Class LinearRankStochasticUniversalSampling

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

public final class LinearRankStochasticUniversalSampling extends StochasticUniversalSampling

This class implements linear rank selection using Stochastic Universal Sampling (SUS). Linear rank selection begins be determining the rank of each population member, where the least fit member of the population has rank 1, and the most fit member of the population has rank N, where the population size is N. During selection, the population member with rank r is chosen randomly with probability proportional to: 2 - c + 2(r - 1)(c - 1)/(N - 1). The c is a real-valued parameter that must be in the interval [1, 2]. When c is equal to 1, all population members are equally likely chosen. When c is equal to 2, the expected number of times the most fit population member will be chosen is 2, the least fit member won't be selected at all, and the expected number of times the other population members will be chosen in a generation will vary between 0 and 2 based upon rank. To avoid a probability of 0 of choosing the least fit population member, then ensure that c is less than 2. To ensure that the selection operator doesn't degenerate into a uniform random selection, then set c greater than 1. The value of c can be interpreted as the expected number of times the most fit population member will be selected in a generation.

Linear rank selection was introduced by Baker (1985). According to "An Introduction to Genetic Algorithms" (Melanie Mitchell, 1998), Baker recommended c = 1.1.

However, whereas the standard form of linear rank selection is like spinning a carnival wheel with a single pointer M times to select M members of the population, this SUS version instead is like spinning a carnival wheel that has M equidistant pointers a single time to select all M simultaneously. One statistical consequence of this is that it reduces the variance of the selected copies of population members as compared to the other approach. Another consequence is that SUS is typically much faster since only a single random floating point number is needed per generation, compared to M random floating-point numbers.

The runtime to select M population members from a population of size N is O(N lg N + M), which includes the need to generate only a single random double, and O(M) random ints..

  • Constructor Details

    • LinearRankStochasticUniversalSampling

      public LinearRankStochasticUniversalSampling(double c)
      Construct a linear rank selection operator that uses stochastic universal sampling.
      Parameters:
      c - The expected number of times the most fit population member should be selected during one generation, which must be in the interval [1.0, 2.0].
      Throws:
      IllegalArgumentException - if c is less than 1 or greater than 2.
  • Method Details

    • 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>
      Overrides:
      split in class StochasticUniversalSampling
      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.
    • select

      public final 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 final 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().