Sequential projection pursuit (SPP) is a useful tool for revealing interesting structures hidden in high-dimensional data. SPP constructs sequentially the bases of a low-dimensional space where the projected data evidence such structures. Genetic algorithms (GAs) are promising finders of these bases, but their performance is determined by the choice of the crossover operator. Until now it is not clear which operator is more suitable for SPP. In this paper we compare the performance of eight crossover operators: three available in literature (arithmetic, single-point and multi-point) and five newly proposed here (two hyperconic, two fitness-biased and one extension of arithmetic crossover). The results on five benchmark datasets showed that the proposed hyperconic operators have the best performance in finding high-fitness projections. The performance of a canonical GA with one of these hyperconic operators was compared against two representative SPP optimizers, the PSO and the RSSA algorithms. We found that our GA with the hyperconic operator tends to find better solutions than the other methods at different numbers of fitness computations. These results suggest that the optimization of SPP can be improved with GAs by taking advantage of the exploratory capabilities of the proposed hyperconic operators. © 2013 Elsevier B.V.