ENH: added a null space approach to update the design variables

src/optimisation/adjointOptimisation/adjoint/Make/files

@@ -178,6 +178,7 @@ $(updateMethod)/LBFGS/LBFGS.C
 $(updateMethod)/SR1/SR1.C
 $(updateMethod)/conjugateGradient/conjugateGradient.C
 $(updateMethod)/MMA/MMA.C
+$(updateMethod)/nullSpace/nullSpace.C
 $(updateMethod)/constraintProjection/constraintProjection.C
 $(updateMethod)/SQPBase/SQPBase.C
 $(updateMethod)/SQP/SQP.C

src/optimisation/adjointOptimisation/adjoint/optimisation/updateMethod/nullSpace/nullSpace.H

+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2023 PCOpt/NTUA
+    Copyright (C) 2023 FOSS GP
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+
+Class
+    Foam::nullSpace
+
+Description
+    Update design variables using a null space approach.
+    Can handle inequality and bound constraints.
+
+    Reference:
+    \verbatim
+        Feppon, F., Allaire, G., & Dapogny, C. (2020).
+        Null space gradient flows for constrained optimization with
+        applications to shape optimization.
+        ESAIM: COCV, 26, 90.
+        https://doi.org/10.1051/cocv/2020015
+    \endverbatim
+
+SourceFiles
+    nullSpace.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef nullSpace_H
+#define nullSpace_H
+
+#include "constrainedOptimisationMethod.H"
+#include "updateMethod.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+                          Class nullSpace Declaration
+\*---------------------------------------------------------------------------*/
+
+class nullSpace
+:
+    public constrainedOptimisationMethod,
+    public updateMethod
+{
+protected:
+
+    // Protected data
+
+        //- Are bound constraints included?
+        bool includeBoundConstraints_;
+
+        //- Lagrange multipliers for flow-reated constraints
+        scalarField mu_;
+
+        //- Lagrange multipliers for the lower bound constraints
+        scalarField l_;
+
+        //- Lagrange multipliers for the upper bound constraints
+        scalarField u_;
+
+
+        // Dual variables
+
+            //- Solve the dual problem?
+            bool solveDualProblem_;
+
+            //- Lagrange multipliers of the dual problem for flow-related
+            //- constraints
+            scalarField dualMu_;
+
+            //- Lagrange multipliers of the dual problem for the lower bound
+            //- constraints
+            scalarField dualL_;
+
+            //- Lagrange multipliers of the dual problem for the upper bound
+            //- constraints
+            scalarField dualU_;
+
+
+        // Constraint subsets
+
+            //- List of saturated or violated constraints
+            //  List[0]: flow related constraints
+            //  List[1]: lower bound constraints
+            //  List[2]: upper bound constraints
+            //  Sub-list meaning is the same for all labelListLists that follow
+            labelListList iTilda_;
+
+            //- List of saturated or violated constraints (up to epsConstr_)
+            labelListList iTildaEps_;
+
+            //- List of constraints that must remain active
+            //  Determines the null space update
+            labelListList iHat_;
+
+            //- List of constraints the values of which need to be reduced
+            //  Determines the range space update
+            labelListList iRangeSpace_;
+
+
+        // Fields holding the updates of the Lagrange multipliers of the primal
+        // and dual problems
+
+            scalarField deltaMu_;
+            scalarField deltaL_;
+            scalarField deltaU_;
+            scalarField deltaDualMu_;
+            scalarField deltaDualL_;
+            scalarField deltaDualU_;
+
+
+        //- Infinitesimal quantity
+        //  Updated during the inner iterations of the dual problem
+        scalar eps_;
+
+        //- Maxmimum number of Newton iterations for the dual problem
+        label maxNewtonIters_;
+
+        //- Maxmimum number of line search iterations for each Newton iteration
+        //- of the dual problem
+        label maxLineSearchIters_;
+
+        //- Maxmimum number of CG iterations for obtaining the null space and
+        //- range space updates
+        label maxCGIters_;
+
+        //- Tolerance of the dual problem
+        scalar dualTolerance_;
+
+
+        // Constant parameters
+
+            //- Value for considering a constraint as marginally active
+            //  Used to avoid the frequent change of the active set of
+            //  constraints
+            scalar epsConstr_;
+
+            //- Multiplier of the null space update
+            scalar aJ_;
+
+            //- Multiplier of the range space update
+            scalar aC_;
+
+            //- Change aJ and aC adaptively
+            bool adaptiveStep_;
+
+            //- Last cycle on which to reset aJ
+            label lastAcceleratedCycle_;
+
+            //- Max change of the design variables, pertaining to the objective
+            //- reduction.
+            //  If adaptiveStep is set to true, aJ will be set in such a way
+            //  to obtain a maxDVChange_ for the design variables, for all
+            //  optimisation cycles up to lastAcceleratedCycle_
+            autoPtr<scalar> maxDVChange_;
+
+            //- Whether to impose maxDVChange strictly on all optimisation
+            //- cycles or just up to the lastAcceleratedCycle
+            bool strictMaxDVChange_;
+
+            //- Target reduction of active constraints (range in [0-1])
+            //  1: active constraints will become zero (first-order approx)
+            //  0: no change in the constraints
+            scalar targetConstraintReduction_;
+
+            //- Downplay the importance of the bound constraint reduction
+            //- by this ammount
+            scalar bcMult_;
+
+
+    // Protected Member Functions
+
+        //- Update sizes of fields related to the constraints
+        void initialise();
+
+        //- Zero the updates computed in the previous optimisation cycle
+        void zeroUpdates();
+
+
+        // Functions related to the solution of the dual subproblem
+
+            //- Solve the dual problem for computing the Lagrange multiplier
+            //- using a Newton solver
+            void solveDualProblem();
+
+            //- Compute and return residuals based on the current solution
+            tmp<scalarField> computeResiduals();
+
+            //- Compute direction for the Newton problem
+            void computeNewtonDirection();
+
+            //- Perform line search and return max residual corresponding to
+            //- the updated solution
+            scalar lineSearch();
+
+            //- Update the current solution using the known direction and the
+            //- given step length
+            void updateSolution(const scalar step);
+
+            //- Adjust step to satisfy cireteria
+            void adjustStep
+            (
+                scalar& step,
+                const scalar value,
+                const scalar update
+            );
+
+
+        // Functions related to the computation of the design variables update
+
+            //- Update the constraint subsets
+            void updateViolatedConstraintsSubsets();
+
+            //- Update the constraint subsets
+            void updateNullAndRangeSpaceSubsets();
+
+            //- Update violated constraints indices (iTilda and iTildaEps)
+            void updateViolatedIndices
+            (
+                const label i,
+                const scalarField& constraints
+            );
+
+            //- Update constraint indices related to the null and range space
+            //- part of the correction
+            void updateCorrectionIndices
+            (
+                const label i,
+                const scalarField& LagrangeMults,
+                const scalarField& dual
+            );
+
+            //- Compute the update of the design variables as a combination of
+            //- null space and range space parts
+            void correction();
+
+            //- A & v
+            //  where A is the Jacobian of all constraints, identified by
+            //  the labelList addressings, w.r.t. the active design variables
+            tmp<scalarField> Av
+            (
+                const scalarField& v,
+                const labelListList& subsets
+            );
+
+            //- A.T & v
+            //  where A is the Jacobian of all constraints, identified by
+            //  the labelList addressings, w.r.t. the active design variables
+            tmp<scalarField> ATv
+            (
+                const scalarField& v,
+                const labelListList& subsets
+            );
+
+            //- Collect all constraint values corresponding to the provided
+            //- indices
+            tmp<scalarField> activeConstraints
+            (
+                const labelListList& subsets
+            );
+
+            //- Computes the parts of ksiJ and ksiC that require a system
+            //- solution
+            //  Formulated in terms of the flow constraints, which are usually
+            //  few
+            tmp<scalarField> constraintRelatedUpdate
+            (
+                const scalarField& rhs,
+                const labelListList& subsets
+            );
+
+            //- Print statistics on the number of flow- and bound-related
+            //- constraints included in the subset
+            void statistics
+            (
+                const labelListList& subset,
+                const word& description
+            );
+
+
+private:
+
+    // Private Member Functions
+
+        //- No copy construct
+        nullSpace(const nullSpace&) = delete;
+
+        //- No copy assignment
+        void operator=(const nullSpace&) = delete;
+
+
+public:
+
+    //- Runtime type information
+    TypeName("nullSpace");
+
+
+    // Constructors
+
+        //- Construct from components
+        nullSpace
+        (
+            const fvMesh& mesh,
+            const dictionary& dict,
+            autoPtr<designVariables>& designVars,
+            const label nConstraints,
+            const word& type
+        );
+
+
+    //- Destructor
+    virtual ~nullSpace() = default;
+
+
+    // Member Functions
+
+        //- Compute design variables correction
+        virtual void computeCorrection();
+
+        //- Compute the merit function for line search
+        virtual scalar computeMeritFunction();
+
+        //- Directional derivative of the merit function, in the direction of
+        //- the correction
+        virtual scalar meritFunctionDirectionalDerivative();
+
+        //- Write useful quantities to files
+        virtual bool writeData(Ostream& os) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //