An adaptive algorithm optimizing single-particle translational displacement parameters in Metropolis Monte Carlo simulations is presented. The optimization is based on maximizing the mean square displacement of a trial move. It is shown that a large mean square displacement is strongly correlated with a high precision of average potential energy. The method is here demonstrated on model systems representing a Lennard-Jones fluid and a dilute polymer solution at poor solvent conditions. Our adaptive algorithm removes the need to provide values of displacement parameters in simulations, and it is easily extendable to optimize parameters of other types of trial moves.