Dakota Reference Manual: branch_and_bound

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branch_and_bound

(Experimental Capability) Solves a mixed integer nonlinear optimization problem

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required (Choose One) | Local Optimizer Selection (Group 1) | method_pointer | Pointer to sub-method to apply to a surrogate or branch-and-bound sub-problem
method_name | Specify sub-method by name
| Optional | scaling | Turn on scaling for variables, responses, and constraints

## Description

The branch-and-bound optimization methods solves mixed integer nonlinear optimization problems. It does so by partitioning the parameter space according to some criteria along the integer or discrete variables. It then relaxes (i.e., treats all variables as continuous) the sub-problems created by the partitions and solves each sub-problem with a continuous nonlinear optimization method. Results of the sub-problems are combined in such a way that yields the solution to the original optimization problem.

Default Behavior

Branch-and-bound expects all discrete variables to be relaxable. If your problem has categorical or otherwise non-relaxable discrete variables, then this is not the optimization method you are looking for.

Expected Output

The optimal solution and associated parameters will be printed to the screen output.

Usage Tips

The user must choose a nonlinear optimization method to solve the sub- problems. We recommend choosing a method that would be chosen to solve a continuous problem that has similar form to the mixed integer problem.

## Examples

    environment
      method_pointer = 'BandB'

    method
      id_method = 'BandB'
      branch_and_bound
        output verbose
        method_pointer = 'SubNLP'

    method
      id_method = 'SubNLP'
      coliny_ea
        seed = 12345
        max_iterations = 100
        max_function_evaluations = 100

    variables,
      continuous_design = 3
        initial_point   -1.0    1.5   2.0
        upper_bounds    10.0   10.0  10.0
        lower_bounds   -10.0  -10.0 -10.0
        descriptors      'x1'  'x2'  'x3'
      discrete_design_range = 2
        initial_point      2     2
        lower_bounds       1     1
        upper_bounds       4     9
        descriptors      'y1'   'y2'

    interface,
            fork
              analysis_driver = 'text_book'

    responses,
            objective_functions = 1
            nonlinear_inequality_constraints = 2
            numerical_gradients
            no_hessians