Class TruncationSelection

java.lang.Object
org.cicirello.search.evo.TruncationSelection
All Implemented Interfaces:
Splittable<SelectionOperator>, SelectionOperator

public final class TruncationSelection extends Object implements SelectionOperator

This class implements truncation selection for evolutionary algorithms. In truncation selection, the proportion p ∈ [0.0, 1.0) of the population with greatest fitness is determined. Selection then proceeds randomly, with each member of the next generation chosen uniformly at random from among the p*N members of the population with highest fitness, where N is the size of the population. For example, if p=0.5, and if the population size N=100, then truncation selection will select individuals uniformly at random from among the 50 population members with highest fitness.

Note that in this implementation, we modify the definition slightly, without loss of generality. Specifically, rather than defining the operator in terms of a proportion, the constructor of this class includes a parameter k, which is the absolute number of greatest fitness population members to select from. For example, if population size is N, and if we want the equivalent behavior for a proportion p=0.5, we would pass 50 for k.

This selection operator is compatible with all fitness functions, even in the case of negative fitness values, since it simply compares which fitness values are higher.

The runtime to select M population members from a population of size N is O(N + M), which includes generating O(M) random int values. In a typical generational model, M=N, and this is simply O(N). Note that you will often see the runtime for truncation selection cited as O(N lg N), mistakenly assuming that sorting the population by fitness is necessary. However, it is possible to determine the k most fit members of the population without a full sort in O(N) time, as we can partition the population into the set of the k most-fit and the set of the N-k least fit using a modification of a typical order-statistics algorithm in linear time since we don't actually need a total ordering over either of those sets.

  • Constructor Details

    • TruncationSelection

      public TruncationSelection(int k)
      Constructs a truncation selection operator that selects uniformly at random from the k most fit current members of the population.
      Parameters:
      k - The number of the most fit individuals to base selection upon. The value of k must be at least 1. However, 1 is not likely to be a good choice since this means that all offspring will be based upon the single most fit individual, which means crossover will always lead to the same children.
      Throws:
      IllegalArgumentException - if k is less than 1.
  • Method Details

    • select

      public void select(PopulationFitnessVector.Integer fitnesses, int[] selected)
      Description copied from interface: SelectionOperator
      Selects a set of members of the population based on fitness. Implementations should ensure that the array of indexes of population members is in a random order. For some selection operators, this required behavior is met by definition (e.g., the common fitness proportionate selection will have this behavior as is). But other selection operators may require randomizing the array of indexes after selection. For example, the obvious implementation of stochastic universal sampling will likely have all copies of an individual population member ordered together, and thus will require a shuffling of the array before returning.
      Specified by:
      select in interface SelectionOperator
      Parameters:
      fitnesses - A vector of fitnesses of the members of the population.
      selected - An array for the result. The selection operator should select selected.length members of the population based on fitnesses, populating selected with the indexes of the chosen members. Note that selected.length may be different than the fitnesses.size().
    • select

      public void select(PopulationFitnessVector.Double fitnesses, int[] selected)
      Description copied from interface: SelectionOperator
      Selects a set of members of the population based on fitness. Implementations should ensure that the array of indexes of population members is in a random order. For some selection operators, this required behavior is met by definition (e.g., the common fitness proportionate selection will have this behavior as is). But other selection operators may require randomizing the array of indexes after selection. For example, the obvious implementation of stochastic universal sampling will likely have all copies of an individual population member ordered together, and thus will require a shuffling of the array before returning.
      Specified by:
      select in interface SelectionOperator
      Parameters:
      fitnesses - A vector of fitnesses of the members of the population.
      selected - An array for the result. The selection operator should select selected.length members of the population based on fitnesses, populating selected with the indexes of the chosen members. Note that selected.length may be different than the fitnesses.size().
    • split

      public TruncationSelection split()
      Description copied from interface: Splittable
      Generates a functionally identical copy of this object, for use in multithreaded implementations of search algorithms. The state of the object that is returned may or may not be identical to that of the original. Thus, this is a distinct concept from the functionality of the Copyable interface. Classes that implement this interface must ensure that the object returned performs the same functionality, and that it does not share any state data that would be either unsafe or inefficient for concurrent access by multiple threads. The split method is allowed to simply return the this reference, provided that it is both safe and efficient for multiple threads to share a single copy of the Splittable object. The intention is to provide a multithreaded search with the capability to provide spawned threads with their own distinct search operators. Such multithreaded algorithms can call the split method for each thread it spawns to generate a functionally identical copy of the operator, but with independent state.
      Specified by:
      split in interface Splittable<SelectionOperator>
      Returns:
      A functionally identical copy of the object, or a reference to this if it is both safe and efficient for multiple threads to share a single instance of this Splittable object.