Planning as satisfiability: parallel plans and algorithms for plan search (original) (raw)

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Parallel Encodings of Classical Planning as Satisfiability

Lecture Notes in Computer Science, 2004

We consider a number of semantics for plans with parallel operator application. The standard semantics used most often in earlier work requires that parallel operators are independent and can therefore be executed in any order. We consider a more relaxed definition of parallel plans, first proposed by Dimopoulos et al., as well as normal forms for parallel plans that require every operator to be executed as early as possible. We formalize the semantics of parallel plans emerging in this setting, and propose effective translations of these semantics into the propositional logic. And finally we show that one of the semantics yields an approach to classical planning that is sometimes much more efficient than the existing SAT-based planners.

SAT-Based Parallel Planning Using a Split Representation of Actions

2009

Planning based on propositional SAT(isfiability) is a powerful approach to computing step-optimal plans given a parallel execution semantics. In this setting: (i) a solution plan must be minimal in the number of plan steps required, and (ii) non-conflicting actions can be executed instantaneously in parallel at a plan step. Underlying SAT-based approaches is the invocation of a decision procedure on a SAT encoding of a bounded version of the problem. A fundamental limitation of existing approaches is the size of these encodings. This problem stems from the use of a direct representation of actions -i.e. each action has a corresponding variable in the encoding. A longtime goal in planning has been to mitigate this limitation by developing a more compact split -also termed lifted -representation of actions in SAT encodings of parallel step-optimal problems. This paper describes such a representation. In particular, each action and each parallel execution of actions is represented uniquely as a conjunct of variables. Here, each variable is derived from action pre and post-conditions. Because multiple actions share conditions, our encoding of the planning constraints is factored and relatively compact. We find experimentally that our encoding yields a much more efficient and scalable planning procedure over the state-of-the-art in a large set of planning benchmarks.

A Compact and Efficient SAT Encoding for Planning

2008

In the planning-as-SAT paradigm there have been numerous recent developments towards improving the speed and scalability of planning at the cost of finding a step-optimal parallel plan. These developments have been towards: (1) Query strategies that efficiently yield approximately optimal plans, and (2) Having a SAT procedure compute plans from relaxed encodings of the corresponding decision problems in such a way that conflicts in a plan arising from the relaxation are resolved cheaply during a post-processing phase. In this paper we examine a third direction of tightening constraints in order to achieve a more compact, efficient, and scalable SAT-based encoding of the planning problem. For the first time, we use lifting (i.e., operator splitting) and factoring to encode the corresponding n-step decision problems with a parallel action semantics. To ensure compactness we exploit reachability and neededness analysis of the plangraph. Our encoding also captures state-dependent mutex constraints computed during that analysis. Because we adopt a lifted action representation, our encoding cannot generally support full action parallelism. Thus, our approach could be termed approximate, planning for a number of steps between that required in the optimal parallel case and the optimal linear case. We perform a detailed experimental analysis of our approach with 3 state-of-the-art SAT-based planners using benchmarks from recent international planning competitions. We find that our approach dominates optimal SAT-based planners, and is more efficient than the relaxed planners for domains where the plan existence problem is hard.

A novel constraint model for parallel planning

A parallel plan is a sequence of sets of actions such that any ordering of actions in the sets gives a traditional sequential plan. Parallel planning was popularized by the Graphplan algorithm and it is one of the key components of successful SAT-based planers. SAT-based planners have recently begun to exploit multi-valued state variables-an area which seems traditionally more suited for constraint-based planners-and they improved their performance further. In this paper we propose a novel view of constraint-based planning that uses parallel plans and multi-valued state variables. Rather than starting with the planning graph structure like other parallel planners, this novel approach is based on the idea of timelines and their synchronization.

Encoding plans in propositional logic

1996

In recent work we showed that planning problems can be efficiently solved by general propositional satisfiability algorithms (Kautz and Selman 1996). A key issue in this approach is the development of practical reductions of planning to SAT. We introduce a series of different SAT encodings for STRIPS-style planning, which are sound and complete representations of the original STRIPS specification, and relate our encodings to the Graphplan system of Blum and Furst (1995). We analyze the size complexity of the various encodings, both in terms of number of variables and total length of the resulting formulas. This paper complements the empirical evaluation of several of the encodings reported in Kautz and Selman (1996). We also introduce a novel encoding based on the theory of causal planning, that exploits the notion of "lifting" from the theorem-proving community. This new encoding strictly dominates the others in terms of asymptotic complexity. Finally, we consider further reductions in the number of variables used by our encodings, by compiling away either statevariables or action-variables.

Act, and the rest will follow: Exploiting determinism in planning as satisfiability

1998

In this paper we focus on Planning as Satisfiability (SAT). We build from the simple consideration that the values of fluents at a certain time point derive deterministically from the initial situation and the sequence of actions performed till that point. Thus, the choice of actions to perform is the only source of nondeterminism. This is a rather trivial consideration, but which has important positive consequences if implemented in current planners via SAT. In fact, it produces a dramatic size reduction of the space of the truth assignments searched in by the SAT decider used to solve the final SAT problem. To justify this claim, we repeat many of the experiments reported in (Ernst, Millstein, ~ Weld 1997), and show that the CPU time requested to solve a problem can go down up to 4 orders of magnitude.

Planning with effectively propositional logic

… of Papers Dedicated to Har-ald …, 2007

We present a fragment of predicate logic which allows the use of equality and quantification but whose models are limited to finite Herbrand interpretations. Formulae in this logic can be thought as syntactic sugar on top of the Bernays-Schönfinkel fragment and can, therefore, still be effectively grounded into a propositional representation. We motivate the study of this logic by showing that practical problems from the area of planning can be naturally and succinctly represented using the added syntactic features. Moreover, from a theoretical point of view, we show that this logic allows, when compared to the propositional approach, not only more compact encodings but also exponentially shorter refutation proofs.

LPG: A Planner Based on Local Search for Planning Graphs with Action Costs

2002

We present LPG, a fast planner using local search for solving planning graphs. LPG can use various heuristics based on a parametrized objective function. These parameters weight different types of inconsistencies in the partial plan represented by the current search state, and are dynamically evaluated during search using Lagrange multipliers. LPG's basic heuristic was inspired by Walksat, which in Kautz and Selman's Blackbox can be used to solve the SAT-encoding of a planning graph. An advantage of LPG is that its heuristics exploit the structure of the planning graph, while Blackbox relies on general heuristics for SAT-problems, and requires the translation of the planning graph into propositional clauses. Another major difference is that LPG can handle action costs to produce good quality plans. This is achieved by an "anytime" process minimizing an objective function based on the number of inconsistencies in the partial plan and on its overall cost. The objective function can also take into account the number of parallel steps and the overall plan duration. Experimental results illustrate the efficiency of our approach showing, in particular, that for a set of well-known benchmark domains LPG is significantly faster than existing Graphplan-style planners. evaluated using Lagrange multipliers. LPG's basic heuristic, Walkplan, was inspired by Walksat (Selman, Kautz, and Cohen 1994), a stochastic local search procedure which in Kautz and Selman's Blackbox (1999) can be used to solve the SAT-encoding of a planning graph .

Lpg: a planner based on local search for planning graphs

2002

We present LPG, a fast planner using local search for solving planning graphs. LPG can use various heuristics based on a parametrized objective function. These parameters weight different types of inconsistencies in the partial plan represented by the current search state, and are dynamically evaluated during search using Lagrange multipliers. LPG's basic heuristic was inspired by Walksat, which in Kautz and Selman's Blackbox can be used to solve the SAT-encoding of a planning graph. An advantage of LPG is that its heuristics exploit the structure of the planning graph, while Blackbox relies on general heuristics for SAT-problems, and requires the translation of the planning graph into propositional clauses. Another major difference is that LPG can handle action costs to produce good quality plans. This is achieved by an "anytime" process minimizing an objective function based on the number of inconsistencies in the partial plan and on its overall cost. The objective function can also take into account the number of parallel steps and the overall plan duration. Experimental results illustrate the efficiency of our approach showing, in particular, that for a set of well-known benchmark domains LPG is significantly faster than existing Graphplan-style planners. evaluated using Lagrange multipliers. LPG's basic heuristic, Walkplan, was inspired by Walksat (Selman, Kautz, and Cohen 1994), a stochastic local search procedure which in Kautz and Selman's Blackbox (1999) can be used to solve the SAT-encoding of a planning graph .

Experimental Evaluation of a Planning Language Suitable for Formal Verification

Lecture Notes in Computer Science, 2009

The marriage of model checking and planning faces two seemingly diverging alternatives: the need for a planning language expressive enough to capture the complexity of real-life applications, as opposed to a language simple, yet robust enough to be amenable to exhaustive verification and validation techniques. In an attempt to reconcile these differences, we have designed an abstract plan description language, ANMLite, inspired from the Action Notation Modeling Language (ANML). We present the basic concepts of the ANMLite language as well as an automatic translator from ANMLite to the model checker SAL (Symbolic Analysis Laboratory). We discuss various aspects of specifying a plan in terms of constraints and explore the implications of choosing a robust logic behind the specification of constraints, rather than simply propose a new planning language. Additionally, we provide an initial assessment of the efficiency of model checking to search for solutions of planning problems. To this end, we design a basic test benchmark and study the scalability of the generated SAL models in terms of plan complexity.