static void Main(string[] args)
{
try
{
int n = 10;
if (args.Length > 0)
{
n = Int32.Parse(args[0]);
}
if ((n % 2) == 1)
{
n++;
}
Console.WriteLine("Finding schedule for {0} teams", n);
int nbWeeks = 2 * (n - 1);
int nbGamesPerWeek = n / 2;
int nbGames = n * (n - 1);
CP cp = new CP();
IIntVar[][] games = new IIntVar[nbWeeks][];
IIntVar[][] home = new IIntVar[nbWeeks][];
IIntVar[][] away = new IIntVar[nbWeeks][];
for (int i = 0; i < nbWeeks; i++)
{
home[i] = cp.IntVarArray(nbGamesPerWeek, 0, n - 1);
away[i] = cp.IntVarArray(nbGamesPerWeek, 0, n - 1);
games[i] = cp.IntVarArray(nbGamesPerWeek, 0, nbGames - 1);
}
//
// For each play slot, set up correspondance between game id,
// home team, and away team
//
IIntTupleSet gha = cp.IntTable(3);
int[] tuple = new int[3];
for (int i = 0; i < n; i++)
{
tuple[0] = i;
for (int j = 0; j < n; j++)
{
if (i != j)
{
tuple[1] = j;
tuple[2] = Game(i, j, n);
cp.AddTuple(gha, tuple);
}
}
}
for (int i = 0; i < nbWeeks; i++)
{
for (int j = 0; j < nbGamesPerWeek; j++)
{
IIntVar[] vars = cp.IntVarArray(3);
vars[0] = home[i][j];
vars[1] = away[i][j];
vars[2] = games[i][j];
cp.Add(cp.AllowedAssignments(vars, gha));
}
}
//
// All teams play each week
//
for (int i = 0; i < nbWeeks; i++)
{
IIntVar[] teamsThisWeek = cp.IntVarArray(n);
for (int j = 0; j < nbGamesPerWeek; j++)
{
teamsThisWeek[j] = home[i][j];
teamsThisWeek[nbGamesPerWeek + j] = away[i][j];
}
cp.Add(cp.AllDiff(teamsThisWeek));
}
//
// Dual representation: for each game id, the play slot is maintained
//
IIntVar[] weekOfGame = cp.IntVarArray(nbGames, 0, nbWeeks - 1);
IIntVar[] allGames = cp.IntVarArray(nbGames);
IIntVar[] allSlots = cp.IntVarArray(nbGames, 0, nbGames - 1);
for (int i = 0; i < nbWeeks; i++)
{
for (int j = 0; j < nbGamesPerWeek; j++)
{
allGames[i * nbGamesPerWeek + j] = games[i][j];
}
}
cp.Add(cp.Inverse(allGames, allSlots));
for (int i = 0; i < nbGames; i++)
{
cp.Add(cp.Eq(weekOfGame[i], cp.Div(allSlots[i], nbGamesPerWeek)));
}
//
// Two half schedules. Cannot play the same pair twice in the same half.
// Plus, impose a minimum number of weeks between two games involving
// the same teams (up to six weeks)
//
int mid = nbWeeks / 2;
int overlap = 0;
if (n >= 6)
{
overlap = min(n / 2, 6);
}
for (int i = 0; i < n; i++)
{
for (int j = i + 1; j < n; j++)
{
int g1 = Game(i, j, n);
int g2 = Game(j, i, n);
cp.Add(cp.Equiv(cp.Ge(weekOfGame[g1], mid), cp.Lt(weekOfGame[g2], mid)));
// Six week difference...
if (overlap != 0)
{
cp.Add(cp.Ge(cp.Abs(cp.Diff(weekOfGame[g1], weekOfGame[g2])), overlap));
}
}
}
//
// Can't have three homes or three aways in a row.
//
IIntVar[][] playHome = new IIntVar[n][];
for (int i = 0; i < n; i++)
{
playHome[i] = cp.IntVarArray(nbWeeks, 0, 1);
for (int j = 0; j < nbWeeks; j++)
{
cp.Add(cp.Eq(playHome[i][j], cp.Count(home[j], i)));
}
for (int j = 0; j < nbWeeks - 3; j++)
{
IIntVar[] window = cp.IntVarArray(3);
for (int k = j; k < j + 3; k++)
{
window[k - j] = playHome[i][k];
}
IIntExpr windowSum = cp.Sum(window);
cp.Add(cp.Le(1, windowSum));
cp.Add(cp.Le(windowSum, 2));
}
}
//
// If we start the season home, we finish away and vice versa.
//
for (int i = 0; i < n; i++)
{
cp.Add(cp.Neq(playHome[i][0], playHome[i][nbWeeks - 1]));
}
//
// Objective: minimize the number of `breaks'. A break is
// two consecutive home or away matches for a
// particular team
IIntVar[] teamBreaks = cp.IntVarArray(n, 0, nbWeeks / 2);
for (int i = 0; i < n; i++)
{
IIntExpr nbreaks = cp.Constant(0);
for (int j = 1; j < nbWeeks; j++)
{
nbreaks = cp.Sum(nbreaks, cp.IntExpr(cp.Eq(playHome[i][j - 1], playHome[i][j])));
}
cp.Add(cp.Eq(teamBreaks[i], nbreaks));
}
IIntVar breaks = cp.IntVar(n - 2, n * (nbWeeks / 2));
cp.Add(cp.Eq(breaks, cp.Sum(teamBreaks)));
cp.Add(cp.Minimize(breaks));
//
// Catalyzing constraints
//
// Each team plays home the same number of times as away
for (int i = 0; i < n; i++)
{
cp.Add(cp.Eq(cp.Sum(playHome[i]), nbWeeks / 2));
}
// Breaks must be even for each team
for (int i = 0; i < n; i++)
{
cp.Add(cp.Eq(cp.Modulo(teamBreaks[i], 2), 0));
}
//
// Symmetry breaking constraints
//
// Teams are interchangeable. Fix first week.
// Also breaks reflection symmetry of the whole schedule.
for (int i = 0; i < nbGamesPerWeek; i++)
{
cp.Add(cp.Eq(home[0][i], i * 2));
cp.Add(cp.Eq(away[0][i], i * 2 + 1));
}
// Order of games in each week is arbitrary.
// Break symmetry by forcing an order.
for (int i = 0; i < nbWeeks; i++)
{
for (int j = 1; j < nbGamesPerWeek; j++)
{
cp.Add(cp.Gt(games[i][j], games[i][j - 1]));
}
}
cp.SetParameter(CP.DoubleParam.TimeLimit, 20);
cp.SetParameter(CP.IntParam.LogPeriod, 10000);
IVarSelector varSel = cp.SelectSmallest(cp.VarIndex(allGames));;
IValueSelector valSel = cp.SelectRandomValue();
ISearchPhase phase = cp.SearchPhase(allGames,
cp.IntVarChooser(varSel),
cp.IntValueChooser(valSel));
cp.SetSearchPhases(phase);
cp.StartNewSearch();
while (cp.Next())
{
Console.WriteLine("Solution at {0}", cp.GetValue(breaks));
}
cp.EndSearch();
}
catch (ILOG.Concert.Exception e)
{
Console.WriteLine("Error {0}", e);
}
}
static void Main(string[] args)
{
CP cp = new CP();
coaching = new int[nbPersons];
int i;
for (i = 0; i < nbPersons; i++)
{
coaching[i] = -1;
}
for (i = 0; i < 12; i = i + 2) // the 12 first of Service A are couples of coached/coach
{
coaching[i] = i + 1;
coaching[i + 1] = i;
}
for (i = 20; i < 32; i = i + 2)// the 12 first of Service B are couples of coached/coach
{
coaching[i] = i + 1;
coaching[i + 1] = i;
}
for (i = 40; i < nbPersons; i += 5) // the 4 first of Services C,D,E,F are couples of coached/coach
{
coaching[i] = i + 1;
coaching[i + 1] = i;
coaching[i + 2] = i + 3;
coaching[i + 3] = i + 2;
}
//compute the possible solutions of a team
IIntTupleSet tupleSet = MakeTeamTuples(cp);
// groups[i] represents the ordered set of people in the team i
IIntVar[][] groups = new IIntVar[nbTeams][];
for (i = 0; i < nbTeams; i++)
{
groups[i] = cp.IntVarArray(teamSize, 0, nbPersons - 1);
cp.Add(cp.AllowedAssignments(groups[i], tupleSet));
}
IIntVar[] allVars = cp.IntVarArray(nbPersons);
int s = 0;
int w;
int p;
for (w = 0; w < nbTeams; ++w)
{
for (p = 0; p < teamSize; ++p)
{
allVars[s] = groups[w][p];
++s;
}
}
cp.Add(cp.AllDiff(allVars));
// team[i] represents the number of the team of people number i
IIntVar[] team = cp.IntVarArray(nbPersons, 0, nbTeams);
for (w = 0; w < nbTeams; ++w)
{
for (p = 0; p < teamSize; ++p)
{
cp.Add(cp.Eq(cp.Element(team, groups[w][p]), w));
}
}
// Additional constraints
// to improve efficiency we could force the following
// first three constraints directly in MakeTeamTuples but the fourth
// constraint cannot be expressed as a restriction of
// the tuple set, since it is not local to a tuple
cp.Add(cp.Or(cp.Eq(team[5], team[41]), cp.Eq(team[5], team[51])));
cp.Add(cp.Or(cp.Eq(team[15], team[40]), cp.Eq(team[15], team[51])));
cp.Add(cp.Or(cp.Eq(team[25], team[40]), cp.Eq(team[25], team[50])));
cp.Add(cp.Or(cp.Eq(team[20], team[24]), cp.Eq(team[22], team[50])));
//break symmetry: the teams are ordered according to the smallest in each team
for (i = 0; i < nbTeams - 1; i++)
{
cp.Add(cp.Lt(groups[i][0], groups[i + 1][0]));
}
cp.SetParameter(CP.IntParam.AllDiffInferenceLevel,
CP.ParameterValues.Extended);
if (cp.Solve())
{
Console.WriteLine();
Console.WriteLine("SOLUTION");
for (p = 0; p < nbTeams; ++p)
{
Console.Write("team " + p + " : ");
for (w = 0; w < teamSize; ++w)
{
Console.Write((int)cp.GetValue(groups[p][w]) + " ");
}
Console.WriteLine();
}
}
else
{
Console.WriteLine("**** NO SOLUTION ****");
}
}
/*
* MakeTeamTuples return a IIntTupleSet containing all the possible configurations of a team.
* The team members in a tuple are ordered to break symmetry.
*/
public static IIntTupleSet MakeTeamTuples(CP mainCP)
{
CP cp = new CP();
int i;
int[] newEmployee = new int[nbPersons];
int[] service = new int[nbPersons];
for (i = 0; i < nbPersons; i++)
{
if ((i % 2) == 0)
{
newEmployee[i] = 1;
}
else
{
newEmployee[i] = 0;
}
if (i < 20)
{
service[i] = 0;
}
else if (i < 40)
{
service[i] = 1;
}
else if (i < 45)
{
service[i] = 2;
}
else if (i < 50)
{
service[i] = 3;
}
else if (i < 55)
{
service[i] = 4;
}
else
{
service[i] = 5;
}
}
IIntTupleSet ts = mainCP.IntTable(teamSize);
IIntVar[] teamMembers = cp.IntVarArray(teamSize, 0, nbPersons - 1);
//number of new employees among the teamMembers = number of teamMembers / 2
IIntExpr nbNewEmployees = cp.Constant(0);
for (i = 0; i < teamSize; i++)
{
nbNewEmployees = cp.Sum(nbNewEmployees, cp.Element(newEmployee, teamMembers[i]));
}
cp.Add(cp.Eq(nbNewEmployees, teamSize / 2));
//a new employee and his coach must be in the same team
for (i = 0; i < 60; i += 2)
{
if (coaching[i] >= 0)
{
cp.Add(cp.Eq(cp.Count(teamMembers, i), cp.Count(teamMembers, coaching[i])));
}
}
IIntVar[] serviceVar = cp.IntVarArray(teamSize, 0, numServices - 1);
for (i = 0; i < teamSize; i++)
{
cp.Add(cp.Eq(serviceVar[i], cp.Element(service, teamMembers[i])));
}
// at most 4 people of the same service
for (i = 0; i < numServices; i++)
{
cp.Add(cp.Le(cp.Count(serviceVar, i), 4));
}
//Persons of Services A and B cannot be in the same team
//Persons of Services E and F cannot be in the same team
cp.Add(cp.Or(cp.Eq(cp.Count(serviceVar, 0), 0), cp.Eq(cp.Count(serviceVar, 1), 0)));
cp.Add(cp.Or(cp.Eq(cp.Count(serviceVar, 4), 0), cp.Eq(cp.Count(serviceVar, 5), 0)));
// order the teamMembers to break symmetry
for (i = 0; i < teamSize - 1; i++)
{
cp.Add(cp.Lt(teamMembers[i], teamMembers[i + 1]));
}
int[] tuple = new int[teamSize];
cp.SetParameter(CP.IntParam.LogVerbosity,
CP.ParameterValues.Quiet);
cp.SetParameter(CP.IntParam.SearchType,
CP.ParameterValues.DepthFirst);
cp.StartNewSearch();
while (cp.Next())
{
for (i = 0; i < teamSize; i++)
{
tuple[i] = (int)cp.GetValue(teamMembers[i]);
}
cp.AddTuple(ts, tuple);
}
return(ts);
}
static public void Main(string[] args)
{
CP cp = new CP();
int nbTruckConfigs = 7; // number of possible configurations for the truck
int nbOrders = 21;
int nbCustomers = 3;
int nbTrucks = 15; //max number of travels of the truck
int[] maxTruckConfigLoad = //Capacity of the truck depends on its config
{
11, 11, 11, 11, 10, 10, 10
};
int maxLoad = Max(maxTruckConfigLoad);
int[] customerOfOrder =
{
0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
1, 1, 1, 1, 1, 2, 2, 2, 2, 2,
2
};
int[] volumes =
{
3, 4, 3, 2, 5, 4, 11, 4, 5, 2,
4, 7, 3, 5, 2, 5, 6, 11, 1, 6,
3
};
int[] colors =
{
1, 2, 0, 1, 1, 1, 0, 0, 0, 0,
2, 2, 2, 0, 2, 1, 0, 2, 0, 0,
0
};
int[] truckCost = //cost for loading a truck of a given config
{
2, 2, 2, 3, 3, 3, 4
};
//Decision variables
IIntVar[] truckConfigs = cp.IntVarArray(nbTrucks, 0, nbTruckConfigs - 1); //configuration of the truck
IIntVar[] where = cp.IntVarArray(nbOrders, 0, nbTrucks - 1); //In which truck is an order
IIntVar[] load = cp.IntVarArray(nbTrucks, 0, maxLoad); //load of a truck
IIntVar numUsed = cp.IntVar(0, nbTrucks); // number of trucks used
IIntVar[] customerOfTruck = cp.IntVarArray(nbTrucks, 0, nbCustomers);
// transition costs between trucks
IIntTupleSet costTuples = cp.IntTable(3);
cp.AddTuple(costTuples, new int[] { 0, 0, 0 });
cp.AddTuple(costTuples, new int[] { 0, 1, 0 });
cp.AddTuple(costTuples, new int[] { 0, 2, 0 });
cp.AddTuple(costTuples, new int[] { 0, 3, 10 });
cp.AddTuple(costTuples, new int[] { 0, 4, 10 });
cp.AddTuple(costTuples, new int[] { 0, 5, 10 });
cp.AddTuple(costTuples, new int[] { 0, 6, 15 });
cp.AddTuple(costTuples, new int[] { 1, 0, 0 });
cp.AddTuple(costTuples, new int[] { 1, 1, 0 });
cp.AddTuple(costTuples, new int[] { 1, 2, 0 });
cp.AddTuple(costTuples, new int[] { 1, 3, 10 });
cp.AddTuple(costTuples, new int[] { 1, 4, 10 });
cp.AddTuple(costTuples, new int[] { 1, 5, 10 });
cp.AddTuple(costTuples, new int[] { 1, 6, 15 });
cp.AddTuple(costTuples, new int[] { 2, 0, 0 });
cp.AddTuple(costTuples, new int[] { 2, 1, 0 });
cp.AddTuple(costTuples, new int[] { 2, 2, 0 });
cp.AddTuple(costTuples, new int[] { 2, 3, 10 });
cp.AddTuple(costTuples, new int[] { 2, 4, 10 });
cp.AddTuple(costTuples, new int[] { 2, 5, 10 });
cp.AddTuple(costTuples, new int[] { 2, 6, 15 });
cp.AddTuple(costTuples, new int[] { 3, 0, 3 });
cp.AddTuple(costTuples, new int[] { 3, 1, 3 });
cp.AddTuple(costTuples, new int[] { 3, 2, 3 });
cp.AddTuple(costTuples, new int[] { 3, 3, 0 });
cp.AddTuple(costTuples, new int[] { 3, 4, 10 });
cp.AddTuple(costTuples, new int[] { 3, 5, 10 });
cp.AddTuple(costTuples, new int[] { 3, 6, 15 });
cp.AddTuple(costTuples, new int[] { 4, 0, 3 });
cp.AddTuple(costTuples, new int[] { 4, 1, 3 });
cp.AddTuple(costTuples, new int[] { 4, 2, 3 });
cp.AddTuple(costTuples, new int[] { 4, 3, 10 });
cp.AddTuple(costTuples, new int[] { 4, 4, 0 });
cp.AddTuple(costTuples, new int[] { 4, 5, 10 });
cp.AddTuple(costTuples, new int[] { 4, 6, 15 });
cp.AddTuple(costTuples, new int[] { 5, 0, 3 });
cp.AddTuple(costTuples, new int[] { 5, 1, 3 });
cp.AddTuple(costTuples, new int[] { 5, 2, 3 });
cp.AddTuple(costTuples, new int[] { 5, 3, 10 });
cp.AddTuple(costTuples, new int[] { 5, 4, 10 });
cp.AddTuple(costTuples, new int[] { 5, 5, 0 });
cp.AddTuple(costTuples, new int[] { 5, 6, 15 });
cp.AddTuple(costTuples, new int[] { 6, 0, 3 });
cp.AddTuple(costTuples, new int[] { 6, 1, 3 });
cp.AddTuple(costTuples, new int[] { 6, 2, 3 });
cp.AddTuple(costTuples, new int[] { 6, 3, 10 });
cp.AddTuple(costTuples, new int[] { 6, 4, 10 });
cp.AddTuple(costTuples, new int[] { 6, 5, 10 });
cp.AddTuple(costTuples, new int[] { 6, 6, 0 });
IIntVar[] transitionCost = cp.IntVarArray(nbTrucks - 1, 0, 1000);
for (int i = 1; i < nbTrucks; i++)
{
IIntVar[] auxVars = new IIntVar[3];
auxVars[0] = truckConfigs[i - 1];
auxVars[1] = truckConfigs[i];
auxVars[2] = transitionCost[i - 1];
cp.Add(cp.AllowedAssignments(auxVars, costTuples));
}
// constrain the volume of the orders in each truck
cp.Add(cp.Pack(load, where, volumes, numUsed));
for (int i = 0; i < nbTrucks; i++)
{
cp.Add(cp.Le(load[i], cp.Element(maxTruckConfigLoad, truckConfigs[i])));
}
// compatibility between the colors of an order and the configuration of its truck
int[][] allowedContainerConfigs = new int[3][];
allowedContainerConfigs[0] = new int[] { 0, 3, 4, 6 };
allowedContainerConfigs[1] = new int[] { 1, 3, 5, 6 };
allowedContainerConfigs[2] = new int[] { 2, 4, 5, 6 };
for (int j = 0; j < nbOrders; j++)
{
IIntVar configOfContainer = cp.IntVar(allowedContainerConfigs[colors[j]]);
cp.Add(cp.Eq(configOfContainer, cp.Element(truckConfigs, where[j])));
}
// only one customer per truck
for (int j = 0; j < nbOrders; j++)
{
cp.Add(cp.Eq(cp.Element(customerOfTruck, where[j]), customerOfOrder[j]));
}
// non used trucks are at the end
for (int j = 1; j < nbTrucks; j++)
{
cp.Add(cp.Or(cp.Gt(load[j - 1], 0), cp.Eq(load[j], 0)));
}
// Dominance: the non used trucks keep the last used configuration
cp.Add(cp.Gt(load[0], 0));
for (int i = 1; i < nbTrucks; i++)
{
cp.Add(cp.Or(cp.Gt(load[i], 0), cp.Eq(truckConfigs[i], truckConfigs[i - 1])));
}
//Dominance: regroup deliveries with same configuration
for (int i = nbTrucks - 2; i > 0; i--)
{
IConstraint Ct = cp.TrueConstraint();
for (int p = i + 1; p < nbTrucks; p++)
{
Ct = cp.And(cp.Neq(truckConfigs[p], truckConfigs[i - 1]), Ct);
}
cp.Add(cp.Or(cp.Eq(truckConfigs[i], truckConfigs[i - 1]), Ct));
}
// Objective: first criterion for minimizing the cost for configuring and loading trucks
// second criterion for minimizing the number of trucks
IIntExpr obj1 = cp.Constant(0);
for (int i = 0; i < nbTrucks; i++)
{
obj1 = cp.Sum(obj1, cp.Prod(cp.Element(truckCost, truckConfigs[i]), cp.Neq(load[i], 0)));
}
obj1 = cp.Sum(obj1, cp.Sum(transitionCost));
IIntExpr obj2 = numUsed;
// Multicriteria lexicographic optimization
cp.Add(cp.Minimize(cp.StaticLex(obj1, obj2)));
cp.SetParameter(CP.DoubleParam.TimeLimit, 20);
cp.SetParameter(CP.IntParam.LogPeriod, 50000);
cp.Solve();
double[] obj = cp.GetObjValues();
Console.WriteLine("Configuration cost: " + (int)obj[0] +
" Number of Trucks: " + (int)obj[1]);
for (int i = 0; i < nbTrucks; i++)
{
if (cp.GetValue(load[i]) > 0)
{
Console.Write("Truck " + i +
": Config=" + cp.GetIntValue(truckConfigs[i])
+ " Items= ");
for (int j = 0; j < nbOrders; j++)
{
if (cp.GetValue(where[j]) == i)
{
Console.Write("<" + j + "," + colors[j] + "," + volumes[j] + "> ");
}
}
Console.WriteLine();
}
}
}
