LocalSubSystemALADIN¶

Source: Distributed_Design_Optimizer/subsystem/LocalSubSystemALADIN.py

ALADIN local subsystem module.

This module provides the local subsystem implementation for the ALADIN coordination method.

Classes¶

LocalSubSystemALADIN¶

Inherits from: LocalSubSystemBasis

Local subsystem for ALADIN coordination.

Implements the local subsystem functionality for the ALADIN distributed optimization method.

Methods¶

init(self, id: str, level: int, neighborid: List[str], analysis: AnalysisInterface, localobjective: LocalObjectiveInterface, localconstraints: LocalConstraintsInterface, optimization: OptimizationInterface, local_convergenceindicator_innerloop: Local_ConvergenceIndicator_Innerloop_Interface, local_convergenceindicator_outerloop: Local_ConvergenceIndicator_Outerloop_Interface, updatecouplingparametermethod_outerloop: UpdateCouplingParameterMethodInterface) → None

📐 Pseudocode: Require hyperparameters ν, Σ, s and initial Δd, λ (Lines 1, 2, 3) → Augmented Lagrangian Alternating Direction Inexact Newton

Create a new instance of LocalSubSystemALADIN.

Args:

id: Identifier for the subsystem.
level: Level identifier for the subsystem in the hierarchy.
neighborid: List of identifiers for neighboring subsystems.
analysis: Analysis interface for the subsystem.
localobjective: Local objective function interface.
localconstraints: Local constraints function interface.
optimization: Optimization interface.
local_convergenceindicator_innerloop: Local convergence indicator for inner loop.
local_convergenceindicator_outerloop: Local convergence indicator for outer loop.
updatecouplingparametermethod_outerloop: Strategy for updating coupling parameters in outer loop.

validate_inputs(self) → None

Validate the components handed to this subsystem by the ALADIN coordination method.

Validates that the outer-loop update coupling parameter method and the local inner/outer loop convergence indicators are compatible with ALADIN.

Raises:

ValueError: If a provided component is not compatible with ALADIN.

get_Nu(self) → float

📐 Pseudocode: Require hyperparameters ν, Σ, s and initial Δd, λ (Lines 1, 2, 3) → Augmented Lagrangian Alternating Direction Inexact Newton

Return the hyperparameter nu of the proximal term in the primal subproblem.

Returns:

The hyperparameter nu value.

set_Nu(self, nu_in: float) → None

Set the hyperparameter nu of the proximal term in the primal subproblem.

Args:

nu_in: The hyperparameter nu value to set.

get_Sigma_i(self) → List[List[float]]

📐 Pseudocode: Require hyperparameters ν, Σ, s and initial Δd, λ (Lines 1, 2, 3) → Augmented Lagrangian Alternating Direction Inexact Newton

Get the hyperparameter Sigma_i of the proximal term in the primal subproblem.

Returns:

The proximal matrix Sigma_i (positive definite).

set_Sigma_i(self, sigma_i_in: List[List[float]]) → None

Set the hyperparameter Sigma_i of the proximal term in the primal subproblem.

Args:

sigma_i_in: The proximal matrix Sigma_i to set (positive definite).

get_HessianApproximation_LocalObjective(self) → HessianApproximationBFGS | None

Get the BFGS Hessian approximation of the local objective.

Returns:

The BFGS approximation object, or None if not initialized.

set_HessianApproximation_LocalObjective(self, hessianapproximation_localobjective_in: HessianApproximationBFGS) → None

Set the BFGS Hessian approximation of the local objective.

Args:

hessianapproximation_localobjective_in: The BFGS approximation object to set.

get_HessianApproximation_LocalEqualityConstraints(self) → List[HessianApproximationBFGS] | None

Get the list of BFGS Hessian approximations of the local equality constraints.

Returns:

One BFGS object per equality constraint, or None if not initialized.

set_HessianApproximation_LocalEqualityConstraints(self, hessianapproximation_localequalityconstraints_in: List[HessianApproximationBFGS]) → None

Set the list of BFGS Hessian approximations of the local equality constraints.

Args:

hessianapproximation_localequalityconstraints_in: One BFGS object per equality constraint.

get_HessianApproximation_LocalInequalityConstraints(self) → List[HessianApproximationBFGS] | None

Get the list of BFGS Hessian approximations of the local inequality constraints.

Returns:

One BFGS object per inequality constraint, or None if not initialized.

set_HessianApproximation_LocalInequalityConstraints(self, hessianapproximation_localinequalityconstraints_in: List[HessianApproximationBFGS]) → None

Set the list of BFGS Hessian approximations of the local inequality constraints.

Args:

hessianapproximation_localinequalityconstraints_in: One BFGS object per inequality constraint.

get_HessianApproximation_MappedResponses(self) → List[List[HessianApproximationBFGS] | None] | None

Get the list of BFGS Hessian approximations of the mapped responses.

Each entry corresponds to one local-to-local coupling. Since a coupling may not include mapped responses, entries can be None.

Returns:

Nested list of BFGS objects per coupling, or None.

set_HessianApproximation_MappedResponses(self, hessianapproximations_mappedresponses_in: List[List[HessianApproximationBFGS] | None]) → None

Set the list of BFGS Hessian approximations of the mapped responses.

Args:

hessianapproximations_mappedresponses_in: Nested list of BFGS objects per coupling.

append_Controller(self) → None

Update local subsystems by appending controller and adding necessary coupling parameters.

get_LocalToController_CouplingParameters(self) → LocalToController_CouplingParametersALADIN

Return the controller coupling parameters.

Returns:

The controller coupling parameters object.

synchronize_AllLocalGlobalCouplingParameters(self) → None

Synchronize all local-global coupling parameters to the controller.

This method synchronizes every information that is needed by the controller and stored in the local couplings between i and j to the controller coupling parameters object's LocalToLocalForController_CouplingParameters objects.

synchronize_LocalGlobalCouplingParameter(self, localtolocal_couplingparameter: LocalCouplingParametersALADIN, localtolocalforcontroller_couplingparameter: LocalToLocalForController_CouplingParameters) → None

Synchronize a single local-global coupling parameter to the controller.

This method synchronizes every information that is needed by the controller and stored in the local couplings between i and j to the controller coupling parameters object's LocalToLocalForController_CouplingParameters objects.

Args:

localtolocal_couplingparameter: Local coupling parameters between subsystems i and j.
localtolocalforcontroller_couplingparameter: Coupling parameters from local subsystem to controller.

mapToController(self) → None

📐 Pseudocode: Copy gradients, Hessians, coupling to controller (Lines 13, 14, 15) → Augmented Lagrangian Alternating Direction Inexact Newton

Synchronize necessary information with the controller.

Only subsystem i's information like e.g. Jacobians, Hessians, local multipliers, ..., are computed and stored in couplingparameters in postprocess_Optimization.

evaluateCoordinationObjective(self) → None

📐 Pseudocode: Local subsystem NLP optimization (Line 12) → Augmented Lagrangian Alternating Direction Inexact Newton

Evaluate the coordination objective including inner product and proximal terms.

evaluate_Gradient_CoordinationObjective(self) → None

📐 Pseudocode: Copy gradients, Hessians, coupling to controller (Lines 13, 14, 15) → Augmented Lagrangian Alternating Direction Inexact Newton

Evaluate the analytical gradient of the coordination objective.

Assumes the mapped responses Jacobian was evaluated already.

evaluateCoordinationEqualityConstraint(self) → None

Evaluate the coordination equality constraint for ALADIN.

evaluateCoordinationInequalityConstraint(self) → None

Evaluate the coordination inequality constraint for ALADIN.

evaluate_Jacobian_CoordinationEqualityConstraints(self) → None

📐 Pseudocode: Copy gradients, Hessians, coupling to controller (Lines 13, 14, 15) → Augmented Lagrangian Alternating Direction Inexact Newton

Evaluate the Jacobian of the coordination equality constraints.

ALADIN does not have coordination equality constraints, hence no-op.

evaluate_Jacobian_CoordinationInEqualityConstraints(self) → None

📐 Pseudocode: Copy gradients, Hessians, coupling to controller (Lines 13, 14, 15) → Augmented Lagrangian Alternating Direction Inexact Newton

Evaluate the Jacobian of the coordination inequality constraints.

ALADIN does not have coordination inequality constraints, hence no-op.

prepare_OptimizationProblem(self) → None

📐 Pseudocode: Local subsystem NLP optimization (Line 12) → Augmented Lagrangian Alternating Direction Inexact Newton

Update d_hat.

postprocess_Optimization(self) → None

Perform ALADIN's postprocessing.

evaluate_Hessian_Lagrangian(self, local_hessians: Dict[str, List[List[float]] | List[List[List[float]] | None] | None]) → List[List[float]]

Compute the Hessian of the Lagrangian w.r.t. local and coordination constraints.

Given the Hessians of each summand of the Lagrangian, this function computes the combined Hessian of the Lagrangian.

Args:

local_hessians: Dictionary mapping constraint type names to their Hessian
matrices. Keys include "Local Objective", "Local Equality Constraints",
and "Local Inequality Constraints".

Returns:

The combined Hessian of the Lagrangian as a 2D list.

check_MultipliersNotSet(self) → bool

Return True if any existing constraint is missing its corresponding multiplier in optimdata.

Returns:

True if at least one constraint has no corresponding multiplier set.

evaluateAllHessians(self) → Dict[str, List[List[float]] | List[List[List[float]] | List[List[List[List[float]]]] | None] | None]

📐 Pseudocode: Copy gradients, Hessians, coupling to controller (Lines 13, 14, 15) → Augmented Lagrangian Alternating Direction Inexact Newton

Evaluate all Hessians of local objective, local equality constraints and local inequality constraints.

If they exist and were provided by the user, those are used; else, BFGS approximations are used.

Returns:

Dictionary with keys 'Local Objective', 'Local Equality Constraints',
'Local Inequality Constraints', and 'Mapped Responses'.

evaluate_Complete_Hessian_LocalObjective(self) → List[List[float]]

Evaluate a complete Hessian of the local objective.

If the user-provided Hessian is complete, this will be used
Else, the BFGS-approximation of the Hessian of the local objective

Returns:

Complete Hessian matrix of the local objective.

evaluate_Complete_Hessian_LocalEqualityConstraints(self) → List[List[List[float]]]

Evaluate complete Hessians of all local equality constraints.

If the user-provided Hessian for a constraint is complete, this will be used
Else, the BFGS-approximation of the Hessian of that equality constraint

Returns:

List of complete Hessian matrices, one per equality constraint.

evaluate_Hessian_LocalInequalityConstraints(self) → List[List[List[float]] | None]

Evaluate the Hessians of all local inequality constraints.

If the user-provided Hessian for a constraint is complete, this will be used
Else, the BFGS-approximation of the Hessian of that inequality constraint

Returns:

List of complete Hessian matrices, one per inequality constraint.

evaluate_Complete_Hessian_MappedResponses(self) → List[List[List[List[float]]] | None]

Compute the Hessians of the mapped responses for each local-to-local coupling.

Returns:

Hessian matrices per coupling, None if no mapped responses.

return_initialized_CouplingParameters(self) → List[LocalToController_CouplingParametersALADIN | LocalCouplingParametersALADIN]

Return a fresh set of initialized coupling parameters for this subsystem.

Returns:

Fresh coupling parameters, one per neighbor.

initializeCouplingParameters_before_CopyToMiddleLevel(self) → None

📐 Pseudocode: Require hyperparameters ν, Σ, s and initial Δd, λ (Lines 1, 2, 3) → Augmented Lagrangian Alternating Direction Inexact Newton

Initialize coupling parameters before copying communicated information from neighboring subsystem.

Create empty placeholders for coupling parameters, i.e. communicated quantities in the algorithms, Lagrange multipliers, penalty weights, ... The sizes are read by already initialized quantities from the inner loop iteration

initializeCouplingParameters_after_CopyFromMiddleLevel(self) → None

Initialize coupling parameters after copying communicated information from neighboring subsystems.

Create empty placeholders for coupling parameters, i.e. communicated quantities in the algorithms, Lagrange multipliers, penalty weights, ... The sizes are read by already initialized quantities from the inner loop iteration

initializeCouplingParameters_after_Second_CopyFromMiddleLevel(self) → None

Initialize the rest of the coupling parameters by solving the controller QP in ALADIN.

prepare_updateCouplingParameters(self) → None

📐 Pseudocode: Compute outerloop iterate d_hat and prepare hatted coupling quantities (Lines 27, 28, 29, 30, 31, 32) → Augmented Lagrangian Alternating Direction Inexact Newton

Synchronize all coupling parameters to controller.

updateCouplingParameters_innerLoop(self) → None

📐 Pseudocode: Local: Copy Δd from controller, compute d_hat (Lines 8, 9, 10, 11) → Augmented Lagrangian Alternating Direction Inexact Newton

Update coupling parameters in the inner loop.

In ALADIN, empty, but synchronize.

updateCouplingParameters_outerLoop(self) → None

📐 Pseudocode: Dual Update (Lagrange multiplier update) (Lines 34, 35, 36, 37, 38) → Augmented Lagrangian Alternating Direction Inexact Newton

Update coupling parameters during outer loop iteration.

updateSubsystem(self, perturbed_designvariables: List[float]) → None

Update the subsystem based on the inputted design variables.

Args:

perturbed_designvariables: Design variables to evaluate the subsystem at.

evaluate_Inconsistencies(self) → None

📐 Pseudocode: Outerloop convergence and return (Lines 40, 41, 42, 43) → Augmented Lagrangian Alternating Direction Inexact Newton

Compute the difference between stored coupling and mapped variables.

Compared to the latest available data from a subsystem. It returns a matrix containing three vectors. The first row vector are the mapped-response side differences of the coupling circle. The second row vector returns differences of the coupling-variable side of the coupling circle. The third row returns the difference between the shared design variable vector.

return_initialized_Inconsistencies(self) → List[InConsistencySize]

Return a fresh set of initialized inconsistency objects.

Returns:

One inconsistency object per coupling parameter.

set_CoordinationMultipliers_MappedResponse_Minus_CopyCouplingVariable(self, neighborid: str, multipliersin: List[float]) → None

📐 Pseudocode: Dual Update (Lagrange multiplier update) (Lines 34, 35, 36, 37, 38) → Augmented Lagrangian Alternating Direction Inexact Newton

Set coordination multipliers for the mapped response minus copied coupling variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
multipliersin: List of multiplier values to set.

set_CoordinationMultipliers_CopyMappedResponse_Minus_CouplingVariable(self, neighborid: str, multipliersin: List[float]) → None

📐 Pseudocode: Dual Update (Lagrange multiplier update) (Lines 34, 35, 36, 37, 38) → Augmented Lagrangian Alternating Direction Inexact Newton

Set coordination multipliers for the copied mapped response minus coupling variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
multipliersin: List of multiplier values to set.

set_CoordinationMultipliers_SharedDesignVariable_Minus_CopyTargetSharedDesignVariable(self, neighborid: str, multipliersin: List[float]) → None

📐 Pseudocode: Dual Update (Lagrange multiplier update) (Lines 34, 35, 36, 37, 38) → Augmented Lagrangian Alternating Direction Inexact Newton

Set coordination multipliers for the shared design variable minus copied target shared design variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
multipliersin: List of multiplier values to set.

set_CoordinationMultipliers_CopySharedDesignVariable_Minus_TargetSharedDesignVariable(self, neighborid: str, multipliersin: List[float]) → None

📐 Pseudocode: Dual Update (Lagrange multiplier update) (Lines 34, 35, 36, 37, 38) → Augmented Lagrangian Alternating Direction Inexact Newton

Set coordination multipliers for the copied shared design variable minus target shared design variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
multipliersin: List of multiplier values to set.

set_CoordinationWeights_MappedResponse_Minus_CopyCouplingVariable(self, neighborid: str, penaltyweightsin: List[float]) → None

Set coordination weights for the mapped response minus copied coupling variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
penaltyweightsin: List of penalty weight values to set.

set_CoordinationWeights_CopyMappedResponse_Minus_CouplingVariable(self, neighborid: str, penaltyweightsin: List[float]) → None

Set coordination weights for the copied mapped response minus coupling variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
penaltyweightsin: List of penalty weight values to set.

set_CoordinationWeights_SharedDesignVariable_Minus_CopyTargetSharedDesignVariable(self, neighborid: str, penaltyweightsin: List[float]) → None

Set coordination weights for the shared design variable minus copied target shared design variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
penaltyweightsin: List of penalty weight values to set.

set_CoordinationWeights_CopySharedDesignVariable_Minus_TargetSharedDesignVariable(self, neighborid: str, penaltyweightsin: List[float]) → None

Set coordination weights for the copied shared design variable minus target shared design variable inconsistency of a neighbor.

Args:

neighborid: Identifier of the neighboring subsystem.
penaltyweightsin: List of penalty weight values to set.

update_state(self, other_subsystem: LocalSubSystemALADIN) → None

Update the state of this LocalSubSystemALADIN instance with values from another instance.

This method is necessary for multiprocessing. When subsystems are executed in parallel using multiprocessing.Pool, they are serialized and deserialized, creating new objects in separate memory spaces. After parallel execution completes, this method updates the original object's attribute values while preserving their memory addresses.

The update preserves memory addresses by modifying attribute contents in-place where possible, rather than reassigning references. This is essential for maintaining object identity across the multiprocessing boundary.

Args:

other_subsystem: The source LocalSubSystemALADIN containing updated values
from parallel execution.