Many algorithms require the tuning of parameters in order to achieve optimal performance. Usually the best values of these parameters depend on both the particular conditions under which the experimental data have been acquired and the kind of information that we aim to obtain. The performance of an algorithm can be measured by means of numerical observers called Figures of Merit (FOMs). Usually there are no analytical formulas expressing the dependence of the FOMs on the parameters, but the nature of such dependence can be observed by the use of computational experiments. This article proposes a methodology for assigning values to the algorithmic parameters in the presence of a high number of FOMs. A multiobjective optimization framework is provided that identifies a set of optimal parameter values whose performance, from several points of view based on the initial FOMs, is statistically indistinguishable. This methodology is illustrated by applying it to the three-dimensional reconstruction (using an algebraic reconstruction technique) of single particles in electron microscopy.