Our main objective in this article is to achieve minimum side lobe levels for a specific first null beam-width and also a minimum size of the circumference by an optimization-based design method for non-uniform, planar, and circular antenna arrays. Our approach is based on a new variant of Particle swarm Optimization technique. This new technique is a hybrid of Local Neighborhood based PSO with Hierarchical PSO Algorithms termed as Hierarchical Dynamic Local Neighborhood Based PSO (HDLPSO) Algorithm. Three difficult instances of the circular array design problem have been presented to illustrate the effectiveness of the proposed HDLPSO algorithm. The design results obtained with HDLPSO have been shown to comfortably beat the results obtained with other state-of-the-art meta-heuristics like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Invasive Weed Optimization (IWO) and Differential Evolution (DE) in a statistically significant manner.