generalized_minkowski_distance

negmas.outcomes.generalized_minkowski_distance(a: Outcome, b: Outcome, outcome_space: OutcomeSpace | None, *, weights: Sequence[float] | None = None, dist_power: float = 2) → float[source]

Calculates the difference between two outcomes given an outcome-space (optionally with issue weights). This is defined as the distance.

Parameters:

  • outcome_space – The outcome space used for comparison (If None an apporximate implementation is provided)

  • a – first outcome

  • b – second outcome

  • weights – Issue weights

  • dist_power – The exponent used when calculating the distance

Remarks:

  • Implements the following distance measure:

    \[d(a, b) = \left( \sum_{i=1}^{N} w_i {\left| a_i - b_i \right|}^p \right)^{frac{1}{p}}\]

    where $a, b$ are the outocmes, $x_i$ is value for issue $i$ of outcoem $x$, $w_i$ is the weight of issue $i$ and $p$ is the dist_power passsed. Categorical issue differences is defined as $1$ if the values are not equal and $0$ otherwise.

  • Becomes the Euclidean distance if all issues are numeric and no weights are given

  • You can control the power:

    • Setting it to 1 is the city-block distance

    • Setting it to 0 is the maximum issue difference