.. _method-surrogate_based_local: """"""""""""""""""""" surrogate_based_local """"""""""""""""""""" Local Surrogate Based Optimization **Topics** surrogate_based_optimization_methods .. toctree:: :hidden: :maxdepth: 1 method-surrogate_based_local-method_pointer method-surrogate_based_local-method_name method-surrogate_based_local-model_pointer method-surrogate_based_local-soft_convergence_limit method-surrogate_based_local-truth_surrogate_bypass method-surrogate_based_local-approx_subproblem method-surrogate_based_local-merit_function method-surrogate_based_local-acceptance_logic method-surrogate_based_local-constraint_relax method-surrogate_based_local-trust_region method-surrogate_based_local-max_iterations method-surrogate_based_local-convergence_tolerance method-surrogate_based_local-constraint_tolerance **Specification** - *Alias:* None - *Arguments:* None **Child Keywords:** +-------------------------+--------------------+----------------------------+-----------------------------------------------+ | Required/Optional | Description of | Dakota Keyword | Dakota Keyword Description | | | Group | | | +=========================+====================+============================+===============================================+ | Required (Choose One) | Subproblem | `method_pointer`__ | Pointer to sub-method to apply to a surrogate | | | Optimizer | | or branch-and-bound sub-problem | | | Selection +----------------------------+-----------------------------------------------+ | | | `method_name`__ | Specify sub-method by name | +-------------------------+--------------------+----------------------------+-----------------------------------------------+ | Required | `model_pointer`__ | Identifier for model block to be used by a | | | | method | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `soft_convergence_limit`__ | Limit number of iterations w/ little | | | | improvement | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `truth_surrogate_bypass`__ | Bypass lower level surrogates when performing | | | | truth verifications on a top level surrogate | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `approx_subproblem`__ | Identify functions to be included in | | | | surrogate merit function | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `merit_function`__ | Select type of penalty or merit function | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `acceptance_logic`__ | Set criteria for trusted surrogate | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `constraint_relax`__ | Enable constraint relaxation | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `trust_region`__ | Specification group for trust region model | | | | management | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `max_iterations`__ | Number of iterations allowed for optimizers | | | | and adaptive UQ methods | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `convergence_tolerance`__ | Stopping criterion based on objective | | | | function or statistics convergence | +----------------------------------------------+----------------------------+-----------------------------------------------+ | Optional | `constraint_tolerance`__ | Maximum allowable constraint violation still | | | | considered feasible | +----------------------------------------------+----------------------------+-----------------------------------------------+ .. __: method-surrogate_based_local-method_pointer.html __ method-surrogate_based_local-method_name.html __ method-surrogate_based_local-model_pointer.html __ method-surrogate_based_local-soft_convergence_limit.html __ method-surrogate_based_local-truth_surrogate_bypass.html __ method-surrogate_based_local-approx_subproblem.html __ method-surrogate_based_local-merit_function.html __ method-surrogate_based_local-acceptance_logic.html __ method-surrogate_based_local-constraint_relax.html __ method-surrogate_based_local-trust_region.html __ method-surrogate_based_local-max_iterations.html __ method-surrogate_based_local-convergence_tolerance.html __ method-surrogate_based_local-constraint_tolerance.html **Description** 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. In the surrogate-based local method, a trust region approach is used to manage the minimization process to maintain acceptable accuracy between the surrogate model and the truth model (by limiting the range over which the surrogate model is trusted). The process involves a sequence of minimizations performed on the surrogate model and bounded by the trust region. At the end of each approximate minimization, the candidate optimum point is validated using the truth model. If sufficient decrease has been obtained in the truth model, the trust region is re-centered around the candidate optimum point and the trust region will either shrink, expand, or remain the same size depending on the accuracy with which the surrogate model predicted the truth model decrease. If sufficient decrease has not been attained, the trust region center is not updated and the entire trust region shrinks by a user-specified factor. The cycle then repeats with the construction of a new surrogate model, a minimization, and another test for sufficient decrease in the truth model. This cycle continues until convergence is attained. *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) **Theory** For surrogate_based_local problems with nonlinear constraints, a number of algorithm formulations exist as described in :cite:p:`Eld06b` and as summarized in :ref:`adv_meth:sbm:sblm`.