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 N1 (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 N1 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 (N^{2}/2) when N is even and (N^{2}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 orderbased 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.


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

Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
distancef(Permutation p1, Permutation p2)
Measures the distance between two permutationsdouble
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].



Method Detail

distancef
public double distancef(Permutation p1, Permutation p2)
Measures the distance between two permutations Specified by:
distancef
in interfacePermutationDistanceMeasurerDouble
 Parameters:
p1
 first permutationp2
 second permutation Returns:
 distance between p1 and p2
 Throws:
IllegalArgumentException
 if p1.length() is not equal to p2.length().

maxf
public double maxf(int length)
Description copied from interface:NormalizedPermutationDistanceMeasurerDouble
Computes the maximum possible distance between permutations of a specified length. Specified by:
maxf
in interfaceNormalizedPermutationDistanceMeasurerDouble
 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 interfaceNormalizedPermutationDistanceMeasurerDouble
 Parameters:
p1
 first permutationp2
 second permutation Returns:
 distance between p1 and p2 normalized to the interval [0.0, 1.0]
 Throws:
IllegalArgumentException
 if p1.length() is not equal to p2.length().

