Cellular automata with cell clustering

We consider the modelling of a particular layout optimisation problem with cellular automata, namely, the LEGO construction problem. We show that this problem can be modelled easily with cellular automata, provided that cells are considered as clusters which can merge or split during each time step of the evolution of the cellular automaton. The LEGO construction problem has previously been solved with optimisation techniques based on simulated annealing and with a beam search approach, but we show that the use of cellular automata gives comparable results in general, and improves the results in many respects.