Summary: We propose three model-free feature extraction approaches for solving the multiple class classification problem; we use multi-objective genetic programming (MOGP) to derive (near-)optimal feature extraction stages as a precursor to classification with a simple and fast-to-train classifier. Statistically-founded comparisons are made between our three proposed approaches and seven conventional classifiers over seven datasets from the UCI Machine Learning database. We also make comparisons with other reported evolutionary computation techniques. On almost all the benchmark datasets, the MOGP approaches give better or identical performance to the best of the conventional methods. Of our proposed MOGP-based algorithms, we conclude that hierarchical feature extraction performs best on multi-classification problems.