A physics-based model for the prediction of wildfire propagation, which combines the cellular automata concept with virtual Lagrangian fire particles, is further developed to include fire extinction actions. Deposition of water and firebreaks are included in the formulation. The fire propagation model is then coupled with a Monte Carlo Tree Search (MCTS) algorithm to optimize the allocation of fire extinction actions. Starting from an ignited fire, and fixing the amount of resources available for firefighting, the model suggests which series of actions minimizes the loss of wildland. The model has been assessed and validated with model fires and then applied to a realistic scenario. MCTS optimization is found to autonomously outperform human intuition for medium-scale fires and to successfully enhance human decision-making capabilities for large-scale fires with the use of convolution-based terrain re-sampling. This study opens up new possibilities for the development of decision-making tools to assist the real-time allocation of firefighting resources as well as to support the design of preventive measures to preserve the environment and reduce the potential impact of wildfires.