Class ExponentialRankStochasticUniversalSampling

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

public final class ExponentialRankStochasticUniversalSampling extends StochasticUniversalSampling

This class implements exponential rank selection using Stochastic Universal Sampling (SUS). Exponential 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: cN-r. The c is a real-valued parameter that must be in the interval (0, 1). The most-fit member of the population will be chosen with probability proportional to 1, while the least-fit will be chosen with probability proportional to cN-1. In the limit as c approaches 1, exponential selection converges to a uniform random selection method. Whereas in the limit as c approaches 0, exponential selection converges upon a degenerate selection method that chooses an entire population of copies of the single most-fit population member. The lower the value of c, the faster the degree of exponential decline in weight given to lower ranked population members.

However, whereas the standard form of exponential 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

    • ExponentialRankStochasticUniversalSampling

      public ExponentialRankStochasticUniversalSampling(double c)
      Construct an exponential rank selection operator that uses stochastic universal sampling.
      Parameters:
      c - The base of the exponential, such that c is in the interval (0.0, 1.0). The closer c is to 0, the faster the selection weights decline from most-fit population member to least-fit, and the closer c is to 1, the closer the selection method is to a uniform random process.
      Throws:
      IllegalArgumentException - if c is less than or equal to 0 or greater than or equal to 1.
  • 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().