A multiplicity-preserving crossover operator on graphs. Extended version

Evolutionary algorithms usually explore a search space of solutions by means of crossover and mutation. While a mutation consists of a small, local modification of a solution, crossover mixes the genetic information of two solutions to compute a new one. For model-driven optimization (MDO), where models directly serve as possible solutions (instead of first transforming them into another representation), only recently a generic crossover operator has been developed. Using graphs as a formal foundation for models, we further refine this operator in such a way that additional well-formedness constraints are preserved: We prove that, given two models that satisfy a given set of multiplicity constraints as input, our refined crossover operator computes two new models as output that also satisfy the set of constraints.