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IDE-style treadle pump material minimization problem
====================================================

A citation-backed nonlinear optimization benchmark that fixes a low-flow Zone I IDE-style treadle-pump operating point and minimizes a reduced material-volume proxy.

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

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

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   * - Field
     - Value
   * - Problem ID
     - ``treadle_pump_ide_material_min``
   * - Problem Family
     - optimization
   * - Implementation
     - ``design_research_problems.problems.optimization._ide_treadle:IDETreadlePumpMaterialMin``
   * - Capabilities
     - ``baseline-solver``, ``bounded-variables``, ``citation-backed``, ``equality-constraint``, ``statement-markdown``
   * - Study Suitability
     - none
   * - Tags
     - ``optimization``, ``continuous``, ``nonlinear``, ``hydraulic``, ``scalarized``, ``treadle-pump``

Taxonomy
--------

Formulation
   nonlinear_program
Convexity
   not_guaranteed
Design Variable Type
   continuous
Is Dynamic
   no
Orientation
   engineering-practical
Feasibility Ratio Hint
   0.2
Objective Mode
   single
Constraint Nature
   hard
Bounds Summary
   four continuous variables with fixed low-flow Zone I targets and an analytic two-variable baseline reconstruction
Tags
   ``optimization``, ``continuous``, ``nonlinear``, ``hydraulic``, ``scalarized``, ``treadle-pump``

Statement
---------

This packaged optimization problem is a scalarized, citation-backed surrogate derived from the published IDE-style treadle pump studies. It fixes a low-flow Zone I operating point at 2.5 L/s and 1.9 m suction lift, then minimizes a reduced material-volume proxy for the pump.

To fit the current single-objective API cleanly, the packaged instance uses four continuous design variables: cylinder radius, hose radius, treadle length, and stepping cadence. The built-in baseline solver searches over the two primary geometric variables and analytically reconstructs the hose radius and cadence needed to satisfy the flow and lift equalities at each candidate.

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

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   * - Field
     - Value
   * - Design Variable Count
     - 4
   * - Bound Summary
     - four continuous variables with fixed low-flow Zone I targets and an analytic two-variable baseline reconstruction
   * - Total Constraint Count
     - 5
   * - Equality Constraint Count
     - 2
   * - Inequality Constraint Count
     - 3

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

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   * - Variable
     - Lower Bound
     - Upper Bound
   * - ``x[0]``
     - 0.018
     - 0.035
   * - ``x[1]``
     - 0.01
     - 0.028
   * - ``x[2]``
     - 1.2
     - 2.2
   * - ``x[3]``
     - 0.6
     - 2

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

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   * - Key
     - Value
   * - target_flow_rate_lps
     - 2.5
   * - target_lift_height_m
     - 1.9

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

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

Sources
-------

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   * - Key
     - Summary
   * - ``santaeufemia2014treadle``
     - Santaeufemia et al. (2014).
   * - ``mccomb2016idetreadle``
     - McComb et al. (2016).

Raw Citation Records
--------------------

.. code-block:: text

   Santaeufemia, P. S., Johnson, N. G., McComb, C., and Shimada, K. (2014). Improving irrigation in remote areas: multi-objective optimization of a treadle pump. Proceedings of the ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2014-35463.

.. code-block:: text

   McComb, C., Johnson, N. G., and Gorman, B. T. (2016). Scenario-based robustness analysis of optimized I.D.E.-style treadle pump designs. Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2016-60127.