Defining Topology Optimization Solver and Constraints

You add the created cost function [objective] to the Topology Optimization solver as the objective. Besides the solver built-in constraint—Volume Ratio Constraint, you can also define user-defined constraints which require adjoint cost functions.

  1. Select the Solvers > Topology Optimization node and modify the following properties if necessary:
    Property Guidance
    Mode Determines the optimization mode. That is, whether you want the optimizer to find the minimum (Minimize) or maximum value (Maximize) of this objective.
    Objective Defines the optimization objective. Set Objective to your chosen cost function.
    Step Size Specifies the normalized step size for optimization.

    For guidelines on selecting step size, refer to Step Size.
    Link to the Reference Topic Topology Optimization Solver Properties
  2. Select the Solvers > Topology Optimization > Optimization Settings node and modify the following properties:
    Property Set Up
    Penalty Controls how aggressively the optimizer attempts to satisfy the specified constraints.

    For guidelines, refer to Penalty.
    Use Sensitivity Normalization Normalizes the optimization problem by the maximum sensitivity values.

    For guidelines, refer to Use Sensitivity Normalization.
    Re- normalization Frequency Specifies the frequency with which the optimization problem is re-normalized.

    For guidelines, refer to Re-normalization Frequency.
    ADAM: Beta 1 Determines the under-relaxation performed on the gradient.

    For guidelines, refer to ADAM: Beta 1.
    ADAM: Beta 2 Determines the under-relaxation of the variance in the gradient, which is used to scale the optimization search direction.

    For guidelines, refer to ADAM: Beta 2.
    Link to the Reference Topic Optimization Settings
To create a built-in volume ratio constraint:
  1. Right-click the Solvers > Topology Optimization > Constraints node and select New > Volume Ratio Constraint to define a minimum volume ratio of a selected phase.
To create an extra user-defined optimization constraint:
  1. Right-click the Solvers > Topology Optimization > Constraints node and select New > User-Defined Constraint.
  2. Select the User-Defined Constraint node, add the previously created cost-function [user-defined constraint] as Constraint and set other properties.
  3. If you want to monitor the Lagrangian multiplier associated with the optimization constraint, create a Lagrange Multiplier report. See Lagrange Multiplier.
    1. Right-click the Reports node and select New Report > System > Lagrange Multiplier.
    2. Set Constraint to the previously created [user-defined constraint] or [volume ratio constraint].