LagrangianRelaxationModelBuilder.cs

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using LotSizingDataModel.Solver.Modeling;
 
namespace LotSizingDataModel.Solver.Algorithms.Relaxation;
 
/// <summary>
/// Builds a source-preserving Lagrangian relaxation for a
/// minimization model.
/// </summary>
/// <remarks>
/// For every selected constraint the residual is
/// <c>lhs - rhs</c>. The term
/// <c>lambda * (lhs - rhs)</c> is added to the objective and the
/// cloned constraint is disabled. Multiplier signs are validated
/// by <see cref="LagrangianMultiplierDomain"/>.
/// </remarks>
public sealed class LagrangianRelaxationModelBuilder
{
    public LagrangianRelaxationBuildResult Build(
        MathematicalModel sourceModel,
        LagrangianRelaxationSpecification specification)
    {
        ArgumentNullException.ThrowIfNull(
            sourceModel);
 
        ArgumentNullException.ThrowIfNull(
            specification);
 
        sourceModel.EnsureValid();
 
        specification.EnsureValidAgainst(
            sourceModel);
 
        MathematicalModel relaxedModel =
            sourceModel.Clone();
 
        var relaxedIdentifiers =
            new List<int>();
 
        foreach (LagrangianMultiplier multiplier
                 in specification.Multipliers)
        {
            LinearConstraint sourceConstraint =
                sourceModel.Constraints.Single(
                    constraint =>
                        constraint.Id ==
                        multiplier.ConstraintId);
 
            LinearConstraint relaxedConstraint =
                relaxedModel.Constraints.Single(
                    constraint =>
                        constraint.Id ==
                        multiplier.ConstraintId);
 
            var residual =
                sourceConstraint.LeftHandSide.Clone();
 
            residual.AddConstant(
                -sourceConstraint.RightHandSide);
 
            residual.MultiplyBy(
                multiplier.Value);
 
            relaxedModel.Objective.Expression.Add(
                residual);
 
            relaxedConstraint.IsEnabled =
                false;
 
            relaxedIdentifiers.Add(
                sourceConstraint.Id);
        }
 
        relaxedModel.Description =
            string.IsNullOrWhiteSpace(
                sourceModel.Description)
                ? "Lagrangian-relaxed clone."
                : sourceModel.Description.Trim() +
                  " Lagrangian-relaxed clone.";
 
        relaxedModel.EnsureValid();
 
        return new LagrangianRelaxationBuildResult(
            relaxedModel,
            relaxedIdentifiers);
    }
}