Circular antenna array (CAA) is one of the most widely used antenna array designs. This paper addresses the design challenges of the CAA with the non-uniform single ring, which is placed in an X-Y plane with the best sidelobe level (SLL) and improved first null beamwidth (FNBW). It has been solved using differential evolution, craziness-based particle swarm optimization (CRPSO), and novel particle swarm optimization (NPSO) techniques. An optimal combination of feeding current and inter-element spacing provides an array pattern with the best SLL and improved FNBW, as well as some other parameter calculations of the antenna array like maximum directivity, maximum effective aperture, total effective aperture, maximum beam area, total beam area, circumference, and radius of the CAAs using these techniques. There are six designs of CAAs with different antenna elements (i.e., 10-, 12-, 16-, 20-, 36-, and 64-elements) which have been taken into account. Simulations are done in MATLAB. Based on various simulation results, we can analyze the performance of SLL and FNBW with other parameters using NPSO and compare them with different techniques of CAAs, as shown in the numerical analysis and simulation result section.