Blurb::
Adaptive Global Surrogate-Based Optimization
Description::
The ``surrogate_based_global`` method iteratively performs optimization
on a global surrogate using the same bounds during each iteration.


- In one iteration, optimal solutions are found on the surrogate     model, and a subset of these are passed to the next iteration.
- At the next iteration, these surrogate-optimal variable sets are     evaluated with the "truth" model, and added to the set of points     over which the next surrogate is constructed.

In this way, the optimization operates on a more accurate surrogate
during each iteration, presumably driving to optimality quickly. In
contrast to :dakkw:`method-surrogate_based_local`, this approach has no
guarantee of convergence.

*Usage Tips*

*Attention:* This adaptive method is not recommended for
"build-once" surrogates trained from (static) imported data or trained
online using a single Dakota design of experiments. Instead, any
Dakota optimization method can be used with a (build-once) global
surrogate by specifying the ``id_model`` of a global surrogate model
with the optimizer's ``model_pointer`` keyword.

Configuring the method:


- The sub-method, specified with either :dakkw:`method-surrogate_based_global-method_pointer` or :dakkw:`method-surrogate_based_global-method_name` should typically be an optimizer that returns multiple final solutions, such as :dakkw:`method-moga` or :dakkw:`method-soga`.
- The :dakkw:`method-surrogate_based_global-model_pointer` keyword must identify a surrogate model which includes an underlying truth model, typically via :dakkw:`model-surrogate-global-truth_model_pointer` or :dakkw:`model-surrogate-global-dace_method_pointer`

Workflow:


- One might first try a single minimization method coupled with a surrogate model prior to using this surrogate-based global method. This is essentially equivalent to setting ``max_iterations`` to 1 and will allow one to get a sense of what surrogate types are the most accurate to use for the problem.
- Consider starting with a small number of maximum iterations, such as 3--5, to get a sense of how the optimization evolves as the surrogate gets updated. If it is still changing significantly, then a larger number (used in combination with restart) may be needed.
- Surrogates can be built for all primary functions and constraints or for only a subset of these functions and constraints. This allows one to use a "truth" model directly for some of the response functions, perhaps due to them being much less expensive than other functions.

*Known Issue: When using discrete variables, there have been
sometimes significant differences in surrogate behavior observed
across computing platforms in some cases.  The cause has not yet been
fully diagnosed and is currently under investigation.  In addition,
guidance on appropriate construction and use of surrogates with
discrete variables is under development.  In the meantime, users
should therefore be aware that there is a risk of inaccurate results
when using surrogates with discrete variables.*

*Expected HDF5 Output*

If Dakota was built with HDF5 support and run with the
:dakkw:`environment-results_output-hdf5` keyword, this method
writes the following results to HDF5:


- :ref:`hdf5_results-best_params`
- :ref:`hdf5_results-best_obj_fncs` (when :dakkw:`responses-objective_functions`) are specified)
- :ref:`hdf5_results-best_constraints`
- :ref:`hdf5_results-calibration` (when :dakkw:`responses-calibration_terms` are specified)
Topics::
surrogate_based_optimization_methods
Examples::

Theory::
In surrogate-based optimization (SBO) and surrogate-based nonlinear
least squares (SBNLS), minimization occurs using a set of one or more
approximations, defined from a surrogate model, that are built and
periodically updated using data from a "truth" model. The surrogate
model can be a global data fit (e.g., regression or interpolation of
data generated from a design of computer experiments), a multipoint
approximation, a local Taylor Series expansion, or a model hierarchy
approximation (e.g., a low-fidelity simulation model), whereas the
truth model involves a high-fidelity simulation model. The goals of
surrogate-based methods are to reduce the total number of truth model
simulations and, in the case of global data fit surrogates, to smooth
noisy data with an easily navigated analytic function.

The ``surrogate_based_global`` method was originally designed for MOGA
(a multi-objective genetic algorithm). Since genetic algorithms often
need thousands or tens of thousands of points to produce optimal or
near-optimal solutions, the use of surrogates can be helpful for
reducing the truth model evaluations. Instead of creating one set of
surrogates for the individual objectives and running the optimization
algorithm on the surrogate once, the idea is to select points along
the (surrogate) Pareto frontier, which can be used to supplement the
existing points.

In this way, one does not need to use many points initially to get a
very accurate surrogate. The surrogate becomes more accurate as the
iterations progress.
Faq::

See_Also::
