org.cicirello.permutations.distance

Class SquaredDeviationDistance

java.lang.Object

org.cicirello.permutations.distance.SquaredDeviationDistance

All Implemented Interfaces:

NormalizedPermutationDistanceMeasurer, NormalizedPermutationDistanceMeasurerDouble, PermutationDistanceMeasurer, PermutationDistanceMeasurerDouble

public final class SquaredDeviationDistance
extends Object

Squared Deviation Distance:

Squared Deviation distance is the sum of the squares of the positional deviations of the permutation elements. The positional deviation of an element is the difference in its location in the two permutations.

For example, consider p1 = [0, 1, 2, 3, 4, 5] and p2 = [1, 0, 5, 2, 4, 3]. Element 0 is displaced by 1 position. Likewise for elements 1 and 2. Element 3 is displaced by 2 positions. Element 4 is in the same position in both. Element 5 is displaced by 3 positions.

Sum the squared deviations: 1^2 + 1^2 + 1^2 + 2^2 + 0^2 + 3^2 = 1 + 1 + 1 + 4 + 9 = 16.

Runtime: O(n), where n is the permutation length.

Squared deviation distance is described in:
M. Sevaux and K. Sorensen, "Permutation distance measures for memetic algorithms with population management," The 6th Metaheuristics International Conference, August, 2005.

Since:

1.0

Constructor Summary

Constructors

Constructor and Description
SquaredDeviationDistance() Constructs the distance measurer as specified in the class documentation.

Method Summary

Modifier and Type	Method and Description
int	distance(Permutation p1, Permutation p2) Measures the distance between two permutations.
double	distancef(Permutation p1, Permutation p2) Measures the distance between two permutations
int	max(int length) Computes the maximum possible distance between permutations of a specified length.
double	maxf(int length) Computes the maximum possible distance between permutations of a specified length.
double	normalizedDistance(Permutation p1, Permutation p2) Measures the distance between two permutations, normalized to the interval [0.0, 1.0].

Methods inherited from class java.lang.Object

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

Constructor Detail

SquaredDeviationDistance

public SquaredDeviationDistance()

Constructs the distance measurer as specified in the class documentation.

Method Detail

distance

public int distance(Permutation p1,
                    Permutation p2)

Measures the distance between two permutations.

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

max

public int max(int length)

Computes the maximum possible distance between permutations of a specified length.

Parameters:

length - Permutation length.

Returns:

the maximum distance between a pair of permutations of the specified length.

distancef

public final double distancef(Permutation p1,
                              Permutation p2)

Measures the distance between two permutations

Specified by:

distancef in interface PermutationDistanceMeasurerDouble

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

maxf

public final double maxf(int length)

Computes the maximum possible distance between permutations of a specified length.

Specified by:

maxf in interface NormalizedPermutationDistanceMeasurerDouble

Parameters:

length - Permutation length.

Returns:

the maximum distance between a pair of permutations of the specified length.

normalizedDistance

public final double normalizedDistance(Permutation p1,
                                       Permutation p2)

Measures the distance between two permutations, normalized to the interval [0.0, 1.0].

Specified by:

normalizedDistance in interface NormalizedPermutationDistanceMeasurerDouble

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2 normalized to the interval [0.0, 1.0]