  We describe a genetic algorithm to find candidates for $h^*$-vectors
satisfying given properties in the space of integers vectors of finite length.
We use an implementation of such algorithm to find a 52-dimensional lattice
polytope having a non-unimodal $h^*$-vector which is the Cartesian product of
two lattice polytopes having unimodal $h^*$-vectors. This counterexample
answers negatively to a question by Ferroni and Higashitani.
