io.jenetics.ext.moea

Class Pareto

java.lang.Object

io.jenetics.ext.moea.Pareto

public final class Pareto
extends Object

Low-level utility methods for doing pareto-optimal calculations. This methods are mostly for users who wants to extend the existing MOEA classes.

Since:

4.1

Version:

4.1

Author:

Franz Wilhelmstötter

Method Summary

Modifier and Type	Method and Description
static <T> double[]	crowdingDistance(Seq<? extends T> set, ElementComparator<? super T> comparator, ElementDistance<? super T> distance, ToIntFunction<? super T> dimension) The crowding distance value of a solution provides an estimate of the density of solutions surrounding that solution.
static <T> double[]	crowdingDistance(Seq<? extends Vec<T>> set) The crowding distance value of a solution provides an estimate of the density of solutions surrounding that solution.
static <C extends Comparable<? super C>> int	dominance(C[] u, C[] v) Calculates the Pareto Dominance of the two vectors u and v.
static int	dominance(double[] u, double[] v) Calculates the Pareto Dominance of the two vectors u and v.
static int	dominance(int[] u, int[] v) Calculates the Pareto Dominance of the two vectors u and v.
static int	dominance(long[] u, long[] v) Calculates the Pareto Dominance of the two vectors u and v.
static <T> int	dominance(T[] u, T[] v, Comparator<? super T> comparator) Calculates the Pareto Dominance of the two vectors u and v.
static <T> ISeq<T>	front(Seq<? extends T> set, Comparator<? super T> dominance) Return the elements, from the given input set, which are part of the pareto front.
static <T> ISeq<Vec<T>>	front(Seq<? extends Vec<T>> set) Return the elements, from the given input set, which are part of the pareto front.
static <T> int[]	rank(Seq<? extends T> set, Comparator<? super T> dominance) Calculates the non-domination rank of the given input set, using the given dominance comparator.
static <T> int[]	rank(Seq<? extends Vec<T>> set) Calculates the non-domination rank of the given input set, using the natural order of the elements as dominance measure.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

crowdingDistance

public static <T> double[] crowdingDistance(Seq<? extends Vec<T>> set)

The crowding distance value of a solution provides an estimate of the density of solutions surrounding that solution. The crowding distance value of a particular solution is the average distance of its two neighboring solutions.

Type Parameters:

T - the vector type

Parameters:

set - the point set used for calculating the crowding distance

Returns:

the crowded distances of the set points

Throws:

NullPointerException - if the input set is null

IllegalArgumentException - if set.get(0).length() < 2

See Also:

crowdingDistance(Seq, ElementComparator, ElementDistance, ToIntFunction)

API Note:

Calculating the crowding distance has a time complexity of O(d*n*log(n)), where d is the number of dimensions and n the set size.

crowdingDistance

public static <T> double[] crowdingDistance(Seq<? extends T> set,
                                            ElementComparator<? super T> comparator,
                                            ElementDistance<? super T> distance,
                                            ToIntFunction<? super T> dimension)

The crowding distance value of a solution provides an estimate of the density of solutions surrounding that solution. The crowding distance value of a particular solution is the average distance of its two neighboring solutions.

Type Parameters:

T - the vector type

Parameters:

set - the point set used for calculating the crowding distance

comparator - the comparator which defines the (total) order of the vector elements of T

distance - the distance of two vector elements

dimension - the dimension of vector type T

Returns:

the crowded distances of the set points

Throws:

NullPointerException - if one of the arguments is null

See Also:

crowdingDistance(Seq)

API Note:

Calculating the crowding distance has a time complexity of O(d*n*log(n)), where d is the number of dimensions and n the set size.

rank

public static <T> int[] rank(Seq<? extends Vec<T>> set)

Calculates the non-domination rank of the given input set, using the natural order of the elements as dominance measure.

Type Parameters:

T - the element type

Parameters:

set - the input set

Returns:

the non-domination rank of the given input set

API Note:

Calculating the rank has a time complexity of O(n^2, where n the set size.

Reference: Kalyanmoy Deb, Associate Member, IEEE, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II, IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 6, NO. 2, APRIL 2002.

rank

public static <T> int[] rank(Seq<? extends T> set,
                             Comparator<? super T> dominance)

Calculates the non-domination rank of the given input set, using the given dominance comparator.

Type Parameters:

T - the element type

Parameters:

set - the input set

dominance - the dominance comparator used

Returns:

the non-domination rank of the given input set

API Note:

Calculating the rank has a time and space complexity of O(n^2, where n the set size.

Reference: Kalyanmoy Deb, Associate Member, IEEE, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II, IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 6, NO. 2, APRIL 2002.

front

public static <T> ISeq<Vec<T>> front(Seq<? extends Vec<T>> set)

Return the elements, from the given input set, which are part of the pareto front. The Comparable interface defines the dominance measure of the elements, used for calculating the pareto front.

Reference: E. Zitzler and L. Thiele. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach, IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257-271, 1999.

Type Parameters:

T - the element type

Parameters:

set - the input set

Returns:

the elements which are part of the pareto set

Throws:

NullPointerException - if one of the arguments is null

front

public static <T> ISeq<T> front(Seq<? extends T> set,
                                Comparator<? super T> dominance)

Return the elements, from the given input set, which are part of the pareto front.

Reference: E. Zitzler and L. Thiele. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach, IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257-271, 1999.

Type Parameters:

T - the element type

Parameters:

set - the input set

dominance - the dominance comparator used

Returns:

the elements which are part of the pareto set

Throws:

NullPointerException - if one of the arguments is null

dominance

public static <C extends Comparable<? super C>> int dominance(C[] u,
                                                              C[] v)

Calculates the Pareto Dominance of the two vectors u and v.

Type Parameters:

C - the element type of vector u and v

Parameters:

u - the first vector

v - the second vector

Returns:

1 if u ≻ v, -1 if v ≻ u and 0 otherwise

Throws:

NullPointerException - if one of the arguments is null

IllegalArgumentException - if u.length != v.length

See Also:

Vec.dominance(Comparable[], Comparable[])

dominance

public static <T> int dominance(T[] u,
                                T[] v,
                                Comparator<? super T> comparator)

Calculates the Pareto Dominance of the two vectors u and v.

Type Parameters:

T - the element type of vector u and v

Parameters:

u - the first vector

v - the second vector

comparator - the element comparator which is used for calculating the dominance

Returns:

1 if u ≻ v, -1 if v ≻ u and 0 otherwise

Throws:

NullPointerException - if one of the arguments is null

IllegalArgumentException - if u.length != v.length

See Also:

Vec.dominance(Object[], Object[], Comparator)

dominance

public static int dominance(int[] u,
                            int[] v)

Calculates the Pareto Dominance of the two vectors u and v.

Parameters:

u - the first vector

v - the second vector

Returns:

1 if u ≻ v, -1 if v ≻ u and 0 otherwise

Throws:

NullPointerException - if one of the arguments is null

IllegalArgumentException - if u.length != v.length

See Also:

Vec.dominance(int[], int[])

dominance

public static int dominance(long[] u,
                            long[] v)

Calculates the Pareto Dominance of the two vectors u and v.

Parameters:

u - the first vector

v - the second vector

Returns:

1 if u ≻ v, -1 if v ≻ u and 0 otherwise

Throws:

NullPointerException - if one of the arguments is null

IllegalArgumentException - if u.length != v.length

See Also:

Vec.dominance(long[], long[])

dominance

public static int dominance(double[] u,
                            double[] v)

Calculates the Pareto Dominance of the two vectors u and v.

Parameters:

u - the first vector

v - the second vector

Returns:

1 if u ≻ v, -1 if v ≻ u and 0 otherwise

Throws:

NullPointerException - if one of the arguments is null

IllegalArgumentException - if u.length != v.length

See Also:

Vec.dominance(double[], double[])