A Hybrid Strategy to Evolve Cellular Automata Rules with a Desired Dynamical Behavior Applied to the Task Scheduling Problem

Cellular automata (CA) are discrete dynamical systems that generate complex and unpredictable behaviors. CA can exhibit a rich variety of behaviors from ordered to chaotic dynamics. An important issue in several applications is to control this dynamic in order to extract the best performance of CA rules. In the CA-based task scheduling domain, a partial answer is given by recent works that investigate two approaches named µ and ρ to evolve CA rules through a standard genetic algorithm, avoiding an undesirable dynamical behavior denoted by long-cycle and chaotic rules. Both approaches have been shown able to find CA rules with adequate dynamical behavior. However, each one presented its particularities: µ was stronger to avoid long-cycle rules and ρ obtains more refined rules (fixed-point behavior). In the present work, we investigate a new mixed approach named µρ in which the good characteristics of µ and ρ are preserved.