Class BoltzmannStochasticUniversalSampling

All Implemented Interfaces:
Splittable<SelectionOperator>, SelectionOperator

public final class BoltzmannStochasticUniversalSampling extends BiasedStochasticUniversalSampling

This class implements Boltzmann selection using Stochastic Universal Sampling (SUS). Boltzmann selection is similar to a fitness proportional selection, except instead of a population member being weighted by its fitness f in the randomized selection process, Boltzmann selection weights it by ef/T, where f is the fitness of the individual, and T is a temperature parameter, much like that of simulated annealing. T typically decreases over the run of the evolutionary algorithm.

This implementation supports a constant temperature T, as well as two cooling schedules: linear cooling and exponential cooling. In both cases, at the start of the evolutionary algorithm, the temperature T is initialized to a t0. In linear cooling, at the end of each generation, T is updated according to: T = T - r. In exponential cooling, at the end of each generation, T is updated according to: T = r * T. In both cases, if T ever falls below some tMin, it is reset to tMin.

Unlike many other fitness proportional related selection operators, Boltzmann selection, including this SUS version, is applicable even if fitness values can be negative.

SUS and this Boltzmann SUS are similar to fitness proportional selection and a variation of fitness proportional selection biasing selection by the Boltzmann distribution. However, whereas fitness proportional selection is like spinning a carnival wheel with a single pointer M times to select M members of the population, SUS 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 fitness proportional selection. 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 for fitness proportional selection. However, SUS then must randomize the ordering of the population to avoid all of the copies of a single population member from being in sequence so that parent assignment is random, whereas fitness proportional selection has this property built in.

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

For the basic version of Boltzmann selection, see the BoltzmannSelection class. And for the standard version of SUS, see the StochasticUniversalSampling class.

  • Constructor Details

    • BoltzmannStochasticUniversalSampling

      public BoltzmannStochasticUniversalSampling(double t)
      Construct a Boltzmann selection operator with a constant temperature.
      Parameters:
      t - The temperature, which must be positive.
      Throws:
      IllegalArgumentException - if t is not positive
    • BoltzmannStochasticUniversalSampling

      public BoltzmannStochasticUniversalSampling(double t0, double tMin, double r, boolean linearCooling)
      Construct a Boltzmann selection operator, with either a linear cooling schedule or an exponential cooling schedule.
      Parameters:
      t0 - The initial temperature, which must be positive.
      tMin - The minimum temperature. If an update would decrease temperature below tMin, it is set to tMin. Must be positive and no greater than t0.
      r - The update value, which must be positive for linear cooling, and must be in (0.0, 1.0) for exponential cooling.
      linearCooling - If true, uses a linear cooling schedule, and if false it uses an exponential cooling schedule.
      Throws:
      IllegalArgumentException - if tMin is not positive or if t0 is less than tMin or if linear cooling with non-positive r or if exponential cooling with r not in (0,0, 1.0).
  • Method Details

    • init

      public void init(int generations)
      Description copied from interface: SelectionOperator
      Perform any initialization necessary for the selection operator at the start of the run of the evolutionary algorithm. This method is called by the evolutionary algorithm at the start of a run (i.e., whenever an EA's optimize or reoptimize methods are called. The default implementation of this method does nothing, which is appropriate for most selection operators since the behavior of most standard selection operators is doesn't change during runs. However, some selection operators may adjust behavior during the run, such as Boltzmann selection which adjusts a temperature parameter. The init method enables reinitializing such parameters at the start of runs.
      Parameters:
      generations - The number of generations for the run of the evolutionary algorithm about to commence.
    • 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 BiasedStochasticUniversalSampling
      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().