Dakota Reference Manual  Version 6.4 Large-Scale Engineering Optimization and Uncertainty Analysis
branch_and_bound

(Experimental Capability) Solves a mixed integer nonlinear optimization problem

## Specification

Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required
(Choose One)
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