Heterogeneous Parallel Island Models (HePIMs) run different bio-inspired algorithms (BAs) in their islands. From a variety of communication topologies and migration policies fine-tuned for homogeneous PIMs (HoPIMs), which run the same BA in all their islands, previous work introduced HePIMs that provided competitive quality solutions regarding the best-adapted BA in HoPIMs. This work goes a step forward, maintaining the population diversity provided by HePIMs, and increasing their flexibility, allowing BA reconfiguration on islands during execution: according to their performance, islands may substitute their BAs dynamically during the evolutionary process. Experiments with the introduced architectures (RecHePIMs) were applied to the NP-hard problem of sorting permutations by reversals, using four different BAs, namely, simple Genetic Algorithm, Double-point crossover Genetic Algorithm, Differential Evolution, and self-adjusting Particle Swarm Optimization. The results showed that the new reconfigurable heterogeneous models compute better quality solutions than the HePIMs closing the gap with the HoPIM running the best-adapted BA.