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

.. 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>`