Adding ML-Genetic Algorithm example (#2981)

* Adding general workflow for slurm * Adding PyMAPDL job submission * Fixing vale * Adding troubleshooting * Small fixes * small fixes * Add ml_ga example * adding missing command in example * Update doc/source/examples/extended_examples/hpc/requirements.txt Co-authored-by: wiz-inc-572fc38784[bot] <155555808+wiz-inc-572fc38784[bot]@users.noreply.github.com> * Update doc/source/examples/extended_examples/hpc/requirements.txt Co-authored-by: wiz-inc-572fc38784[bot] <155555808+wiz-inc-572fc38784[bot]@users.noreply.github.com> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Rebasing * rebase * rebase2 * Adding troubleshooting * rebase3 * small fixes * Add ml_ga example * adding missing command in example * Update doc/source/examples/extended_examples/hpc/requirements.txt Co-authored-by: wiz-inc-572fc38784[bot] <155555808+wiz-inc-572fc38784[bot]@users.noreply.github.com> * Update doc/source/examples/extended_examples/hpc/requirements.txt Co-authored-by: wiz-inc-572fc38784[bot] <155555808+wiz-inc-572fc38784[bot]@users.noreply.github.com> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Moving to one file * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Adding example reference * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Using normal classes * Remove :py: * Adding surname * Apply suggestions from code review Co-authored-by: Kathy Pippert <[email protected]> * Using literalinclude and mapdlpool context obj * Update doc/source/examples/extended_examples/hpc/hpc_ml_ga.rst * Update doc/source/examples/extended_examples/index.rst * Update doc/source/examples/extended_examples/hpc/requirements.txt Co-authored-by: wiz-inc-572fc38784[bot] <155555808+wiz-inc-572fc38784[bot]@users.noreply.github.com> * Adding links * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Spacing * fix missing ref and spacing --------- Co-authored-by: Camille <[email protected]> Co-authored-by: wiz-inc-572fc38784[bot] <155555808+wiz-inc-572fc38784[bot]@users.noreply.github.com> Co-authored-by: Kathy Pippert <[email protected]> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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diff --git a/doc/source/examples/extended_examples/hpc/hpc_ml_ga.rst b/doc/source/examples/extended_examples/hpc/hpc_ml_ga.rst
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+.. _hpc_ml_ga_example:
+
+==============================
+Genetic algorithms and PyMAPDL
+==============================
+
+This example shows how to use PyMAPDL in an HPC cluster to 
+take advantage of multiple MAPDL instances to calculate each of the
+genetic algorithm population solutions.
+To manage multiple MAPDL instances, you should use the
+:class:`~ansys.mapdl.core.pool.MapdlPool` class, which allows you
+to run multiple jobs in the background.
+
+Introduction
+============
+
+Genetic algorithms are optimization techniques inspired by the principles of natural
+selection and genetics. They are used to find solutions to complex problems by mimicking
+the process of natural selection to evolve potential solutions over successive generations.
+In a genetic algorithm, a population of candidate solutions (chromosomes) undergoes a
+series of operations, including selection, crossover, and mutation, to produce new
+generations of solutions. The fittest chromosomes, which best satisfy the problem
+constraints and objectives, are more likely to be selected for reproduction, thus
+gradually improving the overall quality of solutions over time. Genetic algorithms are
+particularly useful for solving problems where traditional methods are impractical or
+inefficient, such as optimization, search, and machine learning tasks. They find
+applications in various fields, including engineering, economics, biology, and computer science.
+
+Problem definition
+==================
+
+This example shows how to use a generic algorithm to calculate the force
+required for a double-clamped beam to deform a specific amount in its
+center.
+
+The beam model is the same as :ref:`ref_mapdl_beam`.
+It is made of ``BEAM188`` elements that span for 2.2 meters,
+and it fully clamped at both ends.
+
+The PyMAPDL beam model is defined in the ``calculate_beam()`` function as follows:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: def calculate_beam(mapdl, force):
+    :end-at: return UZ_node_12
+
+This function returns the control parameter for the model, which is the displacement at the Z-direction on the node 12 (``UZ_node_12``).
+
+
+MAPDL pool setup
+================
+
+Genetic algorithms are expensive in regard to the amount of calculations needed to reach an optimal solution. As shown earlier, many simulations must be performed to select, cross over, and mutate
+all the chromosomes across all the populations.
+For this reason, to speed up the process, it is desirable to have as many MAPDL instances as possible so that each one can calculate one chromosome fit function.
+
+To manage multiple MAPDL instances, the best approach is to use the :class:`~ansys.mapdl.core.pool.MapdlPool` class.
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: Importing packages
+    :end-at: print(pool)
+
+
+Deflection target
+=================
+
+Because this is a demonstration example, the target displacement is calculated 
+using the beam function itself with a force of 22840 :math:`N/cm^2`.
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: ## Define deflection target
+    :end-at: print(f"Setting target to {target_displacement} for force {force}")
+
+
+Genetic algorithm model
+=======================
+
+Introduction
+------------
+
+You use the `PyGAD <pygad_docs_>`_ library to configure the genetic algorithm.
+
+.. epigraph::
+
+    PyGAD is an open source Python library for building the genetic algorithm and optimizing machine learning algorithms.
+
+    PyGAD supports different types of crossover, mutation, and parent selection operators.
+    PyGAD allows different types of problems to be optimized using the genetic algorithm
+    by customizing the fitness function. It works with both single-objective and
+    multi-objective optimization problems.
+
+    From PyGAD - Python Genetic Algorithm - https://pygad.readthedocs.io/en/latest/
+
+
+Configuration
+-------------
+
+To configure the genetic algorithm, the following code is used:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: Set GA model
+    :end-at: mutation_probability = 0.5
+
+In the preceding code, the most import parameters are:
+
+* ``sol_per_pop``: Number of solutions (chromosomes) within the population.
+* ``num_generations``:  Number of genes in the solution/chromosome.
+  In this case, because only one parameter is simulated (deflection Z at node 12),
+  this value is 1.
+* ``num_parents_mating``: Number of solutions to select as parents.
+* ``parent_selection_type``:  Parent selection type. This example uses the ``rws`` type
+  (for roulette wheel selection). For more information on parent selection type,
+  see `Genetic algorithms with PyGAD: selection, crossover, mutation <ga_article_>`_
+  by Lucy Linder.
+* ``parallel_processing``: Number of parallel workers for the genetic
+  algorithm and how these workers are created. They can be created as a ``"thread"``
+  or ``"process"``. The example creates the workers as threads, and the amount is
+  equal to the number of instances.
+
+
+Helper functions
+----------------
+
+Additionally, for printing purposes, several helper functions are defined:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: import numpy as np
+    :end-at: print("=============")
+
+
+Fitness function
+----------------
+
+After all helper functions are defined, the fitness function can be defined:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: def fitness_func(ga_instance, solution, solution_idx):
+    :end-at: return fitness_criteria
+
+`PyMAPDL <pymapdl_main_>`_ and `PyGAD <pygad_docs_>`_ evaluate each chromosome using this function to
+evaluate how fit is it and assign survival probability.
+
+
+Mutation function
+-----------------
+
+To further demonstrate `PyGAD <pygad_docs_>`_ capabilities, this example uses a custom mutation
+function.
+
+This custom mutation function does two things:
+
+* **To each chromosomes**, it adds a random value between the maximum and minimum of the population.
+* **To two random chromosomes**, it additionally adds a random percentage of the mean across all the
+  population between -10% and 10%. The random chromosomes are selected independently.
+  This is to reduce the possibility of the function converging to a local minimal.
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: def mutation_func(offspring, ga_instance):
+    :end-at: return offspring
+
+
+Model assembly
+--------------
+
+Use the GA class to assemble all the parameters and functions
+created to run the simulation:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: ga_instance = pygad.GA(
+    :end-at: To count the number of generations
+
+
+Simulation
+==========
+
+Once the model is set, use the ``run()`` method to start the simulation:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: import time
+    :end-at: print(f"Time spent (minutes): {(t1-t0)/60}")
+
+
+Plot convergence
+================
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: import os
+    :end-at: print(f"Fitness value of the best solution = {solution_fitness}")
+
+
+Model storage
+==============
+
+You can store the model in a file for later reuse:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: # To save the model data:
+    :end-at: ga_instance.save(filename=filename)
+
+Load the model:
+
+.. literalinclude:: ml_ga_beam.py
+    :language: python
+    :start-at: # Load the saved GA instance
+    :end-at: loaded_ga_instance.plot_fitness()
+
+
+Simulation on an HPC cluster using SLURM
+========================================
+
+The previous steps create the PyMAPDL script.
+To see the file, you can click this link
+:download:`ml_ga_beam.py <ml_ga_beam.py>`.
+
+To run the preceding script in an HPC environment, you must
+create a Python environment, install the packages, and then run
+this script.
+
+1. Log into your HPC cluster.
+   For more information, see :ref:`ref_hpc_login`
+
+2. Create a virtual environment that is accessible from
+   the compute nodes.
+
+   .. code-block:: console
+
+      user@machine:~$ python3 -m venv /home/user/.venv
+
+   If you have problems when creating the virtual environment
+   or accessing it from the compute nodes,
+   see :ref:`ref_hpc_pymapdl_job`.
+
+3. Install the requirements for this example from the
+   :download:`requirements.txt <requirements.txt>` file.
+
+4. Create the bash script ``job.sh``:
+
+   .. code-block:: bash
+
+      #!/bin/bash
+      #SBATCH --job-name=ml_ga_beam
+      #SBATCH --time=01:00:00
+      #SBATCH --time=1:00:00
+      #SBATCH --partition=%your_partition_name%
+      #SBATCH --output=output_%j.txt
+      #SBATCH --error=error_%j.txt
+
+      # Commands to run
+      echo "Running simulation..."
+      source /home/user/.venv/bin/activate  # Activate venv
+      python ml_ga_beam.py
+      echo "Done"
+
+   Remember to replace ``%your_partition_name%`` with your cluster
+   partition.
+
+5. Run the bash script using the `sbatch <slurm_sbatch_>`_ command:
+
+   .. code-block:: console
+    
+      sbatch --nodes=1 --ntasks-per-node=10 job.sh
+
+   The preceding command allocates 10 cores for the job.
+   For optimal performance, this value should be higher than the number
+   of MAPDL instances that the
+   :class:`~ansys.mapdl.core.pool.MapdlPool` instance is creating.
+