Optimization with Multiple FEM Models
=======================================================

This sample explains how to use multiple FEM models
simultaneously within a single optimization problem.


Sample Files
-------------------------------------------------------

.. note::
   Keep the
   :download:`sample project<cylinder-shaft-cooling.femprj>`
   and
   :download:`sample script<optimize_with_multiple_models.py>`
   in the same folder.


What This Sample Will Do
-------------------------------------------------------

This sample performs optimization using two different
analysis models contained in a single project file.

The first model performs a 2D cooling analysis and uses
the maximum temperature as an objective function.

The second model performs a 3D eigenvalue analysis and
uses the difference between the operating frequency and
natural frequency as an objective to maximize.


.. note::

   By using this feature, you can perform thermal analysis
   and structural analysis simultaneously on the same geometry,
   enabling optimization that considers both thermal and
   strength requirements.


.. note::

   You can set variables, objective functions, and constraints
   individually for each FEM model. The overall optimization
   problem integrates the objective functions and constraints
   from all models.


Design Variables and Analysis Settings
--------------------------------------------------------

.. figure:: model-and-analysis-settings.png
   :width: 400
   
   Overview of the model and analysis settings. The design variables are shared between the two analysis models.

==================== ==============================================
Variable Name        Description
==================== ==============================================
internal_radius      The inner radius of the shaft.
cooling_area_radius  The radius of the cooling area.
==================== ==============================================


Objective Functions
--------------------------------------------------------

.. figure:: objectives.png
   :width: 400
   
   Objective function settings

- Maximum Temperature (minimize) - obtained from the 2D thermal-fluid analysis model
- Difference between Operating Frequency and Natural Frequency (maximize) - obtained from the 3D resonance analysis model


Execution Result of the Sample
--------------------------------------------------------

.. figure:: optimization-result.png
   :width: 300

   Screenshot of the result.
   Increasing each radius to improve cooling performance
   causes the natural frequency to decrease and approach
   the operating frequency.


.. warning::

   When performing effective optimization on real-world
   problems, a greater number of trials is necessary.