Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks

Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry. Previous studies have shown that machine learning (ML) based approaches may outperform traditional heuristic ones on selecting the best variable ordering when the number of variables n <= 4. One main challenge for handling the general case is the exponential explosion of number of different orderings when n increases. In this paper, we propose an iterative method for generating candidate variable orderings and an ML approach for selecting the best ordering from them via learning neural network classifiers. Experimentations show that this approach outperforms heuristic ones for n = 4, 5, 6.