  Decision trees are essential yet NP-complete to train, prompting the
widespread use of heuristic methods such as CART, which suffers from
sub-optimal performance due to its greedy nature. Recently, breakthroughs in
finding optimal decision trees have emerged; however, these methods still face
significant computational costs and struggle with continuous features in
large-scale datasets and deep trees. To address these limitations, we introduce
a moving-horizon differential evolution algorithm for classification trees with
continuous features (MH-DEOCT). Our approach consists of a discrete tree
decoding method that eliminates duplicated searches between adjacent samples, a
GPU-accelerated implementation that significantly reduces running time, and a
moving-horizon strategy that iteratively trains shallow subtrees at each node
to balance the vision and optimizer capability. Comprehensive studies on 68 UCI
datasets demonstrate that our approach outperforms the heuristic method CART on
training and testing accuracy by an average of 3.44% and 1.71%, respectively.
Moreover, these numerical studies empirically demonstrate that MH-DEOCT
achieves near-optimal performance (only 0.38% and 0.06% worse than the global
optimal method on training and testing, respectively), while it offers
remarkable scalability for deep trees (e.g., depth=8) and large-scale datasets
(e.g., ten million samples).
