Heterogeneous Parallel Island Models (HePIMs) run different bio-inspired algorithms (BAs) in their islands. From a variety of communication topologies and migration policies finetuned 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 (GA), Double-point crossover Genetic Algorithm (GAD), Differential Evolution (DE), and self-adjusting Particle Swarm Optimization (PSO). 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.