A geometric algorithm for the packing of a given sequence of polydispersed circular particles into containers of regular polygon shape is suggested. The proposed algorithm aims for a twofold goal: obtaining the maximum packing density and following the prescribed homogeneity distribution laws of polydispersed particles. When seeking for maximum density, the obtained packing is further optimized by several heuristic and stochastic optimization algorithms. The objective function for the optimization algorithm is supplied by the oblack-boxo routine, which can either determine the best possible place in the packing for each particle or allow arbitrary narrowing of the placement domain, thus accelerating the computations. The quality of packing rendered by the packing routine depends only on the initial sequence of the particles in a set. The obtained packing is stable with respect to gravitational effects. The performance of optimization methods was studied using benchmark tests of periodic and non-periodic packing of mono- and poly-sized assemblies of circular particles. Simulation quality is controlled by packing density and computational efficiency. The stability of the generated packing is proved using a discrete element method.