public static Cplex BuildLPModel(IFTMDP Ida)
{
Cplex model = new Cplex();
INumVar[][] v = new INumVar[Ida.TimeHorizon][]; //V(t,x)
for (int t = 0; t < Ida.TimeHorizon; t++)
{
v[t] = model.NumVarArray(Ida.SS.Count, -double.MaxValue, double.MaxValue);
}
IObjective RevenueUB = model.AddMinimize(model.Prod(1, v[0][Ida.SS.IndexOf(Ida.InitialState)]));
//time->State->Active-> Expression
for (int t = 0; t < Ida.TimeHorizon; t++)
{
foreach (IMDPState s in Ida.SS)
{
foreach (IMDPDecision a in Ida.GenDecisionSpace(s))
{
INumExpr expr = v[t][Ida.SS.IndexOf(s)];
if (t < Ida.TimeHorizon - 1)
{
foreach (IMDPState k in Ida.GenStateSpace(s, a))
{
expr = model.Sum(expr,
model.Prod(-Ida.Prob(t, s, k, a), v[t + 1][Ida.SS.IndexOf(k)]));
}
}
model.AddGe(expr, Ida.Reward(t, s, a));
}
}
}
//model.SetOut(null);
return(model);
}
public static Cplex BuildDualModel(IFTMDP Ida)
{
Cplex model = new Cplex();
IObjective cost = model.AddMaximize();
IRange[][] constraint = new IRange[Ida.TimeHorizon][];
#region //////////////生成约束//////////////
for (int i = 0; i < Ida.TimeHorizon; i++)
{
constraint[i] = new IRange[Ida.SS.Count];
foreach (IMDPState s in Ida.SS)
{
if (i == 0 && s.Equals(Ida.InitialState))
{
constraint[i][Ida.SS.IndexOf(s)] = model.AddRange(1, 1);
}
else
{
constraint[i][Ida.SS.IndexOf(s)] = model.AddRange(0, 0);
}
}
}
#endregion
#region //////////////生成变量//////////////
for (int t = 0; t < Ida.TimeHorizon; t++)
{
foreach (IMDPState s in Ida.SS)
{
foreach (IMDPDecision a in Ida.GenDecisionSpace(s))
{
Column col = model.Column(cost, Ida.Reward(t, s, a));
col = col.And(model.Column(constraint[t][Ida.SS.IndexOf(s)], 1)); //插入Aj
if (t < Ida.TimeHorizon - 1)
{
foreach (IMDPState k in Ida.GenStateSpace(s, a))
{
col = col.And(model.Column(constraint[t + 1][Ida.SS.IndexOf(k)], -Ida.Prob(t, s, k, a))); //插入Aj
}
}
model.NumVar(col, 0, double.MaxValue, NumVarType.Float);
}
}
}
#endregion
model.SetOut(null);
return(model);
}