algorithms.md

1. Introduction
2. Fitness functions
3. Encodings
4. Algorithms
5. Genetic operators
6. Stop conditions
7. Metrics
8. Miscellaneous

---

Algorithms

The algorithms in the library refer to a part of the GAs, which are used to define different genetic algorithm variants. They consist of a selection and a population replacement strategy, which define the overall evolution process in combination with the genetic operators. For some algorithms, the selection and replacement methods may be specified independently of eachother, while other algorithms might not allow for this and simply use the methods defined as part of that algorithm.

The algorithms implemented by the library generally belong to 2 categories: single-, and multi-objective algorithms. These can only be used for single- and multi-objective optimization problems respectively. It is also possible to implement more general algorithms that work for any type of problem, but the library currently doesn't include such an algorithm.

There are 3 algorithms implemented by the library, defined in the gapp::algorithm namespace:

• SingleObjective (single-objective)
• NSGA-II (multi-objective)
• NSGA-III (multi-objective)

Selecting the algorithm

By default, if no algorithm is explicitly specified for the GA, a default one will automatically be selected based on the number of objectives of the fitness function being used. As a result of this, the default algorithm used by the GA will always be compatible with the fitness function regardless of the number of objectives.

BinaryGA ga;
ga.solve(f); // run using the default algorithm

It is also possible to explicitly select the algorithm to be used by the GA. This can be done either in the constructor or by using the algorithm method:

BinaryGA ga;
ga.algorithm(algorithm::NSGA3{});
ga.solve(f);

The only thing that should be kept in mind when selecting the algorithm this way is that it needs to be compatible with the fitness function used. The single-objective algorithms can only be used for single-objective fitness functions, and the multi-objective algorithms can only be used with multi-objective fitness functions.

If an algorithm was explicitly specified, it can be reset by passing a nullptr to the algorithm setter. This will result in the default algorithm being used, the same as in the case where no algorithm was explicitly set.

ga.algorithm(nullptr);
ga.solve(f); // uses the default algorithm

The single-objective algorithm

The SingleObjective algorithm is not a concrete algorithm implementation like the NSGA-II and NSGA-III algorithms are. It is simply a wrapper that combines a selection and a population replacement method, which can be specified independently of eachother.

The library implements several selection and population replacement methods that can be used. These are defined in the gapp::selection and gapp::replacement namespaces respectively.

BinaryGA ga;
ga.algorithm(algorithm::SingleObjective{}); // use the default selection and replacement methods
ga.solve(f);

// use tournament selection, and elitism for the population replacement methods
ga.algorithm(algorithm::SingleObjective{ selection::Tournament{}, replacement::Elitism{ 5 } });
ga.solve(f);

Custom algorithms

In addition to the algorithms provided by the library, it is also possible to use user-defined algorithms in the GAs. These must be implemented as a class derived from algorithm::Algorithm. The class technically only has to implement the selectImpl and nextPopulationImpl methods, but more complex, and efficient algorithm implementations will want to implement several additional methods.

class MyAlgorithm : public algorithm::Algorithm
{
public:
    // ...
};

Custom selection and replacement methods (single-objective)

For the SingleObjective algorithms, it is possible to define additional selection and replacement methods separately without having to define a completely new algorithm.

Simple selection and population replacement methods can be defined using a lambda function or some other callable type. As an example, a simple tournament selection method could be implemented the following way:

algorithm::SingleObjective algorithm;

algorithm.selection_method([](const GaInfo& context, const FitnessMatrix& fmat)
{
    size_t first  = rng::randomIdx(fmat);
    size_t second = rng::randomIdx(fmat);

    return (fmat[first][0] >= fmat[second][0]) ? first : second;
});

More complex operators can be implemented as classes derived from selection::Selection and replacement::Replacement respectively. The implementation of the simple tournament selection shown above could also be implemented this way:

class MyTournamentSelection : public selection::Selection
{
public:
    size_t selectImpl(const GaInfo& context, const FitnessMatrix& fmat) const override
    {
        size_t first  = rng::randomIdx(fmat);
        size_t second = rng::randomIdx(fmat);
        
        return (fmat[first][0] >= fmat[second][0]) ? first : second;
    }
};

This selection method could then be set for the single-objective algorithm the same way as in the case of using a lambda function:

algorithm::SingleObjective algorithm;
algorithm.selection_method(MyTournamentSelection{});

Note that a more general version of the tournament selection operator is already implemented in the library, called selection::Tournament.

---