Nested Performance Profiles for Benchmarking Software

In order to compare and benchmark the mathematical software, the performance profiles have been introduced [1]. However, it has been proved that the algorithm is not flawless. The main issue with the performance profile is that it may rank the solvers with respect to the best solver, by excluding the best one and running the algorithm on the remaining set of the solvers, the method may rank the solvers in a different way. We characterize such systems of problems-solvers and propose an efficient and reliable algorithm to overcome this negative side effect. The proposed method is unbiased in comparing the solvers and is successful in detecting the top ones
Comment: 9 pages, 3 figures