In this paper time modulated nine-ring concentric circular antenna array (TMCCAA) using fitness based novel hybrid adaptive differential evolution with particle swarm optimization (ADEPSO) has been studied. ADEPSO is hybrid of fitness based adaptive differential evolution and particle swarm optimization (PSO). Differential evolution is a simple and robust evolutionary algorithm but sometimes causes instability problem; PSO is also a simple, population based robust evolutionary algorithm but has the problem of sub-optimality. ADEPSO has overcome the above individual disadvantages faced by both the algorithms and is used for the design of TMCCAA. The comparative case studies as Case-1 and Case-2 are made with three control parameters like uniform inter-element spacing in rings, inter-ring radii and the switching “ON” times of rings. The same array radiates at various harmonic frequencies. The first two harmonic frequencies have been considered in this work. The numerical results show Case-2, outperforms Case-1 with respect to better side lobe level (SLL), and more improved directivity. Apart from this, the authors have computed powers radiated at the center/fundamental frequency and the first two sideband frequencies, and dynamic efficiency. It is found that power radiated by any sideband frequency is very less as compared with the power radiated at the center frequency. It has been observed that as the sideband frequency increases, side band level decreases to the greater extent as compared with SLL. The aperture size is a very important constraint for the array, since there is an upper limit for the aperture size of a given array in real-life environment. Hence, in our optimization design, the maximum radius of the concentric ring array is constrained.