The High-Performance Linpack (HPL) benchmark is the accepted standard for measuring the capacity of the world's most powerful computers, which are ranked twice yearly in the Top 500 List. Since just a small deficit in performance can cost a computer several places, it is important to tune the benchmark to obtain the best possible result. However, the adjustment of HPL's seventeen configuration parameters to obtain maximum performance is a time-consuming task that must be performed by hand. In a previous paper, we provided a preliminary study that proposed the tuning of HPL parameters by means of an Evolutionary Algorithm. The approach was validated on a small cluster. In this article, we extend this initial work by describing Acbea, a fullyautomatic benchmark tuning tool that performs both the configuration and installation of HPL followed by an automatic search for optimized parameters that will lead to the best benchmark results. Experiments have been conducted to validate this tool on several clusters, exploiting in particular the Grid'5000 infrastructure.