Toward Optimal FDM Toolpath Planning with Monte Carlo Tree Search

The most widely used methods for toolpath planning in 3D printing slice the input model into successive 2D layers to construct the toolpath. Unfortunately the methods can incur a substantial amount of wasted motion (i.e., the extruder is moving while not printing). In recent years we have introduced a new paradigm that characterizes the space of feasible toolpaths using a dependency graph on the input model, along with several algorithms that optimize objective functions (wasted motion or print time). A natural question that arises is, under what circumstances can we efficiently compute an optimal toolpath? In this paper, we give an algorithm for computing fused deposition modeling (FDM) toolpaths that utilizes Monte Carlo Tree Search (MCTS), a powerful generalpurpose method for navigating large search spaces that is guaranteed to converge to the optimal solution. Under reasonable assumptions on printer geometry that allow us to compress the dependency graph, our MCTS-based algorithm converges to find the optimal toolpath. We validate our algorithm on a dataset of 75 models and examine the performance on MCTS against our previous best local search-based algorithm in terms of toolpath quality. We show that a relatively short time budget for MCTS yields results on par with local search, while a larger time budget yields a 15% improvement in quality over local search. Additionally, we examine the properties of the models and MCTS executions that lead to better or worse results.