A genetic algorithm to search the space of Ehrhart $h^{\ast }$-vectors

We describe a genetic algorithm to find candidates for $h^{\ast }$-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 $h^{\ast }$-vector which is the Cartesian product of two lattice polytopes having unimodal $h^{\ast }$-vectors. This counterexample answers negatively to a question by Ferroni and Higashitani.