Optimization Module
New Functionality in Version 6.4
Optimization of Final Time
The time-dependent solver can be terminated based on a condition during the optimization, and the gradient computation will account for this, making it possible to minimize the duration of a process that stops once a certain condition is met.
Performance for Constraints
Gradient-based optimization of stationary and time-dependent problems now recycles the factorization and the Jacobian for the sensitivity computation of constraints, which can lead to dramatic performance improvements for problems with many optimization constraints. For transient models, the forward model is no longer recomputed when performing adjoint sensitivity analysis for the constraints, and the checkpointing is also only done once because the adjoints are computed in parallel.
Performance for GCMMA
Gradient-based optimization with the globally convergent method of moving asymptotes (GCMMA) optimization solver now only computes sensitivities for outer iterations.
Parameter Optimization study step
Scaling of control variables is done based on the distance between the bounds in the Parameter Optimization study step. The optimization study step used in previous versions has been renamed General Optimization.
Export of optimized Parameters
Optimized parameters can be used in further analysis because control parameters can now be exported to parameter cases using a checkbox in the General Optimization and Parameter Optimization study steps.
Control function improvements
The Control Function feature has also gained support for export of the optimized values to an Analytic or Interpolation function. The function type depends on the discretization of the function, and export is triggered using a checkbox in the feature. A variable for the average function value has also been added to the feature.
Randomization of BOUNDED GLOBAL CONTROLS
The Parameter Optimization and General Optimization study steps allow randomization of the initial values for bounded global controls based on a Sobol sequence. There is a shift property that can be changed using a Parametric Sweep so that different local optima can be identified.
P-Norm and Standard Deviation
The maximum operator is not differentiable, so it cannot be used with gradient based optimization, but it can be approximated using a p-norm, and this functionality has been built into the P-norm feature. Similarly, it is possible to homogenize a field using the Standard Deviation feature.
SNOPT Has Been Deprecated
The sparse nonlinear optimizer (SNOPT) optimization solver has been deprecated, so second-order convergence is limited to the interior point optimizer (IPOPT) and Levenberg–Marquardt solvers.
MMA Solver at Study Level
Previously, choosing the method of moving asymptotes (MMA) solver at the study level triggered the GCMMA solver, unless the solver configuration was manually changed. Now, it is possible to choose both the GCMMA and MMA solvers on the study level.
Extrusion Manufacturing Constraint
The Density Model feature has gained support for extrusion constraints, so incorporating an extrusion manufacturing constraint no longer requires manual setup with a General Extrusion operator. This functionality is also compatible with the Topology Link and Prescribed Density features.
Far-Field Operator for Gradient-Based Optimization
Operators have been added to the Electromagnetic Waves interface for evaluating the electromagnetic far field in a way that is compatible with gradient-based optimization. The operators — for computing gain, ratio, and other quantities — are available in 2D, 2D axisymmetry, and 3D. The norm of the electromagnetic field can be accessed as comp#.emw#.normEfar_opt(x,y,z).
Nonanalytic Operators in Objectives for Eigenvalue Sensitivity and Optimization
It is now possible to use nonanalytic operators in the expression for the objective when performing eigenvalue sensitivity and optimization. Examples of nonanalytic operators include real(), imag(), and abs().
Accurate Boundary FLUX variables in objectives with Adjoint sensitivity
Gradient-based optimization can now be performed when objectives and/or constraints contain accurate boundary flux variables.
Stability Improvements for Automatic Gradient Method
Stability improvements have been implemented for the automatic gradient method, which selects either the forward or adjoint method depending on the number of objectives and controls, so that the number of model evaluations is minimized.
Minimum and Maximum Center of Scaling in Transformation
Previously, the center of scaling and rotation in the Transformation feature was limited to Average and User defined, but now it is also possible to choose Minimum and Maximum, which is useful whenever an object is next to a Symmetry/Roller feature.