## Class BiasedFitnessProportionalSelection

• All Implemented Interfaces:
`Splittable<SelectionOperator>`, `SelectionOperator`

```public final class BiasedFitnessProportionalSelection
extends FitnessProportionalSelection```

This class implements a variation of fitness proportional selection that applies a bias function to transform the fitness values. In this biased fitness proportional selection, a member of the population is chosen randomly with probability proportional to a bias function of its fitness relative to the total of such biased fitness of the population. For example, if the fitness of population member i is fi, then the probability of selecting population member i is: bias(fi) / ∑j bias(fj), for j ∈ { 1, 2, ..., N }, where N is the population size, and bias is a bias function. To select M members of the population, M independent random decisions are executed in this way, thus requiring generating M random numbers of type double.

As an example bias function, consider: bias(x) = x2, which would square each fitness value x.

This selection operator requires positive fitness values. Behavior is undefined if any fitness values are less than or equal to 0. If your fitness values may be negative, use `BiasedShiftedFitnessProportionalSelection` instead.

The runtime to select M population members from a population of size N is O(N + M lg N), assuming the bias function has a constant runtime.

For the more common standard version of fitness proportional selection, see the `FitnessProportionalSelection` class.

• ### Constructor Summary

Constructors
Constructor Description
`BiasedFitnessProportionalSelection​(FitnessBiasFunction bias)`
Construct a biased fitness proportional selection operator.
• ### Method Summary

All Methods
Modifier and Type Method Description
`void` ```select​(PopulationFitnessVector.Double fitnesses, int[] selected)```
Selects a set of members of the population based on fitness.
`void` ```select​(PopulationFitnessVector.Integer fitnesses, int[] selected)```
Selects a set of members of the population based on fitness.
`BiasedFitnessProportionalSelection` `split()`
Generates a functionally identical copy of this object, for use in multithreaded implementations of search algorithms.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Methods inherited from interface org.cicirello.search.evo.SelectionOperator

`init`
• ### Constructor Detail

• #### BiasedFitnessProportionalSelection

`public BiasedFitnessProportionalSelection​(FitnessBiasFunction bias)`
Construct a biased fitness proportional selection operator.
Parameters:
`bias` - A bias function
• ### Method Detail

• #### split

`public BiasedFitnessProportionalSelection 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 `FitnessProportionalSelection`
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().