Combining Simulated Annealing and Monte Carlo Tree Search for Expression Simplification

Ben Ruijl, Jos Vermaseren, Aske Plaat, Jaap van den Herik

2014

Abstract

In many applications of computer algebra large expressions must be simplified to make repeated numerical evaluations tractable. Previous works presented heuristically guided improvements, e.g., for Horner schemes. The remaining expression is then further reduced by common subexpression elimination. A recent approach successfully applied a relatively new algorithm, Monte Carlo Tree Search (MCTS) with UCT as the selection criterion, to find better variable orderings. Yet, this approach is fit for further improvements since it is sensitive to the so-called “exploration-exploitation” constant Cp and the number of tree updates N. In this paper we propose a new selection criterion called Simulated Annealing UCT (SA-UCT) that has a dynamic exploration-exploitation parameter, which decreases with the iteration number i and thus reduces the importance of exploration over time. First, we provide an intuitive explanation in terms of the exploration-exploitation behavior of the algorithm. Then, we test our algorithm on three large expressions of different origins. We observe that SA-UCT widens the interval of good initial values Cp where best results are achieved. The improvement is large (more than a tenfold) and facilitates the selection of an appropriate Cp.

Paper Citation

in Harvard Style

Ruijl B., Vermaseren J., Plaat A. and van den Herik J. (2014). Combining Simulated Annealing and Monte Carlo Tree Search for Expression Simplification . In Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-758-015-4, pages 724-731. DOI: 10.5220/0004925707240731

in Bibtex Style

@conference{icaart14,
author={Ben Ruijl and Jos Vermaseren and Aske Plaat and Jaap van den Herik},
title={Combining Simulated Annealing and Monte Carlo Tree Search for Expression Simplification},
booktitle={Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2014},
pages={724-731},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004925707240731},
isbn={978-989-758-015-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - Combining Simulated Annealing and Monte Carlo Tree Search for Expression Simplification
SN - 978-989-758-015-4
AU - Ruijl B.
AU - Vermaseren J.
AU - Plaat A.
AU - van den Herik J.
PY - 2014
SP - 724
EP - 731
DO - 10.5220/0004925707240731