## Class DeviationDistanceNormalized

• java.lang.Object
• org.cicirello.permutations.distance.DeviationDistanceNormalized
• All Implemented Interfaces:
`NormalizedPermutationDistanceMeasurerDouble`, `PermutationDistanceMeasurerDouble`

```public final class DeviationDistanceNormalized
extends Object
implements NormalizedPermutationDistanceMeasurerDouble```
Normalized Deviation Distance:

Normalized Deviation distance 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].

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. So, normalized deviation distance is 8 / (6-1) = 1.6.

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

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.

• ### Constructor Summary

Constructors
Constructor Description
`DeviationDistanceNormalized()`
Constructs the distance measurer as specified in the class documentation.
• ### Method Summary

All Methods
Modifier and Type Method 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.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Methods inherited from interface org.cicirello.permutations.distance.NormalizedPermutationDistanceMeasurerDouble

`normalizedDistance`
• ### Constructor Detail

• #### DeviationDistanceNormalized

`public DeviationDistanceNormalized()`
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
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 interface `NormalizedPermutationDistanceMeasurerDouble`
Parameters:
`length` - Permutation length.
Returns:
the maximum distance between a pair of permutations of the specified length.