org.cicirello.permutations.distance

Class DeviationDistanceNormalized2005

java.lang.Object

org.cicirello.permutations.distance.DeviationDistanceNormalized2005

All Implemented Interfaces:

NormalizedPermutationDistanceMeasurerDouble, PermutationDistanceMeasurerDouble

public final class DeviationDistanceNormalized2005
extends Object
implements PermutationDistanceMeasurerDouble, NormalizedPermutationDistanceMeasurerDouble

Normalized Deviation Distance:

The original version of Normalized Deviation distance (Ronald, 1998) is the sum of the positional deviation of the permutation elements divided by N-1 (where N is the length of the permutation). The positional deviation of an element is the difference in its location in the two permutations. Normalizing by dividing by N-1 causes each element's contribution to distance to be in the interval [0,1].

Sevaux and Sorensen (2005) suggested a different normalizing factor that provides a distance in the interval [0,1]. Maximal distance occurs for an inverted permutation. The normalizing factor is (N²/2) when N is even and (N²-1)/2 when N is odd.

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 deviations: 1 + 1 + 1 + 2 + 0 + 3 = 8.

The length is 6, which is even, so we'll divide by 18. So, normalized deviation distance is 8 / 18 = 0.444...

If instead, p2 = [5, 4, 3, 2, 1, 0], then 0 and 5 are both displaced by 5 positions, 1 and 4 are displaced by 3 positions, and 2 and 3 are displaced by 1 position. Sum of deviations is then: 2 * 5 + 2 * 3 + 2 * 1 = 18. The length is still 6, so we again divide by 18, and distance is 1.

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

Original normalized deviation distance was introduced in:
S. Ronald, "More distance functions for order-based encodings," in Proc. IEEE CEC. IEEE Press, 1998, pp. 558–563.

This version of normalized deviation distance was introduced in:
M. Sevaux and K Sorensen, "Permutation distance measures for memetic algorithms with population management," in Proc. of MIC2005, 2005.

Since:

1.2.3

Constructor Summary

Constructors

Constructor and Description
DeviationDistanceNormalized2005() Constructs the distance measurer as specified in the class documentation.

Method Summary

Modifier and Type	Method and Description
double	distancef(Permutation p1, Permutation p2) Measures the distance between two permutations
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

DeviationDistanceNormalized2005

public DeviationDistanceNormalized2005()

Constructs the distance measurer as specified in the class documentation.

Method Detail

distancef

public 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 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 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]