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In many applications of computer algebra large expressions must be simplifiedto make repeated numerical evaluations tractable. Previous works presentedheuristically guided improvements, e.g., for Horner schemes. The remainingexpression is then further reduced by common subexpression elimination. Arecent approach successfully applied a relatively new algorithm, Monte CarloTree Search (MCTS) with UCT as the selection criterion, to find better variableorderings. Yet, this approach is fit for further improvements since it issensitive to the so-called exploration-exploitation constant $C_p$ and thenumber of tree updates $N$. In this paper we propose a new selection criterioncalled Simulated Annealing UCT (SA-UCT) that has a dynamicexploration-exploitation parameter, which decreases with the iteration number$i$ and thus reduces the importance of exploration over time. First, we providean intuitive explanation in terms of the exploration-exploitation behavior ofthe algorithm. Then, we test our algorithm on three large expressions ofdifferent origins. We observe that SA-UCT widens the interval of good initialvalues $C_p$ where best results are achieved. The improvement is large (morethan a tenfold) and facilitates the selection of an appropriate $C_p$.

Combining Simulated Annealing and Monte Carlo Tree Search for Expression Simplification