private static void rationalityConstrPlayer2(State s, Func <State, Action, Action, double> getQ, Dictionary <Tuple <Action, Action>, Decision> actDecisions, Model model, string constPrefix)
{
var rotList = new Queue <Action>();
foreach (Action action in Enum.GetValues(typeof(Action)))
{
rotList.Enqueue(action);
}
var cons_cnt = 0;
for (var i = 0; i < Enum.GetValues(typeof(Action)).Length; ++i)
{
var constRowSum = new SumTermBuilder(5);
var isConstrow = true;
Action contextAction = Action.N;
foreach (Action player2Action in rotList)
{
var otherRowSum = new SumTermBuilder(5);
if (isConstrow)
{
contextAction = player2Action;
}
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
var policy = getActDecision(currentAction, contextAction, actDecisions);
if (isConstrow)
{
var qValue = getQ(s, currentAction, player2Action);
constRowSum.Add(policy * qValue);
}
else
{
var qValue = getQ(s, currentAction, player2Action);
otherRowSum.Add(policy * qValue);
}
}
if (!isConstrow)
{
model.AddConstraint(constPrefix + "const" + cons_cnt, constRowSum.ToTerm() >= otherRowSum.ToTerm());
cons_cnt++;
}
isConstrow = false;
}
//Rotate list
var elementToRotate = rotList.Dequeue();
rotList.Enqueue(elementToRotate);
}
}
public static Tuple <double, List <double> > PlayerBStrategy(List <List <int> > matrix)
{
SolverContext context = SolverContext.GetContext();
context.ClearModel();
Model model = context.CreateModel();
List <Decision> decicionList = new List <Decision>();
for (int j = 0; j < matrix[0].Count; j++)
{
decicionList.Add(new Decision(Domain.RealNonnegative, "B" + j));
}
foreach (var decision in decicionList)
{
model.AddDecision(decision);
}
for (int i = 0; i < matrix.Count; i++)
{
SumTermBuilder rowSum = new SumTermBuilder(decicionList.Count);
for (int j = 0; j < decicionList.Count; j++)
{
rowSum.Add(decicionList[j] * matrix[i][j]);
}
model.AddConstraint("con" + i, rowSum.ToTerm() <= 1);
}
SumTermBuilder decisionSum = new SumTermBuilder(decicionList.Count);
for (int j = 0; j < decicionList.Count; j++)
{
model.AddConstraint("nonneg" + j, decicionList[j] >= 0);
decisionSum.Add(decicionList[j]);
}
model.AddGoal("max", GoalKind.Maximize, decisionSum.ToTerm());
Solution solution = context.Solve(new SimplexDirective());
double gameValue = 1 / solution.Goals.First().ToDouble();
List <double> parsedDecicionList = new List <double>();
foreach (var decision in decicionList)
{
parsedDecicionList.Add(decision.ToDouble() * gameValue);
}
return(new Tuple <double, List <double> >(gameValue, parsedDecicionList));
}
private static void AddObjectiveFunctionTerms(State s, CorrelatedQTable q, Dictionary <Tuple <Action, Action>, Decision> actionDecisions, SumTermBuilder objectiveSum)
{
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action opponentAction in Enum.GetValues(typeof(Action)))
{
var pi = GetActionDecision(currentAction, opponentAction, actionDecisions);
var qValue = q.GetCurrentPlayerQValue(s, currentAction, opponentAction);
objectiveSum.Add(pi * qValue);
}
}
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action opponentAction in Enum.GetValues(typeof(Action)))
{
var pi = GetActionDecision(currentAction, opponentAction, actionDecisions);
var opponentQValue = q.GetOpponentQValue(s, currentAction, opponentAction);
objectiveSum.Add(pi * opponentQValue);
}
}
}
private static void ObjFunctermAdd(State s, CorrelatedQTable q, Dictionary <Tuple <Action, Action>, Decision> actDecisions, SumTermBuilder objectSum)
{
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action player2Action in Enum.GetValues(typeof(Action)))
{
var policy = getActDecision(currentAction, player2Action, actDecisions);
var qValue = q.getCurrPQvalue(s, currentAction, player2Action);
objectSum.Add(policy * qValue);
}
}
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action player2Action in Enum.GetValues(typeof(Action)))
{
var policy = getActDecision(currentAction, player2Action, actDecisions);
var player2Qv = q.getPlayer2Qval(s, currentAction, player2Action);
objectSum.Add(policy * player2Qv);
}
}
}
public static Tuple <double, double> GetValue(State s, CorrelatedQTable q)
{
var contxt = SolverContext.GetContext();
contxt.ClearModel();
var model = contxt.CreateModel();
var actDecisions = new Dictionary <Tuple <Action, Action>, Decision>();
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action player2Action in Enum.GetValues(typeof(Action)))
{
var decision = new Decision(Domain.RealNonnegative, currentAction.ToString() + player2Action.ToString());
model.AddDecisions(decision);
actDecisions.Add(new Tuple <Action, Action>(currentAction, player2Action), decision);
}
}
var actDecisionSum = new SumTermBuilder(25);
foreach (var decision in actDecisions.Values)
{
actDecisionSum.Add(decision);
}
model.AddConstraint("probSumConst", actDecisionSum.ToTerm() == 1.0);
rationalconsts(s, q.getCurrPQvalue, actDecisions, model, "A");
rationalityConstrPlayer2(s, q.getPlayer2Qval, actDecisions, model, "B");
var objectSum = new SumTermBuilder(10);
//Add my terms from my Q table to objective function
ObjFunctermAdd(s, q, actDecisions, objectSum);
model.AddGoal("MaximizeV", GoalKind.Maximize, objectSum.ToTerm());
var sol = contxt.Solve(new SimplexDirective());
if (sol.Quality != SolverQuality.Optimal)
{
contxt.ClearModel();
return(new Tuple <double, double>(1.0, 1.0));
}
double Player1nextVal = 0.0;
double Player2nextVal = 0.0;
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action player2Action in Enum.GetValues(typeof(Action)))
{
var policy = getActDecision(currentAction, player2Action, actDecisions);
var qValue = q.getCurrPQvalue(s, currentAction, player2Action);
Player1nextVal += policy.ToDouble() * qValue;
var player2Qv = q.getPlayer2Qval(s, currentAction, player2Action);
Player2nextVal += policy.ToDouble() * player2Qv;
}
}
return(new Tuple <double, double>(Player1nextVal, Player2nextVal));
}
public SimplexMethod(double[,] table) : this()
{
M = table.GetLength(0);
N = table.GetLength(1);
var decisionsA = new Decision[M];
ResultsA = new double[M];
for (int i = 0; i < M; i++)
{
decisionsA[i] = new Decision(Domain.RealNonnegative, $"A{i}");
}
_model.AddDecisions(decisionsA);
var decisionsB = new Decision[N];
ResultsB = new double[N];
for (int j = 0; j < N; j++)
{
decisionsB[j] = new Decision(Domain.RealNonnegative, $"B{j}");
}
_model.AddDecisions(decisionsB);
for (int j = 0; j < N; j++)
{
var sum = new SumTermBuilder(M);
for (int i = 0; i < M; i++)
{
sum.Add(decisionsA[i] * table[i, j]);
}
_model.AddConstraint($"C_A{j}", sum.ToTerm() >= 1);
}
for (int i = 0; i < M; i++)
{
var sum = new SumTermBuilder(N);
for (int j = 0; j < N; j++)
{
sum.Add(decisionsB[j] * table[i, j]);
}
_model.AddConstraint($"C_B{i}", sum.ToTerm() <= 1);
}
var summinA = new SumTermBuilder(N);
for (int i = 0; i < M; i++)
{
summinA.Add(decisionsA[i]);
}
_model.AddGoal("resA", GoalKind.Minimize, summinA.ToTerm());
var summinB = new SumTermBuilder(N);
for (int j = 0; j < N; j++)
{
summinB.Add(decisionsB[j]);
}
_model.AddGoal("resB", GoalKind.Maximize, summinB.ToTerm());
_solver.Solve();
var gpsumA = 0.0;
for (int i = 0; i < M; i++)
{
ResultsA[i] = decisionsA[i].GetDouble();
gpsumA += ResultsA[i];
}
GamePriceA = 1 / gpsumA;
var gpsumB = 0.0;
for (int j = 0; j < N; j++)
{
ResultsB[j] = decisionsB[j].GetDouble();
gpsumB += ResultsB[j];
}
GamePriceB = 1 / gpsumB;
_solver.ClearModel();
}
public static Tuple <double, double> GetValue(State s, CorrelatedQTable q)
{
var context = SolverContext.GetContext();
context.ClearModel();
var model = context.CreateModel();
var actionDecisions = new Dictionary <Tuple <Action, Action>, Decision>();
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action opponentAction in Enum.GetValues(typeof(Action)))
{
var decision = new Decision(Domain.RealNonnegative, currentAction.ToString() + opponentAction.ToString());
model.AddDecisions(decision);
actionDecisions.Add(new Tuple <Action, Action>(currentAction, opponentAction), decision);
}
}
var actionDecisionSum = new SumTermBuilder(25);
foreach (var decision in actionDecisions.Values)
{
actionDecisionSum.Add(decision);
}
model.AddConstraint("probSumConst", actionDecisionSum.ToTerm() == 1.0);
SetupRationalityConstraints(s, q.GetCurrentPlayerQValue, actionDecisions, model, "A");
SetupRationalityConstraintsOpponent(s, q.GetOpponentQValue, actionDecisions, model, "B");
var objectiveSum = new SumTermBuilder(10);
//Add my terms from my Q table to objective function
AddObjectiveFunctionTerms(s, q, actionDecisions, objectiveSum);
model.AddGoal("MaximizeV", GoalKind.Maximize, objectiveSum.ToTerm());
var solution = context.Solve(new SimplexDirective());
//Console.WriteLine(solution.GetReport());
if (solution.Quality != SolverQuality.Optimal)
{
context.ClearModel();
return(new Tuple <double, double>(1.0, 1.0));
}
double currentPlayerNextValue = 0.0;
double opponentNextValue = 0.0;
foreach (Action currentAction in Enum.GetValues(typeof(Action)))
{
foreach (Action opponentAction in Enum.GetValues(typeof(Action)))
{
var pi = GetActionDecision(currentAction, opponentAction, actionDecisions);
var qValue = q.GetCurrentPlayerQValue(s, currentAction, opponentAction);
currentPlayerNextValue += pi.ToDouble() * qValue;
var opponentQValue = q.GetOpponentQValue(s, currentAction, opponentAction);
opponentNextValue += pi.ToDouble() * opponentQValue;
}
}
return(new Tuple <double, double>(currentPlayerNextValue, opponentNextValue));
}
private void InitializeConstraints(Project project, int eventCount)
{
// Establish the makespan: the maximum finish time over all activities.
model.AddConstraint("c35",
Model.ForEach(events1ToN, e =>
Model.ForEach(tasks, i =>
makespan >= start[e] + (isActive[i, e] - isActive[i, e - 1]) * duration[i])
));
// model.AddConstraint("ValidDeliveryDate",
// Model.ForEach(tasks, e => start[e] + duration[e] <= entrega[e]));
// model.AddConstraint("ModelSwitchPause", Model.ForEach(events1ToN, (t) =>
// start[t] >= start[t - 1] + duration[t - 1] + Model.If(molde[t] != molde[t - 1], 1, 0)
//));
// The first event starts at time 0.
model.AddConstraint("c_36", start[0] == 0);
// Link the isActive decision to the starts of each event and task durations.
model.AddConstraint("c_37",
Model.ForEach(events1ToN, e =>
Model.ForEachWhere(events, f =>
Model.ForEach(tasks, i =>
start[f] >= start[e] + ((isActive[i, e] - isActive[i, e - 1]) - (isActive[i, f] - isActive[i, f - 1]) - 1) * duration[i]
), f => f > e)));
// Link the isActive decision with the first event. This constraint is missing in the original
// paper.
model.AddConstraint("c_37_e0",
Model.ForEach(events1ToN, f =>
Model.ForEach(tasks, i =>
start[f] >= start[0] + (isActive[i, 0] - (isActive[i, f] - isActive[i, f - 1]) - 1) * duration[i]
)));
// Order the events.
model.AddConstraint("c_38", Model.ForEach(events1ToN, e => start[e] >= start[e - 1]));
// Ensure adjacency of events for an in-progress task.
SumTermBuilder sum = new SumTermBuilder(eventCount);
for (int i = 0; i < project.Tasks.Count; i++)
{
for (int e = 1; e < eventCount; e++)
{
sum.Add(isActive[i, e - 1]);
model.AddConstraint("c_39_" + i + "_" + e,
sum.ToTerm() <= e * (1 - (isActive[i, e] - isActive[i, e - 1])));
}
sum.Clear();
}
sum = new SumTermBuilder(eventCount);
for (int i = 0; i < project.Tasks.Count; i++)
{
for (int e = 1; e < eventCount; e++)
{
for (int e1 = e; e1 < eventCount; e1++)
{
sum.Add(isActive[i, e1]); // (it's inefficient to reconstruct this for each value of e.)
}
model.AddConstraint("c_40_" + i + "_" + e,
sum.ToTerm() <= e * (1 + (isActive[i, e] - isActive[i, e - 1])));
sum.Clear();
}
}
// All activities must be active during the project.
model.AddConstraint("c_41", Model.ForEach(tasks, i =>
Model.Sum(Model.ForEach(events, e => isActive[i, e])) >= 1));
// A link (i, j) means that the start of task j must be after the finish of task i.
int c42 = 0;
foreach (TaskDependency link in project.Dependencies)
{
int i = link.Source.ID;
int j = link.Destination.ID;
sum = new SumTermBuilder(eventCount);
for (int e = 0; e < eventCount; e++)
{
sum.Add(isActive[j, e]); // sum now has isActive[j, 0] .. isActive[j, e].
model.AddConstraint("c_42_" + c42++, isActive[i, e] + sum.ToTerm() <= 1 + e * (1 - isActive[i, e]));
}
}
// Resource usage during each event must not exceed resource capacity.
Dictionary <Resource, int> resToId = new Dictionary <Resource, int>(project.Resources.Count);
for (int k = 0; k < project.Resources.Count; k++)
{
resToId[project.Resources[k]] = k;
}
SumTermBuilder[] totalResWork = new SumTermBuilder[project.Resources.Count];
int c43 = 0;
for (int e = 0; e < eventCount; e++)
{
for (int taskID = 0; taskID < project.Tasks.Count; taskID++)
{
foreach (var assn in project.Tasks[taskID].Assignments)
{
int resID = resToId[assn.Resource];
if (totalResWork[resID] == null)
{
totalResWork[resID] = new SumTermBuilder(5); // most tasks will have <= 4 assignments.
}
totalResWork[resID].Add(assn.Units * isActive[taskID, e]);
}
}
for (int resID = 0; resID < totalResWork.Length; resID++)
{
if (totalResWork[resID] != null)
{
model.AddConstraint("c43_" + c43++, totalResWork[resID].ToTerm() <= project.Resources[resID].MaxUnits);
totalResWork[resID] = null; // note: memory churn...
}
}
}
}
public Solution alternative_solve(out Dictionary <Models.Shift, Decision> shiftsN, out Dictionary <Models.Shift, Decision> shiftsO)
{
SolverContext SC = SolverContext.GetContext();
Model model = SC.CreateModel();
var maxRq = HalfHourRequirements.Max(x => x.RequiredForce);
shiftsN = shiftsO = null;
//split shifts into two Dictionaries (each dict holds each Shift as key and the Decision variable as Value)
var normal_shifts = new Dictionary <Models.Shift, Decision>(); //for normal shifts
int i = 0;
Shifts.ForEach(x => {
Decision des = new Decision(Domain.IntegerRange(0, maxRq), string.Format("{0}_{1}", x.Name, i));
normal_shifts.Add(x, des);
model.AddDecision(des);
i++;
});
var overtime_shifts = new Dictionary <Models.Shift, Decision>(); //for overtime shifts
i = 0;
OvertimeShifts.ForEach(x => {
Decision des = new Decision(Domain.IntegerRange(0, maxRq), string.Format("{0}_{1}", x.Name, i));
overtime_shifts.Add(x, des);
model.AddDecision(des);
i++;
});
List <Decision> excess = new List <Decision>(); //used to calculate sum of excess values
HalfHourRequirements.ForEach(hh =>
{
var ShiftsActive = new List <Decision>();
foreach (var entry in normal_shifts)
{
if (entry.Key.IncludesHalfHour(hh.Start))
{
ShiftsActive.Add(entry.Value);
excess.Add(entry.Value);
}
}
foreach (var entry in overtime_shifts)
{
if (entry.Key.IncludesHalfHour(hh.Start))
{
ShiftsActive.Add(entry.Value);
excess.Add(entry.Value);
}
}
//add constraint for sum of force of active shifts on that halfhour
//if we need agents but no shifts exists for a halfhour, do not add a constraint
if (ShiftsActive.Count > 0)
{
var sum_constr = new SumTermBuilder(ShiftsActive.Count);
ShiftsActive.ForEach(s => sum_constr.Add(s));
var constr = sum_constr.ToTerm() >= hh.RequiredForce;
model.AddConstraint(string.Format("_{0:hh}{0:mm}", hh.Start), constr);
//constr = sum_constr.ToTerm() <= hh.RequiredForce * 2.0;
//model.AddConstraint(string.Format("limitconst_for_{0:hh}{0:mm}", hh.Start), constr);
}
});
//Constrain maximum number of agents working 8hour shifts
var max_agents_constraint = new SumTermBuilder(Shifts.Count);
foreach (var entry in normal_shifts)
{
max_agents_constraint.Add(entry.Value);
}
var ma_constr = max_agents_constraint.ToTerm() <= MaxAgents;
model.AddConstraint("Max_agents_constraint", ma_constr);
//1st goal: Minimize overtime shifts (if work manageable by normal shifts, no overtime shifts will be used)
var overtime_obj = new SumTermBuilder(OvertimeShifts.Count);
foreach (var entry in overtime_shifts)
{
overtime_obj.Add(entry.Value);
}
model.AddGoal("Minimize_overtime", GoalKind.Minimize, overtime_obj.ToTerm());
//2st goal: Minimize normal shifts
var normal_obj = new SumTermBuilder(Shifts.Count);
foreach (var entry in normal_shifts)
{
normal_obj.Add(entry.Value);
}
model.AddGoal("Minimize_normal", GoalKind.Minimize, normal_obj.ToTerm());
//3rd goal: Try to minimize excess
var sumReqs = HalfHourRequirements.Sum(x => x.RequiredForce);
model.AddGoal("Minimize_excess", GoalKind.Minimize, Model.Sum(excess.ToArray()) - sumReqs);
SimplexDirective simplex = new SimplexDirective();
Solution solution = SC.Solve(simplex);
shiftsN = normal_shifts;
shiftsO = overtime_shifts;
return(solution);
}