Two new efficient methods for finding stable atomic clusters are introduced in this work. A purely algebraic and geometrical approach based on shape analysis provides a consistent set for optimization of structures which converge to local and global low-energy configurations. A second proposal based on the Thompson theory gives also candidate structures which became in equilibrium faster than the standard stochastic search models. The performance of the approaches is compared in three metal atomic clusters involving magic numbers. Both methods find the global and local low-energy structures reported in literature, but also obtain new structures. For Cu8, Ag8 and Ag18 the shape analysis method provides more structures than the approach based on Thompson theory. © Published under licence by IOP Publishing Ltd.