.. _method-pareto_set:

""""""""""
pareto_set
""""""""""


Pareto set optimization


.. toctree::
   :hidden:
   :maxdepth: 1

   method-pareto_set-method_name
   method-pareto_set-method_pointer
   method-pareto_set-random_weight_sets
   method-pareto_set-weight_sets
   method-pareto_set-iterator_servers
   method-pareto_set-iterator_scheduling
   method-pareto_set-processors_per_iterator


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+-----------------------------+---------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword              | Dakota Keyword Description                  |
|                         | Group              |                             |                                             |
+=========================+====================+=============================+=============================================+
| Required (Choose One)   | Sub-method         | `method_name`__             | Specify sub-method by name                  |
|                         | Selection          +-----------------------------+---------------------------------------------+
|                         |                    | `method_pointer`__          | Pointer to optimization or least-squares    |
|                         |                    |                             | sub-method                                  |
+-------------------------+--------------------+-----------------------------+---------------------------------------------+
| Optional                                     | `random_weight_sets`__      | Number of random weighting sets             |
+----------------------------------------------+-----------------------------+---------------------------------------------+
| Optional                                     | `weight_sets`__             | List of user-specified weighting sets       |
+----------------------------------------------+-----------------------------+---------------------------------------------+
| Optional                                     | `iterator_servers`__        | Specify the number of iterator servers when |
|                                              |                             | Dakota is run in parallel                   |
+----------------------------------------------+-----------------------------+---------------------------------------------+
| Optional                                     | `iterator_scheduling`__     | Specify the scheduling of concurrent        |
|                                              |                             | iterators when Dakota is run in parallel    |
+----------------------------------------------+-----------------------------+---------------------------------------------+
| Optional                                     | `processors_per_iterator`__ | Specify the number of processors per        |
|                                              |                             | iterator server when Dakota is run in       |
|                                              |                             | parallel                                    |
+----------------------------------------------+-----------------------------+---------------------------------------------+

.. __: method-pareto_set-method_name.html
__ method-pareto_set-method_pointer.html
__ method-pareto_set-random_weight_sets.html
__ method-pareto_set-weight_sets.html
__ method-pareto_set-iterator_servers.html
__ method-pareto_set-iterator_scheduling.html
__ method-pareto_set-processors_per_iterator.html



**Description**


In the pareto set minimization method ( ``pareto_set``), a series of
optimization or least squares calibration runs are performed for
different weightings applied to multiple objective functions.  This
set of optimal solutions defines a "Pareto set," which is useful for
investigating design trade-offs between competing objectives.  The
code is similar enough to the ``multi_start`` technique that both
algorithms are implemented in the same ConcurrentMetaIterator class.

The ``pareto_set`` specification must identify an optimization or least
squares calibration method using either a ``method_pointer`` or a
``method_name`` plus optional ``model_pointer``.  This minimizer is
responsible for computing a set of optimal solutions from a set of
response weightings (multi-objective weights or least squares term
weights).  These weightings can be specified as follows: (1) using
``random_weight_sets``, in which case weightings are selected randomly
within [0,1] bounds, (2) using ``weight_sets``, in which the weighting
sets are specified in a list, or (3) using both ``random_weight_sets``
and ``weight_sets``, for which the combined set of weights will be
used.  In aggregate, at least one set of weights must be specified.
The set of optimal solutions is called the "pareto set," which can
provide valuable design trade-off information when there are competing
objectives.

*Expected HDF5 Output*

If Dakota was built with HDF5 support and run with the
:dakkw:`environment-results_output-hdf5` keyword, this method
writes the best parameters and responses returned by each sub-iterator.
The weights are provided as metadata. See the :ref:`hdf5_results-ms_pareto`
documentation for details.