Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances
This work addresses the challenge of experimental design for algorithm comparison, which is crucial for researchers in optimization and machine learning, though it is incremental as it generalizes earlier statistical methods.
The authors tackled the problem of determining how many problem instances are needed to reliably compare multiple algorithms, by developing a method that allows researchers to design experiments based on desired statistical power for detecting differences above a threshold, and they applied it to a case study with 21 variants of Simulated Annealing on scheduling problems.
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.