.. Auto-generated by scripts/generate_problem_catalog_docs.py. Do not edit by hand.

Planar truss span structural optimization (factor-of-safety maximization)
=========================================================================

A fixed-joint binary optimization problem that selects candidate planar-truss members to maximize factor of safety subject to mass and deflection thresholds.

See :doc:`../optimization` for the optimization family index.

Quick Facts
-----------

.. list-table::
   :header-rows: 1
   :widths: 20 80

   * - Field
     - Value
   * - Problem ID
     - ``planar_truss_span_fos_max``
   * - Problem Family
     - optimization
   * - Implementation
     - ``design_research_problems.problems.optimization._truss_topology:PlanarTrussEngineeringOptimizationProblem``
   * - Capabilities
     - ``baseline-solver``, ``bounded-variables``, ``external-adapter``, ``optional-evaluator``, ``statement-markdown``
   * - Study Suitability
     - none
   * - Tags
     - ``optimization``, ``truss``, ``structural``, ``binary``, ``factor-of-safety``

Taxonomy
--------

Formulation
   binary_optimization
Convexity
   nonconvex
Design Variable Type
   discrete
Is Dynamic
   no
Orientation
   engineering_practical
Feasibility Ratio Hint
   0.05
Objective Mode
   single
Constraint Nature
   hard
Bounds Summary
   one binary variable per candidate member over a fixed planar truss joint set
Tags
   ``optimization``, ``truss``, ``structural``, ``binary``, ``factor-of-safety``

Statement
---------

Choose a planar truss topology over a fixed support span and a fixed set of candidate joints. Each binary design variable decides whether one candidate member is present. The optimizer builds a concrete ``PlanarTrussState``, runs the real ``trussme`` structural analysis, and maximizes factor of safety.

Feasible candidates must satisfy maximum mass and maximum deflection thresholds. The built-in baseline uses deterministic binary enumeration with cheap graph and crossing prechecks plus hard structural thresholds.

Problem Shape
-------------

.. list-table::
   :header-rows: 1
   :widths: 30 70

   * - Field
     - Value
   * - Design Variable Count
     - 15
   * - Bound Summary
     - one binary variable per candidate member over a fixed planar truss joint set
   * - Total Constraint Count
     - 5
   * - Equality Constraint Count
     - 0
   * - Inequality Constraint Count
     - 5

Variable Bounds
---------------

.. list-table::
   :header-rows: 1
   :widths: 25 37 38

   * - Variable
     - Lower Bound
     - Upper Bound
   * - ``x[0]``
     - 0
     - 1
   * - ``x[1]``
     - 0
     - 1
   * - ``x[2]``
     - 0
     - 1
   * - ``x[3]``
     - 0
     - 1
   * - ``x[4]``
     - 0
     - 1
   * - ``x[5]``
     - 0
     - 1
   * - ``x[6]``
     - 0
     - 1
   * - ``x[7]``
     - 0
     - 1
   * - ``x[8]``
     - 0
     - 1
   * - ``x[9]``
     - 0
     - 1
   * - ``x[10]``
     - 0
     - 1
   * - ``x[11]``
     - 0
     - 1
   * - ``x[12]``
     - 0
     - 1
   * - ``x[13]``
     - 0
     - 1
   * - ``x[14]``
     - 0
     - 1

Manifest Parameters
-------------------

.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - Key
     - Value
   * - candidate_point_fractions
     - [[0.25, 0.5], [0.5, 0.5], [0.75, 0.5]]
   * - load_magnitude
     - 1000
   * - max_height
     - 5
   * - maximum_deflection
     - 0.2
   * - maximum_mass
     - 20
   * - objective_metric
     - fos-max
   * - span
     - 10

Library Interface
-----------------

- ``generate_initial_solution(seed=None)``
- ``objective(x)``
- ``evaluate(x)``
- ``solve(initial_solution=None, seed=None, maxiter=200)``