Optimization Module Functionality
The Optimization Module is a general purpose add-on to COMSOL Multiphysics and its other modules. It consists of a physics interface, special study steps, solvers, a density topology feature, and an application library.
The Optimization Interface
The Optimization Module adds the Optimization interface (
)to the list of available physics interfaces. The interface can be found under the Mathematics > Optimization and Sensitivity branch when you are adding physics to your model.
The Optimization interface includes a wide range of advanced features for defining an optimization problem separately, or in connection to a physics model:
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Global objectives, including least-squares objectives
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Global constraints
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Global control variables
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Integral objectives on all geometry levels: domains, boundaries, edges, and points
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Integral constraints on all geometry levels
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Pointwise constraints on all geometry levels
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Control variable fields on all geometry levels
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Probe objectives in domains (an objective defined by a point evaluation of an expression)
The Optimization Study Step
The Optimization study step (
) acts as the central control panel for any optimization problem. It can be added to any study, where it will appear as the first step. The remaining steps in the study define the simulation that is being optimized. Note that when a gradient-based optimizer is used, the Optimization study step replaces and cannot be used together with some other study steps, notably Parametric Sweep and its variants.
In the Optimization study step, you can set up objective function contributions, select control variables, and set constraints. Objectives, constraints, and control variables defined in an Optimization interface are displayed in the study step, where they can be disabled or enabled. Note that most optimization tasks can be specified using the Optimization study step alone, needing no Optimization Interface.
The Optimization study step also contains an optimization solver choice, including the most important solver settings, as well as extensive settings for controlling graphics and table output during the solution process.
The Parameter Estimation Study Step
The Parameter Estimation study step (
) is a specialized version of the Optimization study step, intended to simplify some typical parameter estimation tasks. In particular, it contains a user interface for specifying a least-squares objective function based on time-dependent measurements entered or imported into an interpolation function.
The Shape and Topology Optimization Study Steps
Both the Shape Optimization study step (
) and the Topology Optimization study step (
) are stripped-down versions of the Optimization Study step. They only allow gradient-based optimization, and they are incompatible with objectives and constraints in the Optimization interface. They both default to the MMA optimization solver, and they allow limiting the absolute change of individual control variables using a move limit (only for MMA). The move limit is enabled by default and set to 0.1 for the Shape Optimization study step in order to reduce the likelihood of problems with inverted elements.
Topology Optimization with the Density Method
The Density Method is a topology optimization feature located under component definitions. The method allows the user to impose a Helmholtz filter with a custom radius, such that a minimum length scale can be imposed.
The user has to couple the physical material properties with the output of the filter manually, but the feature supports projection and common interpolation functions, so this typically only involves a multiplication.
The Optimization Solvers
The Optimization Module contains the following optimization solvers:
IPOPT:
A gradient-based, general-purpose interior point algorithm for nonlinear constrained problems.
GCMMA:
A general-purpose, interior point method based on successive convex approximations constructed from objective and constraint gradient information, particularly suited to topology optimization.
MMA:
A general-purpose method based on successive convex approximations constructed from objective and constraint gradient information, particularly suited to topology optimization.
Levenberg–Marquardt:
A special-purpose solver for least-squares fitting, using the special problem structure to estimate second-order derivatives from first order gradient data. Constraints are ignored.
Nelder–Mead:
A robust derivative-free, heuristic, simplex search algorithm, including a penalty method for constraint handling.
BOBYQA:
An algorithm sampling the objective function to construct and maintain a quadratic approximation of the objective inside a moving trust region. General constraints can be handled in an augmented Lagrangian wrapper, solving a sequence of unconstrained problems.
COBYLA:
An algorithm sampling both objective function and constraint values to create and maintain a linear approximation inside a moving trust region. General constraints are accepted but may be violated at intermediate solution steps.
EGO:
A method which searches for the global optimum using a Gaussian process function.
)to the list of available physics interfaces. The interface can be found under the Mathematics > Optimization and Sensitivity branch when you are adding physics to your model.
) acts as the central control panel for any optimization problem. It can be added to any study, where it will appear as the first step. The remaining steps in the study define the simulation that is being optimized. Note that when a gradient-based optimizer is used, the Optimization study step replaces and cannot be used together with some other study steps, notably Parametric Sweep and its variants.
) is a specialized version of the Optimization study step, intended to simplify some typical parameter estimation tasks. In particular, it contains a user interface for specifying a least-squares objective function based on time-dependent measurements entered or imported into an interpolation function.
) and the Topology Optimization study step (
) are stripped-down versions of the Optimization Study step. They only allow gradient-based optimization, and they are incompatible with objectives and constraints in the Optimization interface. They both default to the MMA optimization solver, and they allow limiting the absolute change of individual control variables using a move limit (only for MMA). The move limit is enabled by default and set to 0.1 for the Shape Optimization study step in order to reduce the likelihood of problems with inverted elements.