<p><b>A</b>: Two consecutive factor of 4 grid refinements and factor of 2 shell of prospective polling points refinements of the LT-MADS algorithm on a 2-dimensional Cartesian lattice; <b>B</b>: Two consecutive factor of 2 mesh refinements of the <i>位</i>-MADS algorithm on a hexagonal lattice <i>A</i><sub>2</sub> with a shell of prospective polling points at a distance of 1, 2 and 3 grid points for the initial grid (<i>k</i> = 0) and after <i>k</i> = 1 and <i>k</i> = 2 consecutive grid refinements, respectively. Search directions (in blue) of a minimal positive basis connect the current optimum point (in green) with the selected poll designs (red). Current shell of prospective polling points is marked in red, previous shell of prospective polling points is marked in orange.</p
