Design of circular arrays (CAs) and hexagonal arrays (HAs) with low sidelobe level (SLL) and high directivity is usually achieved by increasing the number of array elements, which leads to a high undesired mutual coupling. Therefore this study presents an efficient optimisation method and a framework to show how to design multi-ring concentric CAs (CCA) and concentric HAs (CHAs) configurations using a hybrid enhanced particle swarm optimisation and differential evolution (hybrid EPSO/DE) optimisation technique. The presented optimum CCA and CHA have perfect invariant SLL and high directivity with low mutual coupling by keeping the inter-element spacing not less than half a wavelength which is not possible to be achieved in CA and HA arrangements. Different configurations with two-rings, three-rings and four-rings are presented. The rotation angle of outer rings and the complex excitations of array elements are first optimised. Then, this design is further optimised using a time modulation technique by controlling the switch-on times and the phases of elements excitations of the best CCA and CHA array designs. The presented time modulated (TM) concentric CA and TM concentric HA designs attain ultra-low SLL, reduced sideband level and maximised directivity besides reducing the dynamic range of the array excitations.