Abstract The sequential number-theoretic optimization (SNTO) method for global optimization is improved by means of the clustering technique. In this way the improved SNTO method can easily locate potential regions for sequential search for the global optimum, thus overcoming the difficulty of the original SNTO needing the correct number of points uniformly scattering in search space for the first search. The complexity of the studied object function can be investigated with the help of the star discrepancy D *. The identification of unimodal and multimodal objective functions seems also to be possible. These findings are supported by calculations for simulated and real systems with two-way data.