int j = 0; j < 3; j++)
{
if (Clauses[i, j] >= n)
{
clause[j] = NotLit[Clauses[i, j] - n];
}
else
{
clause[j] = Lit[Clauses[i, j]];
}
}
model.AddGenConstrOr(Cla[i], clause, string.Format("CNSTR_Clause{0}", i));
}
// Link objs with clauses
model.AddGenConstrMin(Obj[0], Cla, GRB.INFINITY, "CNSTR_Obj0");
lhs = new GRBLinExpr();
for (i = 0; i < NCLAUSES; i++)
{
lhs.AddTerm(1.0, Cla[i]);
}
model.AddGenConstrIndicator(Obj[1], 1, lhs, GRB.GREATER_EQUAL, 4.0, "CNSTR_Obj1");
// Set global objective sense
model.ModelSense = GRB.MAXIMIZE;
// Save problem
model.Write("genconstr_cs.mps");
model.Write("genconstr_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 result
double objval = model.ObjVal;
if (objval > 1.9)
{
Console.WriteLine("Logical expression is satisfiable");
}
else if (objval > 0.9)
{
Console.WriteLine("At least four clauses can be satisfied");
}
else
{
Console.WriteLine("Not even three clauses can be satisfied");
}
// Dispose of model and environment
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: {0}. {1}", e.ErrorCode, e.Message);
}
}