| MathModelSolution |
Solution of a MathModel by a solver such as [!:Cplex2] or [!:Scip2].
It provides meta information such as solution status and objectiev function value.
Further, it allows to access solution values of the decision variables.
# Case 1: Feasible
The following example demonstrates a feasible solution case on a trivial model.
Set i = Set("i").HasElementsUntil(3); // { 0, 1, 2 }
Set j = Set("j").HasElementsUntil(4); // { 0, 1, 2, 3 }
VarD2 y = Variable("y").HasIndices(i, j).IsBinary();
Objective maxCount = maximize | sum(over(i, j), y[i, j]);
MathModel model = MathModel.New("dummy model").WithObjective(maxCount).HasNoConstraints();
Cplex solver = new();
CplexParams pars = new();
var resSolution = await solver.Solve(model, pars);
var solution = resSolution.Unwrap(); // normally, check if it is 'IsOk' before unwrapping!
// solution status currently depends on the used solver
Assert.Equal("integer optimal solution", solution.SolutionStatus);
double objFunValue = solution.ObjectiveValue.Unwrap(); // must be okay to Unwrap since status is 'integer optimal'.
Assert.Equal(12, objFunValue);
// ySoln is a map of indices to solution values;
// allows access to solution values of decision variables through indices.
// since y is of type VarD2, it has two indices for i and j.
Dictionary<(int, int), double> ySoln = solution.VarIndicesAndValuesOf(y).Unwrap();
Assert.Equal(1, y[(0, 0)];
Assert.Equal(1, y[(2, 3)];
Assert.False(ySoln.ContainsKey((4, 5)); // y(4, 5) is not a variable of the model, check elements of i and j.
Set i = Set("i").HasElementsUntil(3); // { 0, 1, 2 }
Set j = Set("j").HasElementsUntil(4); // { 0, 1, 2, 3 }
VarD2 y = Variable("y").HasIndices(i, j).IsBinary();
Objective maxCount = maximize | sum(over(i, j), y[i, j]);
Constraint impossible = sum(over(i, j), y[i, j]) >= 100;
MathModel model = MathModel.New("dummy model").WithObjective(maxCount).HasConstraints(impossible);
Scip solver = new();
ScipParams pars = new();
var resSolution = await solver.Solve(model, pars);
var solution = resSolution.Unwrap(); // normally, check if it is 'IsOk' before unwrapping!
// solution status currently depends on the used solver
Assert.Equal("infeasible", solution.SolutionStatus);
// at this point we also know that objective function value and variables' values are not available (None):
Assert.Equal(solution.ObjectiveValue.IsNone);
Assert.Equal(solution.VarIndicesAndValuesOf(y).IsNone);
An easy way to simulate this is to force a wrong path for the solver.
In reality, different problems might cause the solver to fail such as out-of-memory problem.
Set i = Set("i").HasElementsUntil(3); // { 0, 1, 2 }
Set j = Set("j").HasElementsUntil(4); // { 0, 1, 2, 3 }
VarD2 y = Variable("y").HasIndices(i, j).IsBinary();
Objective maxCount = maximize | sum(over(i, j), y[i, j]);
MathModel model = MathModel.New("dummy model").WithObjective(maxCount).HasNoConstraints();
Cplex solver = new("wrong path");
var resSolution = await solver.Solve(model);
Assert.True(resSolution.IsErr); // "resSolution.Unwrap()" would've thrown an exception here; better to check before unwrapping
Assert.True(resSolution.ErrorMessage().Unwrap().Contains("wrong path")); // the error message provides detailes about why the solver failed.
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