Specific crossover and mutation operators for a grouping problem based on interaction data in a regional science context

This paper proposes a set of specific crossover and mutation operators for the delineation of functional regions through evolutionary computation. We consider a problem of dividing a given territory into local labor market areas based on spatial interaction data. Such areas are defined so that a high degree of inter-regional separation and intra-regional integration - in both cases in terms of commuting flows - exist. A genetic algorithm has been designed based on the maximization of a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. Additional requirements, typical of any functional regionalization, include the absence of overlapping between delineated regions and an exhaustive coverage of the whole territory (so all basic spatial units must be allocated to one and only one-region). The complex set of restrictions results in conventional operators often generating invalid solutions, impeding or delaying the evolutionary process. This is the reason why an extensive set of operators has been designed that incorporates knowledge about the problem, allowing the evolution of the set of solutions towards the final result.