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miscellaneous.md

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  1. Introduction
  2. Fitness functions
  3. Constraint handling
  4. Encodings
  5. Algorithms
  6. Genetic operators
  7. Stop conditions
  8. Metrics
  9. 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 with eachother 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 will also involve comparing floating point numbers in this case.

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 these two tolerances. The values used for them can be found using the math::Tolerances::abs and math::Tolerances::rel functions.

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 to be specified 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.

math::ScopedTolerances _(/* abs = */ 1e-10, /* rel = */ 1e-12);

Exact comparisons can be used by setting both tolerance values to 0.

math::ScopedTolerances _(0.0, 0.0);

Note that these tolerance values are global values which will be used for the comparisons on every thread, and changing their values is not thread-safe. This means that instances of the ScopedTolerances class should not be created while a genetic algorithm is running, and instances of this class should also not exist on multiple threads at once.

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 this engine in the rng namespace, so this generator doesn't have to be used directly.

The global 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.

Alternatively, the PRNG can also be reseeded using its seed method.

rng::prng.seed(new_seed);

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 only exception to this is the seed() method of the prng, which is not thread safe and shouldn't be called concurrently with the random number generation methods. In practice, this means that seed() sholdn't be called while a GA is running.

Execution

By default, the library will use multiple threads for running the genetic algorithms, with the number of threads being the number of hardware threads available as indicated by std::thread::hardware_concurrency.

This can be changed using the execution_threads function. The number of threads used will be the value specified as the argument to this function.

execution_threads(1); // run everything on a single thread

The specified thread count should be between 1 and the number of hardware threads. Numbers larger than the number of hardware threads can be set, but they will likely lead to worse performance. If 0 is specified, it will be ignored and a single thread will be used instead.

Note that this function is not thread-safe, and shouldn't be called while a genetic algorithm is running.

Determinism and reproducibility

Due to the library's reliance on random numbers generated from a global generator, the solutions to a problem will generally vary between runs even if the same parameters are used. However, it is possible to reproduce the results of previous runs by seeding the random number generator appropriately.

rng::prng.seed(0x9e3779b97f4a7c15);
const auto solutions1 = ga.solve(f);

rng::prng.seed(0x9e3779b97f4a7c15);
const auto solutions2 = ga.solve(f);

assert(solutions1 == solutions2);

As long as the PRNG is seeded with the same value before each run, the results from the runs will be the same. This will be true regardless of the number of threads used, there is no need to use single-threaded execution for this. However, the number of threads used should not be changed between the runs, as that would lead to different results.

The results also depend on the implementation of the standard library, so they will not be reproducible using different implementations. This also means that results are not generally reproducible across different platforms.