  This work presents a statistically principled method for estimating the
required number of instances in the experimental comparison of multiple
algorithms on a given problem class of interest. This approach generalises
earlier results by allowing researchers to design experiments based on the
desired best, worst, mean or median-case statistical power to detect
differences between algorithms larger than a certain threshold. Holm's
step-down procedure is used to maintain the overall significance level
controlled at desired levels, without resulting in overly conservative
experiments. This paper also presents an approach for sampling each algorithm
on each instance, based on optimal sample size ratios that minimise the total
required number of runs subject to a desired accuracy in the estimation of
paired differences. A case study investigating the effect of 21 variants of a
custom-tailored Simulated Annealing for a class of scheduling problems is used
to illustrate the application of the proposed methods for sample size
calculations in the experimental comparison of algorithms.
