  Model reduction is a central topic in systems biology and dynamical systems
theory, for reducing the complexity of detailed models, finding important
parameters, and developing multi-scale models for instance. While perturbation
theory is a standard mathematical tool to analyze the different time scales of
a dynamical system, and decompose the system accordingly, tropical methods
provide a simple algebraic framework to perform these analyses systematically
in polynomial systems. The crux of these tropicalization methods is in the
computation of tropical equilibrations. In this paper we show that
constraint-based methods, using reified constraints for expressing the
equilibration conditions, make it possible to numerically solve non-linear
tropical equilibration problems, out of reach of standard computation methods.
We illustrate this approach first with the reduction of simple biochemical
mechanisms such as the Michaelis-Menten and Goldbeter-Koshland models, and
second, with performance figures obtained on a large scale on the model
repository \texttt{biomodels.net}
