  Reversible Cellular Automata (RCA) are a particular kind of shift-invariant
transformations characterized by a dynamics composed only of disjoint cycles.
They have many applications in the simulation of physical systems, cryptography
and reversible computing. In this work, we formulate the search of a specific
class of RCA -- namely, those whose local update rules are defined by conserved
landscapes -- as an optimization problem to be tackled with Genetic Algorithms
(GA) and Genetic Programming (GP). In particular, our experimental
investigation revolves around three different research questions, which we
address through a single-objective, a multi-objective, and a lexicographic
approach. The results obtained from our experiments corroborate the previous
findings and shed new light on 1) the difficulty of the associated optimization
problem for GA and GP, 2) the relevance of conserved landscape CA in the domain
of cryptography and reversible computing, and 3) the relationship between the
reversibility property and the Hamming weight.
