  Non-parametric tests can determine the better of two stochastic optimization
algorithms when benchmarking results are ordinal, like the final fitness values
of multiple trials. For many benchmarks, however, a trial can also terminate
once it reaches a pre-specified target value. When only some trials reach the
target value, two variables characterize a trial's outcome: the time it takes
to reach the target value (or not) and its final fitness value. This paper
describes a simple way to impose linear order on this two-variable trial data
set so that traditional non-parametric methods can determine the better
algorithm when neither dominates. We illustrate the method with the
Mann-Whitney U-test. A simulation demonstrates that U-scores are much more
effective than dominance when tasked with identifying the better of two
algorithms. We test U-scores by having them determine the winners of the CEC
2022 Special Session and Competition on Real-Parameter Numerical Optimization.
