From 5e40a0e05bf98e4f606d69107b23a4086e48a2d3 Mon Sep 17 00:00:00 2001
From: KRM7 <70973547+KRM7@users.noreply.github.com>
Date: Tue, 15 Aug 2023 18:47:10 +0200
Subject: [PATCH] Create miscellaneous.md

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+
+1. [Introduction](introduction.md)  
+2. [Fitness functions](fitness-functions.md)  
+3. [Encodings](encodings.md)  
+4. [Algorithms](algorithms.md)  
+5. [Genetic operators](genetic-operators.md)  
+6. [Stop conditions](stop-conditions.md)  
+7. [Metrics](metrics.md)  
+8. **Miscellaneous**  
+
+------------------------------------------------------------------------------------------------
+
+# Miscellaneous
+
+## Floating-point context
+
+There are multiple places during the runs of the genetic algorithms
+where floating-point numbers are compared. First, the fitness vectors
+of the solutions need to be compared to determine which solutions
+are better. Additionally, when the GA uses real-encoding, the chromosomes
+are also encoded as vectors of floating point numbers, so comparing the
+candidate solutions can also involve comparing floating point numbers.
+
+These comparisons are not done as exact comparisons, but instead use
+an absolute and a relative tolerance value. The actual tolerance used for
+a comparison will be the greater of the two tolerances. The values used
+for these can be found using the `math::Tolerances::abs()` and
+`math::Tolerances::rel()` functions.
+
+```cpp
+std::cout << "The default absolute tolerance used is " << math::Tolerances::abs() << "\n";
+std::cout << "The default relative tolerance around 1.0 is " << math::Tolerances::rel(1.0) << "\n";
+```
+
+The tolerance values can be changed using the `ScopedTolerances`
+class, which expects the new absolute and relative tolerance values
+in its constructor. These values will be used for the lifetime of
+the `ScopedTolerances` instance, and the destructor of the class
+will reset the tolerances to their old values.
+
+```cpp
+math::ScopedTolerances _(/* abs = */ 1e-10, /* rel = */ 1e-12);
+```
+
+Exact comparisons can be used by setting both tolerance values to 0.
+
+```cpp
+math::ScopedTolerances _(0.0, 0.0);
+```
+
+
+## Random number generation
+
+Several parts of the GAs depend on random numbers in their
+implementations. These numbers are generated using a single
+global pseudo-random number generator instance. This PRNG
+instance can be accessed as `rng::prng`. There are also
+several utility functions for generating random numbers using
+the engine in the `rng` namespace, so the generator doesn't
+have to be used directly.
+
+The methods of the PRNG and all of the random generation
+utilities are thread-safe, and can be used freely by the user
+if needed, for example in the implementation of custom
+genetic operators.
+
+The generator is seeded using a constant value determined
+by the value of the `GAPP_SEED` macro. The value of this
+can be changed by defining this macro on the command line
+while building and using the library.
+
+The PRNG can also be reseeded using its `seed` method.
+
+```cpp
+rng::prng.seed(new_seed);
+```
+
+------------------------------------------------------------------------------------------------