  In multi-objective optimization, set-based quality indicators are a
cornerstone of benchmarking and performance assessment. They capture the
quality of a set of trade-off solutions by reducing it to a scalar number. One
of the most commonly used set-based metrics is the R2 indicator, which
describes the expected utility of a solution set to a decision-maker under a
distribution of utility functions. Typically, this indicator is applied by
discretizing this distribution of utility functions, yielding a weakly
Pareto-compliant indicator. In consequence, adding a nondominated or dominating
solution to a solution set may - but does not have to - improve the indicator's
value.
  In this paper, we reinvestigate the R2 indicator under the premise that we
have a continuous, uniform distribution of (Tchebycheff) utility functions. We
analyze its properties in detail, demonstrating that this continuous variant is
indeed Pareto-compliant - that is, any beneficial solution will improve the
metric's value. Additionally, we provide an efficient computational procedure
to compute this metric for bi-objective problems in $\mathcal O (N \log N)$. As
a result, this work contributes to the state-of-the-art Pareto-compliant unary
performance metrics, such as the hypervolume indicator, offering an efficient
and promising alternative.
