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.

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.

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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In this work, we address an online job scheduling problem in a large distributed computing environment. Each job has a priority and a demand of resources, takes an unknown amount of time, and is malleable, i.e., the number of allotted workers can fluctuate during its execution. We subdivide the problem into (a) determining a fair amount of resources for each job and (b) assigning each job to an according number of processing elements. Our approach is fully decentralized, uses lightweight communication, and arranges each job as a binary tree of workers which can grow and shrink as necessary. Using the NP-complete problem of propositional satisfiability (SAT) as a case study, we experimentally show on up to 128 machines (6144 cores) that our approach leads to near-optimal utilization, imposes minimal computational overhead, and performs fair scheduling of incoming jobs within a few milliseconds.

Propositional satisfiability (SAT) is the problem of finding a variable assignment for a given propositional formula (i.e., a composition of Boolean variables using logical operators NOT, AND, OR) such that the formula evaluates to true, or reporting that no such assignment exists. The platform Mallob (Malleable Load Balancer, or Massively Parallel Logic Backend) enables processing SAT jobs in a (massively) parallel and distributed system on demand. Mallob's flexible, fair, and decentralized approach to online job scheduling results in scheduling latencies in the range of milliseconds, near-optimal system utilization, and high resource efficiency.

One of the classical approaches to automated planning is the reduction to propositional satisfiability (SAT). Recently, it has been shown that incremental SAT solving can increase the capabilities of several modern encodings for SAT-based planning. In this paper, we present a further improvement to SAT-based planning by introducing a new algorithm named PASAR based on the principles of counterexample guided abstraction refinement (CEGAR). As an abstraction of the original problem, we use a simplified encoding where interference between actions is generally allowed. Abstract plans are converted into actual plans where possible or otherwise used as a counterexample to refine the abstraction. Using benchmark domains from recent International Planning Competitions, we compare our approach to different state-of-the-art planners and find that, in particular, combining PASAR with forward state-space search techniques leads to promising results.