LP-based heuristics for cost-optimal planning

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LP-based heuristics for cost-optimal planning

Proceedings Article•

LP-based heuristics for cost-optimal planning

Florian Pommerening¹, Gabriele Röger¹, Malte Helmert¹, Blai Bonet²•Institutions (2)

University of Basel¹, Simón Bolívar University²

21 Jun 2014-pp 226-234

TL;DR: With this new method of analysis, dominance of the recent LP-based state-equation heuristic over optimal cost partitioning on single-variable abstractions is shown and it is shown that the previously suggested extension of the state- EQUATION heuristic to exploit safe variables cannot lead to an improved heuristic estimate.

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Abstract: Many heuristics for cost-optimal planning are based on linear programming. We cover several interesting heuristics of this type by a common framework that fixes the objective function of the linear program. Within the framework, constraints from different heuristics can be combined in one heuristic estimate which dominates the maximum of the component heuristics. Different heuristics of the framework can be compared on the basis of their constraints. With this new method of analysis, we show dominance of the recent LP-based state-equation heuristic over optimal cost partitioning on single-variable abstractions. We also show that the previously suggested extension of the state-equation heuristic to exploit safe variables cannot lead to an improved heuristic estimate. We experimentally evaluate the potential of the proposed framework on an extensive suite of benchmark tasks.

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Proceedings Article•

From non-negative to general operator cost partitioning

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Florian Pommerening¹, Malte Helmert¹, Gabriele Röger¹, Jendrik Seipp¹•Institutions (1)

University of Basel¹

25 Jan 2015

TL;DR: It is argued that this requirement for non-negative operator costs is not necessary and the benefit of using general cost partitioning is demonstrated, and it is shown that LP heuristics for operator-counting constraints are cost-partitionedHeuristics and that the state equation heuristic computes a cost partitioned over atomic projections.

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Abstract: Operator cost partitioning is a well-known technique to make admissible heuristics additive by distributing the operator costs among individual heuristics. Planning tasks are usually defined with non-negative operator costs and therefore it appears natural to demand the same for the distributed costs. We argue that this requirement is not necessary and demonstrate the benefit of using general cost partitioning. We show that LP heuristics for operator-counting constraints are cost-partitioned heuristics and that the state equation heuristic computes a cost partitioning over atomic projections. We also introduce a new family of potential heuristics and show their relationship to general cost partitioning.

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69 citations

Cites background or methods from "LP-based heuristics for cost-optima..."

...Examples of operator-counting constraints include landmark constraints, net change constraints, posthoc optimization constraints and optimal cost partitioning constraints (Pommerening et al. 2014b)....
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...Proof sketch (full proof in Pommerening et al. 2014a): The linear programs solved for h pot opt sI (s) and the state equa- tion heuristic in the initial state are each other’s duals....
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...Pommerening et al. (2014b) showed that this heuristic dominates the optimal non-negative cost-partitioning over projections to goal variables....
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...If V is a non-goal variable, a slight adaptation is needed, for which we refer to the technical report (Pommerening et al. 2014a)....
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...For the “≥” part, Pommerening et al. (2014b) showed that hSEQ dominates the optimal cost partitioning over atomic abstraction heuristics for goal variables....
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Proceedings Article•

A reminder about the importance of computing and exploiting invariants in planning

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Vidal Alcázar¹, Álvaro Torralba²•Institutions (2)

Charles III University of Madrid¹, Saarland University²

07 Jun 2015

TL;DR: This work focuses on the ability of invariants to simplify the planning task in a preprocessing step and shows that this simplification significantly improves the performance of different optimal and satisficing planners.

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Abstract: Throughout the years, extensive work has pointed out how important computing and exploiting invariants is in planning. However, no recent studies about their empirical impact regarding their ability to simplify and/or complete the model have been done. In particular, an analysis about the impact of invariants computed in regression from the goals is severely lacking, despite the existence of previous attempts to use this kind of invariants in different planning settings. In this work we focus on the ability of invariants to simplify the planning task in a preprocessing step. Our results show that this simplification significantly improves the performance of different optimal and satisficing planners.

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44 citations

Cites background from "LP-based heuristics for cost-optima..."

...The potential of completing the model using invariants is also interesting, e.g.: disambiguating undefined preconditions can positively affect LP-based heuristics (Pommerening et al. 2014) by turning actions that sometimes consume or produce an atom into actions that always do so....
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...: disambiguating undefined preconditions can positively affect LP-based heuristics (Pommerening et al. 2014) by turning actions that sometimes consume or produce an atom into actions that always do so....
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Proceedings Article•

Flow-based heuristics for optimal planning: landmarks and merges

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Blai Bonet¹, Menkes van den Briel²•Institutions (2)

Simón Bolívar University¹, Australian National University²

21 Jun 2014

TL;DR: A flow-based heuristic for optimal planning that exploits landmarks and merges that allows us to partially and incrementally merge variables, thus avoiding the formation of cross products of domains as done when merging variables in the traditional way.

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Abstract: We describe a flow-based heuristic for optimal planning that exploits landmarks and merges. The heuristic solves a linear programming (LP) problem that represents variables in SAS+ planning as a set of interacting network flow problems. The solution to the LP provides a reasonable admissible heuristic for optimal planning, but we improve it considerably by adding constraints derived from action landmarks and from variable merges. Merged variables, however, can quickly grow in size and as a result introduce many new variables and constraints into the LP. In order to control the size of the LP we introduce the concept of dynamic merging that allows us to partially and incrementally merge variables, thus avoiding the formation of cross products of domains as done when merging variables in the traditional way. The two types of improvements (action landmarks and variable merges) to the LP formulation are orthogonal and general. We measure the impact on performance for optimal planning of each improvement in isolation, and also when combined, for a simple merge strategy. The results show that the new heuristic is competitive with the current state of the art.

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33 citations

Cites background from "LP-based heuristics for cost-optima..."

...As shown by Pommerening et al. (2014), these constraints imply the upper bound values in Table 1 (we come back to this issue below)....
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...On the theoretical side, it is an open question to identify the real power of flow-based heuristics in relation to other heuristics, yet a first result in this direction is given by Pommerening et al. (2014)....
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...As said above, these experiments correspond to LPs that only contain lower bounding constraints of the flows for each atom or merge as the upper bounding constraints are redundant (Pommerening et al. 2014)....
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...On the other hand, Pommerening et al. (2014) present an unifying framework for LP-based heuristics for optimal planning....
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Proceedings Article•

Occupation Measure Heuristics for Probabilistic Planning

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Felipe W. Trevizan¹, Sylvie Thiébaux², Patrik Haslum²•Institutions (2)

NICTA¹, Australian National University²

01 Jan 2017

TL;DR: Occupation measure heuristics are derived – the first admissible heuristic for stochastic shortest path problems (SSPs) taking probabilities into account, resulting in a novel probabilistic planning approach in which policy update and heuristic computation work in unison.

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Abstract: For the past 25 years, heuristic search has been used to solve domain-independent probabilistic planning problems, but with heuristics that determinise the problem and ignore precious probabilistic information. To remedy this situation, we explore the use of occupation measures, which represent the expected number of times a given action will be executed in a given state of a policy. By relaxing the well-known linear program that computes them, we derive occupation measure heuristics – the first admissible heuristics for stochastic shortest path problems (SSPs) taking probabilities into account. We show that these heuristics can also be obtained by extending recent operator-counting heuristic formulations used in deterministic planning. Since the heuristics are formulated as linear programs over occupation measures, they can easily be extended to more complex probabilistic planning models, such as constrained SSPs (C-SSPs). Moreover, their formulation can be tightly integrated into i-dual, a recent LP-based heuristic search algorithm for (constrained) SSPs, resulting in a novel probabilistic planning approach in which policy update and heuristic computation work in unison. Our experiments in several domains demonstrate the benefits of these new heuristics and approach.

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25 citations

Cites background from "LP-based heuristics for cost-optima..."

...We have established a bridge between the more general occupation measure constraints and the operator counting constraints used in deterministic planning (Pommerening et al. 2014)....
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...This new LP exploits the fact that occupation measure heuristics can be seen as the probabilistic counterpart of the operator-counting heuristics introduced in classical deterministic planning, e.g., the net change heuristic (Pommerening et al. 2014)....
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...…on delete-relaxation (Bonet and Geffner 2001), critical path (Haslum and Geffner 2000), abstraction (Helmert, Haslum, and Hoffmann 2007), landmark (Helmert and Domshlak 2009), operator-counting (van den Briel et al. 2007, Pommerening et al. 2014), and potential heuristics (Pommerening et al. 2015)....
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...Similarly to operator-counting heuristics used in the deterministic setting (Pommerening et al. 2014), occupation measure heuristics are formulated as linear programs whose variables are occupation measures....
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...Similarly to the operator-counting heuristics (including hroc), our projection occupation measure heuristic can also be augmented with constraints that represent other state-ofthe-art heuristics, e.g., disjunctive action landmarks (Pommerening et al. 2014)....
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Journal Article•DOI•

Saturated Cost Partitioning for Optimal Classical Planning

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Jendrik Seipp, Thomas Keller, Malte Helmert

27 Jan 2020-Journal of Artificial Intelligence Research

TL;DR: This work proposes a greedy algorithm to generate orders and shows how to use hill-climbing search to optimize a given order, which leads to significantly better heuristic estimates than using the best random order that is generated in the same time.

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Abstract: Cost partitioning is a method for admissibly combining a set of admissible heuristic estimators by distributing operator costs among the heuristics. Computing an optimal cost partitioning, i.e., the operator cost distribution that maximizes the heuristic value, is often prohibitively expensive to compute. Saturated cost partitioning is an alternative that is much faster to compute and has been shown to yield high-quality heuristics. However, its greedy nature makes it highly susceptible to the order in which the heuristics are considered. We propose a greedy algorithm to generate orders and show how to use hill-climbing search to optimize a given order. Combining both techniques leads to significantly better heuristic estimates than using the best random order that is generated in the same time. Since there is often no single order that gives good guidance on the whole state space, we use the maximum of multiple orders as a heuristic that is significantly better informed than any single-order heuristic, especially when we actively search for a set of diverse orders.

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24 citations

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Journal Article•DOI•

The fast downward planning system

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Malte Helmert¹•Institutions (1)

University of Freiburg¹

01 May 2006-Journal of Artificial Intelligence Research

TL;DR: Fast Downward as discussed by the authors uses hierarchical decompositions of planning tasks for computing its heuristic function, called the causal graph heuristic, which is very different from traditional HSP-like heuristics based on ignoring negative interactions of operators.

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Abstract: Fast Downward is a classical planning system based on heuristic search. It can deal with general deterministic planning problems encoded in the propositional fragment of PDDL2.2, including advanced features like ADL conditions and effects and derived predicates (axioms). Like other well-known planners such as HSP and FF, Fast Downward is a progression planner, searching the space of world states of a planning task in the forward direction. However, unlike other PDDL planning systems, Fast Downward does not use the propositional PDDL representation of a planning task directly. Instead, the input is first translated into an alternative representation called multivalued planning tasks, which makes many of the implicit constraints of a propositional planning task explicit. Exploiting this alternative representation, Fast Downward uses hierarchical decompositions of planning tasks for computing its heuristic function, called the causal graph heuristic, which is very different from traditional HSP-like heuristics based on ignoring negative interactions of operators. In this article, we give a full account of Fast Downward's approach to solving multivalued planning tasks. We extend our earlier discussion of the causal graph heuristic to tasks involving axioms and conditional effects and present some novel techniques for search control that are used within Fast Downward's best-first search algorithm: preferred operators transfer the idea of helpful actions from local search to global best-first search, deferred evaluation of heuristic functions mitigates the negative effect of large branching factors on search performance, and multiheuristic best-first search combines several heuristic evaluation functions within a single search algorithm in an orthogonal way. We also describe efficient data structures for fast state expansion (successor generators and axiom evaluators) and present a new non-heuristic search algorithm called focused iterative-broadening search, which utilizes the information encoded in causal graphs in a novel way. Fast Downward has proven remarkably successful: It won the "classical" (i. e., propositional, non-optimising) track of the 4th International Planning Competition at ICAPS 2004, following in the footsteps of planners such as FF and LPG. Our experiments show that it also performs very well on the benchmarks of the earlier planning competitions and provide some insights about the usefulness of the new search enhancements.

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1,400 citations

Proceedings Article•

Landmarks, critical paths and abstractions: what's the difference anyway?

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Malte Helmert¹, Carmel Domshlak²•Institutions (2)

University of Freiburg¹, Technion – Israel Institute of Technology²

19 Sep 2009

TL;DR: A new admissible heuristic called the landmark cut heuristic is introduced, which compares favourably with the state of the art in terms of heuristic accuracy and overall performance.

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Abstract: Current heuristic estimators for classical domain-independent planning are usually based on one of four ideas: delete relaxations, critical paths, abstractions, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. We prove that admissible heuristics based on these ideas are in fact very closely related. Exploiting this relationship, we introduce a new admissible heuristic called the landmark cut heuristic, which compares favourably with the state of the art in terms of heuristic accuracy and overall performance.

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410 citations

"LP-based heuristics for cost-optima..." refers background or methods in this paper

...Landmark Constraints A disjunctive action landmark (Zhu and Givan 2003; Helmert and Domshlak 2009) for a state s is a set of operators of which at least one must be part of any s-plan....
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...The LM-cut heuristic (Helmert and Domshlak 2009) computes a cost partitioning for a set of action landmarks it finds....
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...A disjunctive action landmark (Zhu and Givan 2003; Helmert and Domshlak 2009) for a state s is a set of operators of which at least one must be part of any s-plan....
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Planning with Pattern Databases

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Stefan Edelkamp¹•Institutions (1)

University of Bremen¹

21 May 2014

TL;DR: Given a fixed state description based on instantiated predicates, a general abstraction scheme is provided to automatically create admissible domain-independent memory-based heuristics for planning problems, where abstractions are found in factorizing the planning space.

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Abstract: Heuristic search planning effectively finds solutions for large planning problems, but since the estimates are either not admissible or too weak, optimal solutions are found in rare cases only In contrast, heuristic pattern databases are known to significantly improve lower bound estimates for optimally solving challenging single-agent problems like the 24-Puzzle or Rubik’s Cube This paper studies the effect of pattern databases in the context of deterministic planning Given a fixed state description based on instantiated predicates, we provide a general abstraction scheme to automatically create admissible domain-independent memory-based heuristics for planning problems, where abstractions are found in factorizing the planning space We evaluate the impact of pattern database heuristics in A* and hill climbing algorithms for a collection of benchmark domains

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299 citations

"LP-based heuristics for cost-optima..." refers methods in this paper

...An example of suitable heuristics are pattern database (PDB) heuristics (Culberson and Schaeffer 1998; Edelkamp 2001), which are based on projections of a planning task to a subset (called a pattern) of the state variables....
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Proceedings Article•

Cost-optimal planning with landmarks

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Erez Karpas¹, Carmel Domshlak¹•Institutions (1)

Technion – Israel Institute of Technology¹

11 Jul 2009

TL;DR: This work proposes a methodology for deriving admissible heuristic estimates for cost-optimal planning from a set of planning landmarks, and presents a simple best-first search procedure exploiting such heuristics.

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Abstract: Planning landmarks are facts that must be true at some point in every solution plan. Previous work has very successfully exploited planning landmarks in satisficing (non-optimal) planning. We propose a methodology for deriving admissible heuristic estimates for cost-optimal planning from a set of planning landmarks. The resulting heuristics fall into a novel class of multi-path dependent heuristics, and we present a simple best-first search procedure exploiting such heuristics. Our empirical evaluation shows that this framework favorably competes with the state-of-the-art of cost-optimal heuristic search.

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165 citations

"LP-based heuristics for cost-optima..." refers background or methods in this paper

...Landmark heuristic with optimal cost partitioning Optimal cost partitioning for landmarks (Karpas and Domshlak 2009) can be expressed in our framework....
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...Several recent heuristics (van den Briel et al. 2007; Karpas and Domshlak 2009; Bonet 2013; Pommerening, Röger, and Helmert 2013) for cost-optimal planning show that it is feasible and beneficial to obtain heuristic estimates by solving a linear program for every state....
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...Using linear programming to derive heuristic estimates from landmarks was introduced by Karpas and Domshlak (2009) as cost partitioning for landmarks....
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...Introduction Several recent heuristics (van den Briel et al. 2007; Karpas and Domshlak 2009; Bonet 2013; Pommerening, Röger, and Helmert 2013) for cost-optimal planning show that it is feasible and beneficial to obtain heuristic estimates by solving a linear program for every state....
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Proceedings Article•DOI•

Sound and Complete Landmarks for And/Or Graphs

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Emil Keyder¹, Silvia Richter², Malte Helmert³•Institutions (3)

Pompeu Fabra University¹, Griffith University², University of Freiburg³

04 Aug 2010

TL;DR: It is demonstrated that this approach finds strictly more causal landmarks than previous approaches and the relationship between increased computational effort and experimental performance is discussed, using these landmarks in a recently proposed admissible landmark-counting heuristic.

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Abstract: Landmarks for a planning problem are subgoals that are necessarily made true at some point in the execution of any plan. Since verifying that a fact is a landmark is PSPACE-complete, earlier approaches have focused on finding landmarks for the delete relaxation Π+. Furthermore, some of these approaches have approximated this set of landmarks, although it has been shown that the complete set of causal delete-relaxation landmarks can be identified in polynomial time by a simple procedure over the relaxed planning graph. Here, we give a declarative characterisation of this set of landmarks and show that the procedure computes the landmarks described by our characterisation. Building on this, we observe that the procedure can be applied to any delete-relaxation problem and take advantage of a recent compilation of the m-relaxation of a problem into a problem with no delete effects to extract landmarks that take into account delete effects in the original problem. We demonstrate that this approach finds strictly more causal landmarks than previous approaches and discuss the relationship between increased computational effort and experimental performance, using these landmarks in a recently proposed admissible landmark-counting heuristic.

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94 citations

"LP-based heuristics for cost-optima..." refers methods in this paper

...The LP formulation was improved by Keyder, Richter, and Helmert (2010)....
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...As already indicated in the motivation of the landmark constraints, this follows from the related work by Keyder, Richter, and Helmert (2010) and Bonet and Helmert (2010)....
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