//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(string[] args)
{
GRBEnv env = new GRBEnv("TJLinearCharacter.log");
GRBModel model = new GRBModel(env);
//declare the iv variables and key variables
GRBVar[] keyvar = model.AddVars(80, GRB.BINARY); //declare the assignment variables of key variables
GRBVar[] ivvar = model.AddVars(80, GRB.BINARY); //declare the assignment variables of iv variables
GRBVar[] kvf = model.AddVars(80, GRB.BINARY); //declare the flag variables of key variables
GRBVar[] vvf = model.AddVars(80, GRB.BINARY); //declare the flag variables of iv variables
GRBVar[] Uvar = model.AddVars(8000, GRB.BINARY); //interval assignment variables used to long XOR expression into short ones y=k1+k2+k3+k4--> u1=k1+k2, u2=k3+k4, y=u1+u2
GRBVar[] Vvar = model.AddVars(8000, GRB.INTEGER); //interval variables
GRBVar[] Wvar = model.AddVars(8000, GRB.BINARY); //interval variables
GRBVar[] UFvar = model.AddVars(8000, GRB.BINARY); //UFvar[i] is the flag variables corresponding to Uvar[i]
GRBVar[] NUvar = model.AddVars(8000, GRB.BINARY); //NUvar[i]= 1-Uvar[i]
GRBVar[] NUFvar = model.AddVars(8000, GRB.BINARY); //NUFvar[i]= 1-UFvar[i]
GRBVar[] Consvar = model.AddVars(8000, GRB.BINARY); //constant variables
GRBVar[] bvar = model.AddVars(8000, GRB.BINARY); //b variables
int i, j, k;
int loc0 = 0, loc1 = 0, loc2 = 0, loc3 = 0, loc4 = 0, locb = 0;
int locf = 0;
int con = 0;
// name all the variables used in this MILP model
for (i = 0; i < keyvar.Length; i++)
{
keyvar[i].VarName = "k" + i.ToString();
ivvar[i].VarName = "v" + i.ToString();
kvf[i].VarName = "kf" + i.ToString();
vvf[i].VarName = "vf" + i.ToString();
}
for (i = 0; i < Uvar.Length; i++)
{
Uvar[i].VarName = "U" + i.ToString();
Wvar[i].VarName = "W" + i.ToString();
UFvar[i].VarName = "UF" + i.ToString();
Vvar[i].VarName = "V" + i.ToString();
NUvar[i].VarName = "NU" + i.ToString();
NUFvar[i].VarName = "NUF" + i.ToString();
bvar[i].VarName = "b" + i.ToString();
Consvar[i].VarName = "cons" + i.ToString();
}
UInt32[, ,] ConS = new UInt32[1000, 200, 6];//used to store the conditions derived to control the propagation of difference
int[] conlen = new int[1000];
int[] consflag = new int[1000];
int[] rec_loc1 = new int[1000];
int[] rec_locf = new int[1000];
//the number of the conditions
int consnum = 652;
int[] loc = new int[2];
int[] locw = new int[1];
int[] condiassig = new int[consnum];
int[] condiflag = new int[consnum];
GRBLinExpr Tar = new GRBLinExpr();//declare the target linear expression, which is used as the objective function
List <int> indlist = new List <int>()
{
};
List <GRBVar> Varlist = new List <GRBVar>()
{
};
List <GRBVar> VarlistCopy = new List <GRBVar>()
{
};
List <GRBVar> VarFlaglist = new List <GRBVar>()
{
};
//List<GRBVar> VarFlaglistCopy = new List<GRBVar>() { };
StreamWriter sw = new StreamWriter("FinalCons.txt");
//the index of cube variables
List <int> cube = new List <int>()
{
0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78
};
//set the state of cube variables to \delta
for (i = 0; i < cube.Count; i++)
{
model.AddConstr(vvf[cube[i]] == 1, "iniiv" + (cube[i]).ToString());
}
//set the contraints between an assigment variable and the corresponding flag variable
for (i = 0; i < 80; i++)
{
model.AddConstr(keyvar[i] <= 1 - kvf[i], "keyflagrel");
model.AddConstr(ivvar[i] <= 1 - vvf[i], "ivflagrel");
}
model.Update();
//read the derived constraints from the file
ReadCondition(ConS, conlen, consflag);
Console.Write("ReadConditionDone\n");
//model each condition
for (i = 0; i < consnum; i++)
{
loc[0] = loc1;
loc[1] = locf;
VarFlaglist.Clear();
Varlist.Clear();
//linearize a condition and return a list of involved variables.
//In this condition, for condition f, it would linearize it and would return the assignment/flag variable of each monomial in f;
//In paticular, Uvar[0],Uvar[1],...,Uvar[m-1] are the assignment variables of the linearized monomials
//UFvar[0],UFvar[1],...,UFvar[m-1] are the flag variables of the linearized monomials
//For eaxmple, for a condition f=k1+k2*k3+k4, it can be linearized as f=u1+u2+u3 where u2=k2k3.
//Then, Varlist[0],Varlist[1],Varlist[2] are assignment variables of u1,u2,u3
//and VarFlaglist[0],VarFlaglist[1],...,VarFlaglist[2] are the flag variables of u1,u2,u3
Varlist = LinearConstrain(model, Uvar, UFvar, ConS, conlen, i, keyvar, ivvar, loc, kvf, vvf, Wvar, locw, VarFlaglist);
loc1 = loc[0];
locf = loc[1];
//here a condition f is linearized and so it is the XOR of several variables.
//in the following, we would determine the assigment varible and flag variable of f
// and we denote the assigment variable and flag variable of f by f_av and f_fv respectively for short.
//The target expression 'Tar' is determined according to the assigment variable and flag variable of each condition f
//In particular, Tar= sum(f in Conset) f_av +(-10000)*f_fv, where Conset is the set of conditions.
//If the size of f is 1(excluding the constant), namely f consists of only one variable, then we do not need extra operations.
if (Varlist.Count == 1)
{
//if consflag[i]=1, then it means that there is a constant 1 in f.
//In this case, we add (-1.0*f_av) to Tar and increase con by 1 which is added to Tar in the end.
if (consflag[i] == 1)
{
Tar.AddTerm(-1.0, Varlist[0]);
con++;
}
else
{
Tar.AddTerm(1.0, Varlist[0]);
}
//add -10000*f_fv to Tar
Tar.AddTerm(-10000, VarFlaglist[0]);
rec_loc1[i] = loc1;
rec_locf[i] = locf;
}
//If f is the XOR of two variables(assumin that f=u1+u2+c), where c is a constant in {0,1}.
//then we shoule calclate f_av and f_fv according to (u1_av, u2_av) and (u1_fv, u2_fv).
if (Varlist.Count == 2)
{
VarlistCopy.Clear();
GRBVar[] VarFlaglistCopy = new GRBVar[3];
GRBVar[] Vartemplist = new GRBVar[4];
//copy Varlist/VarFlaglist to VarlistCopy/VarFlaglistCopy
for (j = 0; j < Varlist.Count(); j++)
{
VarlistCopy.Add(Varlist[j]);
VarFlaglistCopy[j] = VarFlaglist[j];
}
VarlistCopy.Add(Uvar[loc1]);
//model u1_av+u2_av. Here, VarlistCopy[0]and VarlistCoyp[1] are u1_av and u2_av respectively.
AddCons2Vars(model, VarlistCopy);
//model u1_av+u2_av+c. if consflag[i]=1, then c is 1. In this case, we add an constant variable Consvar[loc0] to the model
//and model u1_av+u2_av+c.
if (consflag[i] == 1)
{
model.AddConstr(Consvar[loc0++] == 1, "Flip" + j.ToString());
VarlistCopy[0] = Uvar[loc1];
VarlistCopy[1] = Consvar[loc0 - 1];
VarlistCopy[2] = Uvar[loc1 + 1];
//Console.WriteLine("*****\n" + loc1 + "\n******\n" + loc0 + "\n*****\n");
loc1++;
AddCons2Vars(model, VarlistCopy);
}
//until now, Uvar[loc1] is corresponding to beta_d in Proposition 2 of our paper.
//Then, we shall show how to obtain the final assignment/flag variable of f.
//UF flip the variables
model.AddConstr(NUvar[loc3++] == 1 - VarFlaglist[0], "Flip1" + (loc3).ToString());
model.AddConstr(NUvar[loc3++] == 1 - VarFlaglist[1], "Flip2" + (loc3).ToString());
VarFlaglistCopy[0] = NUvar[loc3 - 1];
VarFlaglistCopy[1] = VarFlaglist[0];
//Vvar[loc2++]=min(1 - VarFlaglist[1], VarFlaglist[0]). Vvar[loc2] corresponds to T_j in Proposition 2.
model.AddGenConstrMin(Vvar[loc2++], VarFlaglistCopy, 1000, "FlagTransOxr1" + loc2.ToString());
VarFlaglistCopy[0] = NUvar[loc3 - 2];
VarFlaglistCopy[1] = VarFlaglist[1];
//Vvar[loc2++]=min(1 - VarFlaglist[0], VarFlaglist[1]). Vvar[loc2] corresponds to T_j in Proposition 2.
model.AddGenConstrMin(Vvar[loc2++], VarFlaglistCopy, 1000, "FlagTransOxr2" + loc2.ToString());
//UFvar[loc1]=Vvar[loc2-1]+Vvar[loc2-2], UFvar[loc1] is the flag variable of f
// model.AddConstr(UFvar[loc1] == Vvar[loc2 - 1] + Vvar[loc2 - 2], "FlagTransOxr3" + loc2.ToString());
for (j = 0; j < Varlist.Count; j++)
{
Vartemplist[j] = Vvar[loc2 - 1 - j];
}
//UFvar[locf]=max(Vvar[loc2],Vvar[loc2-1],...,). is equivalent to UFvar[locf]= Vvar[loc2]+Vvar[loc2-1]+...+
//since only one of Vvar[loc2],Vvar[loc2-1],..., is equal to 1.
//UFvar[locf] is the flag variable of f, corresponding to F_d in Proposition 2.
model.AddGenConstrMax(UFvar[locf], Vartemplist, 0, "FlagTransXor-2" + loc2.ToString());
//NUFvar[loc4] =1-UFvar[loc1] and increase loc4 by 1. NUFvar[loc4] corresponds to 1-F_d in Proposition 2.
model.AddConstr(NUFvar[loc4++] == 1 - UFvar[locf], "Flip3" + loc4.ToString());
//max(u1_fv,u2_fv). bvar[locb] corresponds to b_d in Proposition 2.
VarFlaglistCopy[0] = VarFlaglist[0];
VarFlaglistCopy[1] = VarFlaglist[1];
model.AddGenConstrMax(bvar[locb++], VarFlaglistCopy, 0, "maxfv" + locb.ToString());
//NUFvar[loc4] =1-bvar[locb++] and increase loc4 by 1. NUFvar[loc4] corresponds to 1-b_d in Proposition 2.
model.AddConstr(NUFvar[loc4++] == 1 - bvar[locb - 1], "Flip3" + loc4.ToString());
VarFlaglistCopy[0] = NUFvar[loc4 - 1]; //corresponding to 1-F_d
VarFlaglistCopy[1] = NUFvar[loc4 - 2]; //corresponding to 1-b_d
VarFlaglistCopy[2] = Uvar[loc1]; //corresponding to beta_d
loc1++;
//Uvar[loc1]=min(NUFvar[loc4-1],NUFvar[loc4-2],loc1), is the assigment variable of f.
model.AddGenConstrMin(Uvar[loc1], VarFlaglistCopy, 1000, "minav" + loc1.ToString());
//model.Update();
Tar.AddTerm(1.0, Uvar[loc1]);
Tar.AddTerm(-10000, UFvar[locf]);
rec_loc1[i] = loc1;
rec_locf[i] = locf;
loc1++;
locf++;
}
//in this case, assume that f=u1+u2+u3+c
if (Varlist.Count == 3)
{
VarlistCopy.Clear();
GRBVar[] VarFlaglistCopy = new GRBVar[4];
GRBVar[] VarFlaglistCopy2 = new GRBVar[4];
GRBVar[] Vartemplist = new GRBVar[4];
for (j = 0; j < Varlist.Count(); j++)
{
VarlistCopy.Add(Varlist[j]);
VarFlaglistCopy[j] = VarFlaglist[j];
}
VarlistCopy.Add(Uvar[loc1]);
//Uvar[loc1]=u1+u2+u3
AddCons3Vars(model, VarlistCopy);
//model.AddGenConstrMax(UFvar[loc1], VarFlaglistCopy, 0, "TransFlagXor" + loc1.ToString());
//if c==1, namely f has the constant term 1, U[loc1+1]=Uvar[loc]+1
if (consflag[i] == 1)
{
model.AddConstr(Consvar[loc0++] == 1, "Flip" + j.ToString());
VarlistCopy[0] = Uvar[loc1];
VarlistCopy[1] = Consvar[loc0 - 1];
VarlistCopy[2] = Uvar[loc1 + 1];
loc1++;
AddCons2Vars(model, VarlistCopy);
}
//filp every variable,
for (j = 0; j < Varlist.Count; j++)
{
model.AddConstr(NUvar[loc3++] == 1 - VarFlaglistCopy[j], "Flip" + j.ToString());
}
//
for (j = 0; j < Varlist.Count; j++)
{
for (k = 0; k < Varlist.Count; k++)
{
if (k != j)
{
Vartemplist[k] = NUvar[loc3 - 1 - (Varlist.Count - 1 - k)];
}
else
{
Vartemplist[k] = VarFlaglistCopy[k];
}
}
//Vvar[loc2]=min(1-VarFlaglistCopy[0],1-VarFlaglistCopy[2],...,VarFlaglistCopy[j],1-VarFlaglistCopy[j],...)
model.AddGenConstrMin(Vvar[loc2++], Vartemplist, 1000, "FlagTransOxr1" + loc2.ToString());
}
for (j = 0; j < Varlist.Count; j++)
{
Vartemplist[j] = Vvar[loc2 - 1 - j];
}
//Since only one of Vvar[loc2 - 1],Vvar[loc2 - 2],..., is equal to 0 and the remainings are equal to 0s,
//UFvar[loc1]=max(Vvar[loc2 - 1],Vvar[loc2 - 2],...,) is equivalently to UFvar[loc1]=Vvar[loc2 - 1]+Vvar[loc2 - 2]+...+
//UFvar[loc1]is the fianl flag variable of f
model.AddGenConstrMax(UFvar[locf], Vartemplist, 0, "FlagTransXor-2" + loc2.ToString());
//NUFvar[loc4] =1-UFvar[loc1] and increase loc4 by 1
model.AddConstr(NUFvar[loc4++] == 1 - UFvar[locf], "Flip3" + loc4.ToString());
//max(u1_fv,u2_fv,u3_fv)
VarFlaglistCopy[0] = VarFlaglist[0];
VarFlaglistCopy[1] = VarFlaglist[1];
VarFlaglistCopy[2] = VarFlaglist[2];
model.AddGenConstrMax(bvar[locb++], VarFlaglistCopy, 0, "maxfv" + locb.ToString());
//NUFvar[loc4] =1-bvar[locb++] and increase loc4 by 1
model.AddConstr(NUFvar[loc4++] == 1 - bvar[locb - 1], "Flip3" + loc4.ToString());
VarFlaglistCopy2[0] = NUFvar[loc4 - 1];
VarFlaglistCopy2[1] = NUFvar[loc4 - 2];
VarFlaglistCopy2[2] = Uvar[loc1];
loc1++;
//Uvar[loc1]=min(NUFvar[loc4-1],NUFvar[loc4-2],loc1), is the assigment variable of f.
model.AddGenConstrMin(Uvar[loc1], VarFlaglistCopy2, 1000, "min_av" + loc1.ToString());
Tar.AddTerm(1.0, Uvar[loc1]);
Tar.AddTerm(-10000, UFvar[locf]);
rec_loc1[i] = loc1;
rec_locf[i] = locf;
loc1++;
locf++;
}
//assuming f=u1+u2+u3+u4+c
if (Varlist.Count == 4)
{
List <GRBVar> templist = new List <GRBVar>()
{
};
GRBVar[] VarFlaglistCopy = new GRBVar[5];
GRBVar[] VarFlaglistCopy2 = new GRBVar[5];
GRBVar[] Vartemplist = new GRBVar[5];
for (j = 0; j < Varlist.Count(); j++)
{
VarFlaglistCopy[j] = VarFlaglist[j];
}
templist.Add(Varlist[0]);
templist.Add(Varlist[1]);
templist.Add(Uvar[loc1]);
AddCons2Vars(model, templist);
templist.Clear();
loc1++;
templist.Add(Varlist[2]);
templist.Add(Varlist[3]);
templist.Add(Uvar[loc1]);
AddCons2Vars(model, templist);
templist.Clear();
loc1++;
templist.Add(Uvar[loc1 - 2]);
templist.Add(Uvar[loc1 - 1]);
templist.Add(Uvar[loc1]);
AddCons2Vars(model, templist);
//if c==1
if (consflag[i] == 1)
{
model.AddConstr(Consvar[loc0++] == 1, "Flip" + j.ToString());
VarlistCopy[0] = Uvar[loc1];
VarlistCopy[1] = Consvar[loc0 - 1];
VarlistCopy[2] = Uvar[loc1 + 1];
loc1++;
AddCons2Vars(model, VarlistCopy);
}
for (j = 0; j < Varlist.Count; j++)
{
model.AddConstr(NUvar[loc3++] == 1 - VarFlaglistCopy[j], "Flip" + j.ToString());
}
for (j = 0; j < Varlist.Count; j++)
{
for (k = 0; k < Varlist.Count; k++)
{
if (k != j)
{
Vartemplist[k] = NUvar[loc3 - 1 - (Varlist.Count - 1 - k)];
}
else
{
Vartemplist[k] = VarFlaglistCopy[k];
}
}
model.AddGenConstrMin(Vvar[loc2++], Vartemplist, 1000, "FlagTransOxr1" + loc2.ToString());
}
for (j = 0; j < Varlist.Count; j++)
{
Vartemplist[j] = Vvar[loc2 - 1 - j];
}
model.AddGenConstrMax(UFvar[locf], Vartemplist, 0, "FlagTransXor-2" + loc2.ToString());
//NUFvar[loc4] =1-UFvar[loc1] and increase loc4 by 1
model.AddConstr(NUFvar[loc4] == 1 - UFvar[locf], "Flip3" + loc4.ToString());
loc4++;
//max(u1_fv,u2_fv,u3_fv,u4_fv)
VarFlaglistCopy[0] = VarFlaglist[0];
VarFlaglistCopy[1] = VarFlaglist[1];
VarFlaglistCopy[2] = VarFlaglist[2];
VarFlaglistCopy[3] = VarFlaglist[3];
model.AddGenConstrMax(bvar[locb++], VarFlaglistCopy, 0, "maxfv" + locb.ToString());
//NUFvar[loc4] =1-bvar[locb++] and increase loc4 by 1
model.AddConstr(NUFvar[loc4] == 1 - bvar[locb - 1], "Flip4" + loc4.ToString());
loc4++;
//VarFlaglistCopy.Initialize();
VarFlaglistCopy2[0] = NUFvar[loc4 - 1];
VarFlaglistCopy2[1] = NUFvar[loc4 - 2];
VarFlaglistCopy2[2] = Uvar[loc1];
loc1++;
//Uvar[loc1]=min(NUFvar[loc4-1],NUFvar[loc4-2],loc1), is the assigment variable of f.
model.AddGenConstrMin(Uvar[loc1], VarFlaglistCopy2, 1000, "min_av" + loc1.ToString());
//Tar=Tar+assigment variable +(-10000)*flag variable
Tar.AddTerm(1.0, Uvar[loc1]);
Tar.AddTerm(-10000, UFvar[locf]);
rec_loc1[i] = loc1;
rec_locf[i] = locf;
loc1++;
locf++;
}
//assuming f=u1+u2+u3+u4+u5+c
if (Varlist.Count == 5)
{
List <GRBVar> templist = new List <GRBVar>()
{
};
GRBVar[] VarFlaglistCopy = new GRBVar[6];
GRBVar[] VarFlaglistCopy2 = new GRBVar[6];
GRBVar[] Vartemplist = new GRBVar[6];
for (j = 0; j < Varlist.Count(); j++)
{
VarFlaglistCopy[j] = VarFlaglist[j];
}
templist.Add(Varlist[0]);
templist.Add(Varlist[1]);
templist.Add(Uvar[loc1]);
AddCons2Vars(model, templist);
templist.Clear();
loc1++;
templist.Add(Varlist[2]);
templist.Add(Varlist[3]);
templist.Add(Varlist[4]);
templist.Add(Uvar[loc1]);
AddCons3Vars(model, templist);
templist.Clear();
loc1++;
templist.Add(Uvar[loc1 - 2]);
templist.Add(Uvar[loc1 - 1]);
templist.Add(Uvar[loc1]);
AddCons2Vars(model, templist);
if (consflag[i] == 1)
{
model.AddConstr(Consvar[loc0++] == 1, "Flip" + j.ToString());
VarlistCopy[0] = Uvar[loc1];
VarlistCopy[1] = Consvar[loc0 - 1];
VarlistCopy[2] = Uvar[loc1 + 1];
loc1++;
AddCons2Vars(model, VarlistCopy);
}
for (j = 0; j < Varlist.Count; j++)
{
model.AddConstr(NUvar[loc3++] == 1 - VarFlaglistCopy[j], "Flip" + j.ToString());
}
//flip and calculate Tj
for (j = 0; j < Varlist.Count; j++)
{
for (k = 0; k < Varlist.Count; k++)
{
if (k != j)
{
Vartemplist[k] = NUvar[loc3 - 1 - (Varlist.Count - 1 - k)];
}
else
{
Vartemplist[k] = VarFlaglistCopy[k];
}
}
model.AddGenConstrMin(Vvar[loc2++], Vartemplist, 1000, "FlagTransOxr1" + loc2.ToString());
}
//
for (j = 0; j < Varlist.Count; j++)
{
Vartemplist[j] = Vvar[loc2 - 1 - j];
}
model.AddGenConstrMax(UFvar[locf], Vartemplist, 0, "FlagTransXor-2" + loc2.ToString());
//NUFvar[loc4] =1-UFvar[loc1] and increase loc4 by 1
model.AddConstr(NUFvar[loc4++] == 1 - UFvar[locf], "Flip3" + loc4.ToString());
//max(u1_fv,u2_fv,u3_fv,u4_fv,u5_fv)
VarFlaglistCopy[0] = VarFlaglist[0];
VarFlaglistCopy[1] = VarFlaglist[1];
VarFlaglistCopy[2] = VarFlaglist[2];
VarFlaglistCopy[3] = VarFlaglist[3];
VarFlaglistCopy[4] = VarFlaglist[4];
model.AddGenConstrMax(bvar[locb++], VarFlaglistCopy, 0, "maxfv" + locb.ToString());
//NUFvar[loc4] =1-bvar[locb++] and increase loc4 by 1
model.AddConstr(NUFvar[loc4++] == 1 - bvar[locb - 1], "Flip4" + loc4.ToString());
VarFlaglistCopy2[0] = NUFvar[loc4 - 1];
VarFlaglistCopy2[1] = NUFvar[loc4 - 2];
VarFlaglistCopy2[2] = Uvar[loc1];
loc1++;
//Uvar[loc1]=min(NUFvar[loc4-1],NUFvar[loc4-2],loc1), is the assigment variable of f.
model.AddGenConstrMin(Uvar[loc1], VarFlaglistCopy2, 1000, "min_av" + loc1.ToString());
Tar.AddTerm(1.0, Uvar[loc1]);
Tar.AddTerm(-10000, UFvar[locf]);
rec_loc1[i] = loc1;
rec_locf[i] = locf;
loc1++;
locf++;
}
//Console.WriteLine("5: " +loc1);
//assuming that f=u1+u2+u3+u4+u5...+um+c, where m>5.
if (Varlist.Count > 5)
{
int length;
length = Varlist.Count;
List <GRBVar> curvarlist = new List <GRBVar>()
{
};
GRBVar[] VarFlaglistCopy = new GRBVar[Varlist.Count + 1];
GRBVar[] VarFlaglistCopy2 = new GRBVar[Varlist.Count + 1];
GRBVar[] Vartemplist = new GRBVar[Varlist.Count + 1];
for (j = 0; j < Varlist.Count; j++)
{
curvarlist.Add(Varlist[j]);
VarFlaglistCopy[j] = VarFlaglist[j];
}
//model f=u1+u2+...+un. The method used here is a slight differnt from that presented in the paper.
//The method used here is more convenient for coding.
while (length > 3)
{
List <GRBVar> nextvarlist = new List <GRBVar>()
{
};
List <GRBVar> templist = new List <GRBVar>()
{
};
//
templist.Add(curvarlist[0]);
templist.Add(curvarlist[1]);
templist.Add(curvarlist[2]);
templist.Add(Uvar[loc1]);
AddCons3Vars(model, templist);
for (j = 3; j < curvarlist.Count; j++)
{
nextvarlist.Add(curvarlist[j]);
}
nextvarlist.Add(Uvar[loc1]);
curvarlist.Clear();
for (j = 0; j < nextvarlist.Count; j++)
{
curvarlist.Add(nextvarlist[j]);
}
length = curvarlist.Count;
loc1++;
}
if (length == 2)
{
curvarlist.Add(Uvar[loc1]);
AddCons2Vars(model, curvarlist);
//if c==1, then we need xor one more constant
if (consflag[i] == 1)
{
model.AddConstr(Consvar[loc0++] == 1, "Flip" + j.ToString());
VarlistCopy[0] = Uvar[loc1];
VarlistCopy[1] = Consvar[loc0 - 1];
VarlistCopy[2] = Uvar[loc1 + 1];
loc1++;
AddCons2Vars(model, VarlistCopy);
}
}
if (length == 3)
{
curvarlist.Add(Uvar[loc1]);
AddCons3Vars(model, curvarlist);
//if c==1, then we need xor one more constant
if (consflag[i] == 1)
{
model.AddConstr(Consvar[loc0++] == 1, "Flip" + j.ToString());
VarlistCopy[0] = Uvar[loc1];
VarlistCopy[1] = Consvar[loc0 - 1];
VarlistCopy[2] = Uvar[loc1 + 1];
loc1++;
AddCons2Vars(model, VarlistCopy);
}
}
for (j = 0; j < Varlist.Count; j++)
{
model.AddConstr(NUvar[loc3++] == 1 - VarFlaglistCopy[j], "Flip" + j.ToString());
}
for (j = 0; j < Varlist.Count; j++)
{
for (k = 0; k < Varlist.Count; k++)
{
if (k != j)
{
Vartemplist[k] = NUvar[loc3 - 1 - (Varlist.Count - 1 - k)];
}
else
{
Vartemplist[k] = VarFlaglistCopy[k];
}
}
model.AddGenConstrMin(Vvar[loc2++], Vartemplist, 1000, "FlagTransOxr1" + loc2.ToString());
}
for (j = 0; j < Varlist.Count; j++)
{
Vartemplist[j] = Vvar[loc2 - 1 - j];
}
model.AddGenConstrMax(UFvar[locf], Vartemplist, 0, "FlagTransXor-2" + loc2.ToString());
//NUFvar[loc4] =1-UFvar[loc1] and increase loc4 by 1
model.AddConstr(NUFvar[loc4++] == 1 - UFvar[locf], "Flip3" + loc4.ToString());
//bvar[locb]=max(u1_fv,u2_fv,u3_fv,u4_fv,...,un_fv) and increase locb by 1
for (j = 0; j < VarFlaglist.Count; j++)
{
VarFlaglistCopy[j] = VarFlaglist[j];
}
model.AddGenConstrMax(bvar[locb++], VarFlaglistCopy, 0, "maxfv" + locb.ToString());
//NUFvar[loc4] =1-bvar[locb++] and increase loc4 by 1
model.AddConstr(NUFvar[loc4++] == 1 - bvar[locb - 1], "Flip4" + loc4.ToString());
VarFlaglistCopy2[0] = NUFvar[loc4 - 1];
VarFlaglistCopy2[1] = NUFvar[loc4 - 2];
VarFlaglistCopy2[2] = Uvar[loc1];
loc1++;
//Uvar[loc1]=min(NUFvar[loc4-1],NUFvar[loc4-2],loc1), is the assigment variable of f.
model.AddGenConstrMin(Uvar[loc1], VarFlaglistCopy2, 1000, "min_av" + loc1.ToString());
Tar.AddTerm(1.0, Uvar[loc1]);
Tar.AddTerm(-10000, UFvar[locf]);
rec_loc1[i] = loc1;
rec_locf[i] = locf;
loc1++;
locf++;
}
}
//
GRBLinExpr keyspace = new GRBLinExpr();
for (i = 0; i < 80; i++)
{
keyspace.AddTerm(1.0, kvf[i]);
}
Tar.AddConstant((double)con);
//Add the condition that Tar>=0. It gurantees that there is not any condition whose flag variable is equal to 1.
model.AddConstr(Tar == 3, "finalcons");
model.SetObjective(keyspace, GRB.MAXIMIZE);
//Set the objective function of the model.
//model.SetObjective(Tar, GRB.MINIMIZE);
model.Optimize();
//output the states of key variables and iv variables
if (model.SolCount > 0)
{
sw.WriteLine("****************************Conditions on single key/iv variables***************************\n");
Console.Write("Free Key bits:\n");
sw.Write("Free Key bits:\n");
for (i = 0; i < 80; i++)
{
if ((keyvar[i].X == 0) && (kvf[i].X == 1))
{
Console.Write(i + ",");
sw.Write(i + ",");
}
}
Console.WriteLine();
sw.WriteLine();
Console.Write("Key bits set to 1:\n");
sw.Write("Key bits set to 1:\n");
for (i = 0; i < 80; i++)
{
if ((keyvar[i].X == 1) && (kvf[i].X == 0))
{
Console.Write(i + ",");
sw.Write(i + ",");
}
}
Console.WriteLine();
sw.WriteLine();
Console.Write("Key bits set 0:\n");
sw.Write("Key bits set 0:\n");
for (i = 0; i < 80; i++)
{
if ((keyvar[i].X == 0) && (kvf[i].X == 0))
{
Console.Write(i + ",");
sw.Write(i + ",");
}
}
Console.WriteLine();
sw.WriteLine();
//for (i = 0; i < loc2; i++)
//{
// if (Vvar[i].X > 1)
// {
// Console.Write(Vvar[i].VarName + " " + Vvar[i].X + "\n");
// }
//}
Console.WriteLine("*******************************************************\n");
sw.WriteLine("*******************************************************\n");
Console.Write("Free Iv bits:\n");
sw.Write("Free Iv bits:\n");
for (i = 0; i < 80; i++)
{
if ((ivvar[i].X == 0) && (vvf[i].X == 1))
{
Console.Write(i + ",");
sw.Write(i + ",");
}
}
Console.WriteLine();
sw.WriteLine();
Console.Write("Iv bits set to 1:\n");
sw.Write("Iv bits set to 1:\n");
for (i = 0; i < 80; i++)
{
if ((ivvar[i].X == 1) && (vvf[i].X == 0))
{
Console.Write(i + ",");
sw.Write(i + ",");
}
}
Console.WriteLine();
sw.WriteLine();
Console.Write("Iv bits set to 0:\n");
sw.Write("Iv bits set to 0:\n");
for (i = 0; i < 80; i++)
{
if ((ivvar[i].X == 0) && (vvf[i].X == 0))
{
Console.Write(i + ",");
sw.Write(i + ",");
}
}
Console.WriteLine();
sw.WriteLine();
double aa = Tar.Value;
Console.WriteLine("*****************The number of 1's*****************");
Console.WriteLine(aa);
Console.WriteLine("***************************************************");
sw.WriteLine("***********************The assigment/flag variable of key and iv variables***********************");
for (i = 0; i < 80; i++)
{
Console.Write(keyvar[i].VarName + "= " + keyvar[i].X + " " + kvf[i].VarName + "= " + kvf[i].X + "\n");
sw.Write(keyvar[i].VarName + "= " + keyvar[i].X + " " + kvf[i].VarName + "= " + kvf[i].X + "\n");
}
Console.WriteLine("*******************************");
for (i = 0; i < 80; i++)
{
Console.Write(ivvar[i].VarName + "= " + ivvar[i].X + " " + vvf[i].VarName + "= " + vvf[i].X + "\n");
sw.Write(ivvar[i].VarName + "= " + ivvar[i].X + " " + vvf[i].VarName + "= " + vvf[i].X + "\n");
}
Console.WriteLine();
//
StreamReader rw = new StreamReader("ConSet.txt");
sw.WriteLine("***************The concrete conditions****************");
for (j = 0; j < consnum; j++)
{
string onecon = rw.ReadLine();
sw.WriteLine(onecon + "=" + Uvar[rec_loc1[j]].X);
}
sw.Close();
}
}
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);
}
}