- All Implemented Interfaces:
public final class DeviationDistanceNormalized2005 extends Object implements NormalizedPermutationDistanceMeasurerDoubleNormalized 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.
Constructors Constructor Description
DeviationDistanceNormalized2005()Constructs the distance measurer as specified in the class documentation.
All Methods Instance Methods Concrete Methods Modifier and Type Method Description
distancef(Permutation p1, Permutation p2)Measures the distance between two permutations
maxf(int length)Computes the maximum possible distance between permutations of a specified length.
normalizedDistance(Permutation p1, Permutation p2)Measures the distance between two permutations, normalized to the interval [0.0, 1.0].
public double distancef(Permutation p1, Permutation p2)Measures the distance between two permutations
public double maxf(int length)Description copied from interface:
NormalizedPermutationDistanceMeasurerDoubleComputes the maximum possible distance between permutations of a specified length.
public double normalizedDistance(Permutation p1, Permutation p2)
Measures the distance between two permutations, normalized to the interval [0.0, 1.0].
- Specified by:
p1- first permutation
p2- second permutation
- distance between p1 and p2 normalized to the interval [0.0, 1.0]
IllegalArgumentException- if p1.length() is not equal to p2.length().