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DRWN-1824 moga docs update #90

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MOGA Doc V1
certara-msale Dec 12, 2025
b3f80b1
DRWN-1824 restructure moga docs
certara-jcraig Dec 12, 2025
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32 changes: 30 additions & 2 deletions docs/Algorithms.rst
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Expand Up @@ -117,6 +117,7 @@ The "star" topology is the only implementation currently available in pyDarwin.
sort of star shape, up to the number of neighbors specified in :ref:`neighbor_number <neighbor_num_options_desc>`.


.. _moo-label:
.. _MOO_desc:

****************************
Expand All @@ -136,9 +137,36 @@ This set is then presented to the user, who selects one or more preferred models
considerations such as biological plausibility and diagnostic plots. A detailed case study of applying pyDarwin to PopPK model
selection using these methods is provided in [#f8]_.

Imagine you are deciding what car to buy. You have two objectives: you would like it to be fast (measured as lap time around the
Nürburgring track) and inexpensive (measured as cost). In addition to these numerical (objective) criteria, you also have subjective
criteria such as comfort and how fun the car is to drive. The subjective criteria cannot easily be captured numerically, and even for
the objective criteria it can be difficult to combine them into a single scalar "goodness" value using penalties, for example:

.. math::

Car \enspace \textit{"goodness"} = Nürburgring \enspace time \enspace (seconds) + \frac{Cost}{500}

In this example the penalty on cost is cost divided by 500. The value 500 is subjective and somewhat arbitrary; another person would
likely choose a different value, and you might choose a different value after your yearly bonus. If that penalty changes after an
optimization has been run, the optimization would need to be repeated. Multi-objective optimization avoids this arbitrariness by
optimizing several objectives simultaneously and presenting a set of "non-dominated" (Pareto optimal) solutions to the user. For each
solution on the Pareto front there is no other solution that is better in every objective, and dominated solutions (worse in all
objectives than some other solution) can be discarded.

The MOO results visualize the trade-offs between the objectives, allowing users to revisit and discuss preferred solutions as
preferences change. A representative plot for the trade-off between two objectives (speed and cost) is depicted below for car
performance and cost:

.. image:: ParetoFrontCars.jpeg
:alt: Car performance vs cost
:width: 700px
:align: center

pyDarwin implements multi-objective optimization using genetic algorithms. The currently available algorithms are
MOGA (based on NSGA-II [#f6]_) and MOGA3 (based on NSGA-III [#f7]_), described in more detail below. These algorithms are configured
through the :ref:`Options List<Options>` (for example, via the ``algorithm`` option and user-specified objective definitions).
MOGA (based on NSGA-II [#f6]_) and MOGA3 (based on NSGA-III [#f7]_), described in more detail below. Additional background on
MOGA3 post-processing with user-defined R/Python code is provided in :ref:`MOGA3 post-processing <moga3_postprocessing>`.
These algorithms are configured through the :ref:`Options List<Options>` (for example, via the ``algorithm`` option and
user-specified objective definitions).

.. _MOGA_desc:

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