The Particles Swarm Optimization (PSO) is an optimization technique that has been gaining attention in the last years. In this work, the PSO method is applied to optimize the productivity and the eluent consumption of the separation of the bi-naphthol enantiomers in a True Moving Bed (TMB) device. Three optimization strategies are presented: the two-steps optimization, the single optimization and a new version of the PSO algorithm, the Parallel PSO. All the three strategies showed to be efficient to perform the desired optimization. Comparing in terms of productivity and computation time (represented by the number of iterations), the Parallel PSO appeared to be the best compromise, which emphasizes the relevance of this new version to perform the optimization of the mentioned separation process. Generally, The TMB optimization results presented in this work had an average productivity that was 30% higher than the results previously reported in the literature. The best result was obtained using the Parallel PSO strategy in which a productivity of 209.2 g/L-ads/day (corresponding to an eluent consumption of only 83.9 dL/g) was achieved. As the TMB is only a theoretical model, simulations with Simulated Moving Bed (SMB) devices with four, eight and twelve columns were obtained using the equivalence between the two models, and the results were compared. (C) 2019 Elsevier Ltd. All rights reserved.