Problem

Any problem can be described by a class implementing the Problem interface, that defines the solution space S and a way of comparing two solutions, by extending the PartialComparator<S>.

public interface Problem<S> extends PartialComparator<S> {}

In most cases, solutions are actually compared according to their quality, i.e., based on their fitness value. We model this in the QualityBasedProblem interface, which adds two functionalities to the Problem interface: a function deputy to mapping a solution to a quality value, and a way of comparing qualities.

public interface QualityBasedProblem<S, Q> extends Problem<S> {
  Function<S, Q> qualityFunction();
  PartialComparator<Q> qualityComparator();
}

Here, Q represents the quality- or fitness-space.

We remark that qualityComparator() returns a PartialComparator<Q> and not a Comparator<Q>, as we do not necessarily want to enforce total ordering between qualities of solutions. For those cases in which we do want to enforce this, we extend QualityBasedProblem to a TotalOrderQualityBasedProblem. This interface adds a totalOrderComparator(), and provides a default implementation for the qualityComparator(), where a PartialComparator is obtained from the Comparator.

public interface TotalOrderQualityBasedProblem<S, Q> extends QualityBasedProblem<S, Q> {
  Comparator<Q> totalOrderComparator();
  @Override
  default PartialComparator<Q> qualityComparator() { /*...*/ }
}

In addition, since oftentimes the quality of a solution is “naturally comparable”, i.e., Q extends Comparable, we model this extending TotalOrderQualityBasedProblem with a ComparableQualityBasedProblem.

public interface ComparableQualityBasedProblem<S, Q extends Comparable<Q>> extends TotalOrderQualityBasedProblem<S, Q> {
  @Override
  default Comparator<Q> totalOrderComparator() {
    return Comparable::compareTo;
  }
}

To model more specific classes of problems, it is sufficient to add interfaces extending or classes implementing Problem (or one of its subinterfaces). Among them, we have already included classification problems, symbolic regression problems (including many synthetic functions recommended as benchmarks), multi-objective problems, and various benchmarks as the Ackley function, the Rastrigin function, or the K landscapes for GP.