  This work presents a new evolutionary optimization algorithm in theoretical
mathematics with important applications in scientific computing. The use of the
evolutionary algorithm is justified by the difficulty of the study of the
parametrization of an algebraic variety, an important problem in algebraic
geometry. We illustrate an application, Evo-Runge-Kutta, in a problem of
numerical analysis. Results show the design and the optimization of particular
algebraic variety, the explicit s levels Runge-Kutta methods of order q. The
mapping between algebraic geometry and evolutionary optimization is direct, and
we expect that many open problems will be modelled in the same way.
