On the crossover operator for Ga-based optimizers in sequential projection pursuit

Sequential Projection Pursuit (SPP) is a useful tool to uncover structures hidden in high-dimensional data by constructing sequentially the basis of a low-dimensional projection space where the structure is exposed. Genetic algorithms (GAs) are promising finders of optimal basis for SPP, but their performance is determined by the choice of the crossover operator. It is unknown until now which operator is more suitable for SPP. In this paper we compare, over four public datasets, the performance of eight crossover operators: three available in literature (arithmetic, single-point and multi-point) and five new proposed here (two hyperconic, two fitness-biased and one extension of arithmetic crossover). The proposed hyperconic operators and the multi-point operator showed the best performance, finding high-fitness projections. However, it was noted that the final selection is dependent on the dataset dimension and the timeframe allowed to get the answer. Some guidelines to select the most appropriate operator for each situation are presented.