One of the oldest and most popular approaches to automated planning is to encode the problem at hand into a propositional formula and use a Satisfiability (SAT) solver to find a solution. In all established SAT-based approaches for Hierarchical Task Network (HTN) planning, grounding the problem is necessary and oftentimes introduces a combinatorial blowup in terms of the number of actions and reductions to encode. Our contribution named Lilotane (Lifted Logic for Task Networks) eliminates this issue for Totally Ordered HTN planning by directly encoding the lifted representation of the problem at hand. We lazily instantiate the problem hierarchy layer by layer and use a novel SAT encoding which allows us to defer decisions regarding method arguments to the stage of SAT solving. We show the correctness of our encoding and compare it to the best performing prior SAT encoding in a worst-case analysis. Empirical evaluations confirm that Lilotane outperforms established SAT-based approaches, often by orders of magnitude, produces much smaller formulae on average, and compares favorably to other state-of-the-art HTN planners regarding robustness and plan quality. In the International Planning Competition (IPC) 2020, a preliminary version of Lilotane scored the second place. We expect these considerable improvements to SAT-based HTN planning to open up new perspectives for SAT-based approaches in related problem classes.

Previous efforts on making Satisfiability (SAT) solving fit for high performance computing (HPC) have led to super-linear speedups on particular formulae, but for most inputs cannot make efficient use of a large number of processors. Moreover, long latencies (minutes to days) of job scheduling make large-scale SAT solving on demand impractical for most applications. We address both issues with Mallob, a framework for job scheduling in the context of SAT solving which exploits malleability, i.e., the ability to add or remove processing power from a job during its computation. Mallob includes a massively parallel, distributed, and malleable SAT solving engine based on HordeSat with a more succinct and communication-efficient approach to clause sharing and numerous further improvements over its precursor. Experiments with up to 2560 cores show that Mallob outperforms an improved version of HordeSat and scales significantly better. Moreover, Mallob can solve many formulae in parallel while dynamically adapting the assigned resources, and jobs arriving in the system are usually initiated within a fraction of a second.

In this paper, we propose a novel SAT-based planning approach to solve totally ordered hierarchical planning problems. Our approach called “Tree-like Reduction Exploration” (Tree-REX) makes two contributions: (1) it allows to rapidly solve hierarchical planning problems by making effective use of incremental SAT solving, and (2) it implements an anytime approach that gradually improves plan quality (makespan) as time resources are allotted. Incremental SAT solving is important as it reduces the encoding volume of planning problems, it builds on information obtained from previous search iterations and speeds up the search for plans. We show that Tree-REX outperforms state-of-the-art SAT-based HTN planning with respect to run times and plan quality on most of the considered IPC domains.

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