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The High-Performance Linpack (HPL)  package is a reference benchmark used worldwide to evaluate high-performance computing platforms. Adjustment of HPLpsilas seventeen tuning parameters to achieve maximum performance is a time-consuming task that must be performed by hand. In this paper, we show how a genetic algorithm may be exploited to automatically determine the best parameters possible to maximize the future results of the benchmark. Indeed we propose a GA based approach, even if we do not really specify a particular GA as our investigation relies on the Acovea framework , which managed repeated runs of the benchmark to explore the very large space of parameter combinations on the test-case cluster. This work opens the possibility of creating a fully-automatic benchmark tuning tool.