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Exact approaches to Frequent Itemsets Mining (FIM) are characterised by poor runtime performance when dealing with large database instances. Several FIM bio-inspired approaches have been proposed to overcome this issue. These are considerably more efficient from the point of view of runtime performance, but they still yield poor quality solutions. The quality of the solution, i.e., the number of frequent itemsets discovered, can be increased by improving the randomised search of the solutions space considering intrinsic features of the FIM problem. This paper proposes a new framework for FIM bio-inspired approaches that considers the recursive property of frequent itemsets, i.e., the same feature exploited by the Apriori exact heuristic, in the search of the solution space. We define two new approaches to FIM, namely GA-Apriori and PSO-Apriori, based on the proposed framework, which use genetic algorithms …