.. index:: single: milp_branch_and_bound
.. _milp_branch_and_bound/0:

.. rst-class:: right

**object**

``milp_branch_and_bound``
=========================

Portable depth-first branch-and-bound solver for small mixed-integer linear programs.

| **Availability:** 
|    ``logtalk_load(linear_programming(loader))``

| **Author:** Paulo Moura
| **Version:** 1:0:0
| **Date:** 2026-09-03

| **Compilation flags:**
|    ``static, context_switching_calls``


| **Imports:**
|    ``public`` :ref:`linear_programming_common <linear_programming_common/0>`
| **Uses:**
|    :ref:`list <list/0>`
|    :ref:`simplex <simplex/0>`

| **Remarks:**

   - Discrete domains: Integer and binary variables must have finite bounds. No cutting planes or primal heuristics are used.
   - LP relaxations: Each search node is solved using the simplex object.
   - Branching: The solver can branch on the first fractional variable or the most fractional variable, with declaration order breaking ties. The lower or upper branch can be explored first.

| **Inherited public predicates:**
|     :ref:`options_protocol/0::check_option/1`  :ref:`options_protocol/0::check_options/1`  :ref:`linear_programming_protocol/0::constraint/5`  :ref:`linear_programming_protocol/0::constraints/3`  :ref:`options_protocol/0::default_option/1`  :ref:`options_protocol/0::default_options/1`  :ref:`linear_programming_protocol/0::new_problem/1`  :ref:`linear_programming_protocol/0::objective/4`  :ref:`linear_programming_protocol/0::objective_value/2`  :ref:`options_protocol/0::option/2`  :ref:`options_protocol/0::option/3`  :ref:`linear_programming_protocol/0::print_problem/1`  :ref:`linear_programming_protocol/0::print_solution/1`  :ref:`linear_programming_protocol/0::problem_from_matrices/8`  :ref:`linear_programming_protocol/0::solve/2`  :ref:`linear_programming_protocol/0::solve/3`  :ref:`linear_programming_protocol/0::statistics/2`  :ref:`linear_programming_protocol/0::status/2`  :ref:`options_protocol/0::valid_option/1`  :ref:`options_protocol/0::valid_options/1`  :ref:`linear_programming_protocol/0::variable/4`  :ref:`linear_programming_protocol/0::variable/6`  :ref:`linear_programming_protocol/0::variable_value/3`  

.. contents::
   :local:
   :backlinks: top

Public predicates
-----------------

(no local declarations; see entity ancestors if any)

Protected predicates
--------------------

(no local declarations; see entity ancestors if any)

Private predicates
------------------

(no local declarations; see entity ancestors if any)

Operators
---------

(none)

.. seealso::

   :ref:`simplex <simplex/0>`, :ref:`linear_programming_protocol <linear_programming_protocol/0>`