Recent real-time heuristic search algorithms have demonstrated outstanding performance in video-game pathfinding. However, their applications have been thus far limited to that domain. We proceed with the aim of facilitating wider applications of real-time search by fostering a greater understanding of the performance of recent algorithms. We first introduce eight algorithm-independent complexity measures for search spaces and correlate their values with algorithm performance. The complexity measures are statistically shown to be significant predictors of algorithm performance across a set of commercial video-game maps. We then extend this analysis to a wider variety of search spaces in the first application of database-driven real-time search to domains outside of video-game pathfinding. In doing so, we gain insight into algorithm performance and possible enhancement as well as into search space complexity.
More recently, Hoffman extended a similar study of heuristic topology The terms topography and topology are used interchangeably in the literature when discussing heuristic functions. to general planning @cite_32 @cite_12 . On a set of @math well-established planning benchmarks, he enumerated topological heuristic features and domain properties to sort the benchmarks into a complexity taxonomy. This is similar to our ranking of search spaces based on complexity in Sections and , although Hoffman does not compute empirical correlations to performance. Hoffman concluded that the benchmark taxonomy would shed insight on the levels of success of heuristic search planning in these benchmarks. He also claimed that it could inform subsequent improvement of heuristic functions, allow prediction of planning performance and assist in developing more challenging benchmark sets.
@cite_32 @cite_12
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Many state-of-the-art heuristic planners derive their heuristic function by relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. Looking at a collection of planning benchmarks, we measure topological properties of state spaces with respect to that relaxation. The results suggest that, given the heuristic based on the relaxation, many planning benchmarks are simple in structure. This sheds light on the recent success of heuristic planners employing local search. Between 1998 and 2004, the planning community has seen vast progress in terms of the sizes of benchmark examples that domain-independent planners can tackle successfully. The key technique behind this progress is the use of heuristic functions based on relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The unprecedented success of such methods, in many commonly used benchmark examples, calls for an understanding of what classes of domains these methods are well suited for. In the investigation at hand, we derive a formal background to such an understanding. We perform a case study covering a range of 30 commonly used STRIPS and ADL benchmark domains, including all examples used in the first four international planning competitions. We prove connections between domain structure and local search topology – heuristic cost surface properties – under an idealized version of the heuristic functions used in modern planners. The idealized heuristic function is called h + , and differs from the practically used functions in that it returns the length of an optimal relaxed plan, which is NP-hard to compute. We identify several key characteristics of the topology under h + , concerning the existence non-existence of unrecognized dead ends, as well as the existence non-existence of constant upper bounds on the difficulty of escaping local minima and benches. These distinctions divide the (set of all) planning domains into a taxonomy of classes of varying h + topology. As it turns out, many of the 30 investigated domains lie in classes with a relatively easy topology. Most particularly, 12 of the domains lie in classes where FF’s search algorithm, provided with h + , is a polynomial solving mechanism. We also present results relating h + to its approximation as implemented in FF. The behavior regarding dead ends is provably the same. We summarize the results of an empirical investigation showing that, in many domains, the topological qualities of h + are largely inherited by the approximation. The overall investigation gives a rare example of a successful analysis of the connections between typical-case problem structure, and search performance. The theoretical investigation also gives hints on how the topological phenomena might be automatically recognizable by domain analysis techniques. We outline some preliminary steps we made into that direction. Many state-of-the-art heuristic planners derive their heuristic function by relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The success of such planners on many of the current benchmarks suggests that in those task's state spaces relaxed goal distances yield a heuristic function of high quality. Recent work has revealed empirical evidence confirming this intuition, stating several hypotheses about the local search topology of the current benchmarks, concerning the non-existence of dead ends and of local minima, as well as a limited maximal distance to exits on benches. Investigating a large range of planning domains, we prove that the above hypotheses do in fact hold true for the majority of the current benchmarks. This explains the recent success of heuristic planners. Specifically, it follows that FF's search algorithm, using an idealized heuristic function, is polynomial in (at least) eight commonly used benchmark domains. Our proof methods shed light on what the structural reasons are behind the topological phenomena, giving hints on how these phenomena might be automatically recognizable. Beam search is commonly used to help maintain tractability in large search spaces at the expense of completeness and optimality. Here we study supervised learning of linear ranking functions for controlling beam search. The goal is to learn ranking functions that allow for beam search to perform nearly as well as unconstrained search, and hence gain computational efficiency without seriously sacrificing optimality. In this paper, we develop theoretical aspects of this learning problem and investigate the application of this framework to learning in the context of automated planning. We first study the computational complexity of the learning problem, showing that even for exponentially large search spaces the general consistency problem is in NP. We also identify tractable and intractable subclasses of the learning problem, giving insight into the problem structure. Next, we analyze the convergence of recently proposed and modified online learning algorithms, where we introduce several notions of problem margin that imply convergence for the various algorithms. Finally, we present empirical results in automated planning, where ranking functions are learned to guide beam search in a number of benchmark planning domains. The results show that our approach is often able to outperform an existing state-of-the-art planning heuristic as well as a recent approach to learning such heuristics. Reduction to SAT is a very successful approach to solving hard combinatorial problems in Artificial Intelligence and computer science in general. Most commonly, problem instances reduced to SAT are solved with a general-purpose SAT solver. Although there is the obvious possibility of improving the SAT solving process with application-specific heuristics, this has rarely been done successfully. In this work we propose a planning-specific variable selection strategy for SAT solving. The strategy is based on generic principles about properties of plans, and its performance with standard planning benchmarks often substantially improves on generic variable selection heuristics, such as VSIDS, and often lifts it to the same level with other search methods such as explicit state-space search with heuristic search algorithms. We consider the problem of learning heuristics for controlling forward state-space beam search in AI planning domains. We draw on a recent framework for "structured output classification" (e.g. syntactic parsing) known as learning as search optimization (LaSO). The LaSO approach uses discriminative learning to optimize heuristic functions for search-based computation of structured outputs and has shown promising results in a number of domains. However, the search problems that arise in AI planning tend to be qualitatively very different from those considered in structured classification, which raises a number of potential difficulties in directly applying LaSO to planning. In this paper, we discuss these issues and describe a LaSO-based approach for discriminative learning of beam-search heuristics in AI planning domains. We give convergence results for this approach and present experiments in several benchmark domains. The results show that the discriminatively trained heuristic can outperform the one used by the planner FF and another recent non-discriminative learning approach. 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. We describe and evaluate the algorithmic techniques that are used in the FF planning system. Like the HSP system, FF relies on forward state space search, using a heuristic that estimates goal distances by ignoring delete lists. Unlike HSP's heuristic, our method does not assume facts to be independent. We introduce a novel search strategy that combines hill-climbing with systematic search, and we show how other powerful heuristic information can be extracted and used to prune the search space. FF was the most successful automatic planner at the recent AIPS-2000 planning competition. We review the results of the competition, give data for other benchmark domains, and investigate the reasons for the runtime performance of FF compared to HSP. Many real-world planning domains, including those used in common benchmark problems, are based on multiagent scenarios. It has long been recognised that breaking down such problems into sub-problems for individual agents may help reduce overall planning complexity. This kind of approach is especially effective in domains where interaction between agents is limited. In this paper we present a fully centralised, offline, sequential, total-order planning algorithm for solving classical planning problems based on this idea. This algorithm consists of an automated decomposition process and a heuristic search method designed specifically for decomposed domains. The decomposition method is part of a preprocessing step and can be used to determine the "multiagent nature" of a planning problem prior to actual plan search. The heuristic search strategy is shown to effectively exploit any decompositions that are found and performs significantly better than current approaches on loosely coupled domains. History (A. Hoffman and P. Wolfe). Motivation and Modeling (R. Garfinkel). Computational Complexity (D. Johnson and C. Papadimitriou). Well-Solved Special Cases (P. Gilmore, et al). Performance Guarantees for Heuristics (D. Johnson and C. Papadimitriou). Probabilistic Analysis of Heuristics (R. Karp and J. Steele). Empirical Analysis of Heuristics (B. Golden and W. Stewart). Polyhedral Theory (M. Grotschel and M. Padberg). Polyhedral Algorithms (M. Padberg and M. Grotschel). Branch and Bound Methods (E. Balas and P. Toth). Hamiltonian Cycles (V. Chvatal). Vehicle Routing (N. Christofides). Bibliography. Real-time heuristic search methods are used by situated agents in applications that require the amount of planning per move to be independent of the problem size. Such agents plan only a few actions at a time in a local search space and avoid getting trapped in local minima by improving their heuristic function over time. We extend a wide class of real-time search algorithms with automatically-built state abstraction and prove completeness and convergence of the resulting family of algorithms. We then analyze the impact of abstraction in an extensive empirical study in real-time pathfinding. Abstraction is found to improve efficiency by providing better trading offs between planning time, learning speed and other negatively correlated performance measures. A number of today's state-of-the-art planners are based on forward state-space search. The impressive performance can be attributed to progress in computing domain independent heuristics that perform well across many domains. However, it is easy to find domains where such heuristics provide poor guidance, leading to planning failure. Motivated by such failures, the focus of this paper is to investigate mechanisms for learning domain-specific knowledge to better control forward search in a given domain. While there has been a large body of work on inductive learning of control knowledge for AI planning, there is a void of work aimed at forward-state-space search. One reason for this may be that it is challenging to specify a knowledge representation for compactly representing important concepts across a wide range of domains. One of the main contributions of this work is to introduce a novel feature space for representing such control knowledge. The key idea is to define features in terms of information computed via relaxed plan extraction, which has been a major source of success for non-learning planners. This gives a new way of leveraging relaxed planning techniques in the context of learning. Using this feature space, we describe three forms of control knowledge---reactive policies (decision list rules and measures of progress) and linear heuristics---and show how to learn them and incorporate them into forward state-space search. Our empirical results show that our approaches are able to surpass state-of-the-art non-learning planners across a wide range of planning competition domains. In the AIPS98 Planning Contest, the HSP planner showed that heuristic search planners can be competitive with state-of-the-art Graphplan and SAT planners. Heuristic search planners like HSP transform planning problems into problems of heuristic search by automatically extracting heuristics from Strips encodings. They differ from specialized problem solvers such as those developed for the 24-Puzzle and Rubik’s Cube in that they use a general declarative language for stating problems and a general mechanism for extracting heuristics from these representations. In this paper, we study a family of heuristic search planners that are based on a simple and general heuristic that assumes that action preconditions are independent. The heuristic is then used in the context of best-first and hill-climbing search algorithms, and is tested over a large collection of domains. We then consider variations and extensions such as reversing the direction of the search for speeding node evaluation, and extracting information about propositional invariants for avoiding dead-ends. We analyze the resulting planners, evaluate their performance, and explain when they do best. We also compare the performance of these planners with two state-of-the-art planners, and show that the simplest planner based on a pure best-first search yields the most solid performance over a large set of problems. We also discuss the strengths and limitations of this approach, establish a correspondence between heuristic search planning and Graphplan, and briefly survey recent ideas that can reduce the current gap in performance between general heuristic search planners and specialized solvers.  2001 Elsevier Science B.V. All rights reserved. This paper proposes FMAP (Forward Multi-Agent Planning), a fully-distributed multi-agent planning method that integrates planning and coordination. Although FMAP is specifically aimed at solving problems that require cooperation among agents, the flexibility of the domain-independent planning model allows FMAP to tackle multi-agent planning tasks of any type. In FMAP, agents jointly explore the plan space by building up refinement plans through a complete and flexible forward-chaining partial-order planner. The search is guided by h D T G , a novel heuristic function that is based on the concepts of Domain Transition Graph and frontier state and is optimized to evaluate plans in distributed environments. Agents in FMAP apply an advanced privacy model that allows them to adequately keep private information while communicating only the data of the refinement plans that is relevant to each of the participating agents. Experimental results show that FMAP is a general-purpose approach that efficiently solves tightly-coupled domains that have specialized agents and cooperative goals as well as loosely-coupled problems. Specifically, the empirical evaluation shows that FMAP outperforms current MAP systems at solving complex planning tasks that are adapted from the International Planning Competition benchmarks. The ignoring delete lists relaxation is of paramount importance for both satisficing and optimal planning. In earlier work (Hoffmann 2005), it was observed that the optimal relaxation heuristic h+ has amazing qualities in many classical planning benchmarks, in particular pertaining to the complete absence of local minima. The proofs of this are hand-made, raising the question whether such proofs can be lead automatically by domain analysis techniques. In contrast to earlier disappointing results (Hoffmann 2005) - the analysis method has exponential runtime and succeeds only in two extremely simple benchmark domains - we herein answer this question in the affirmative. We establish connections between causal graph structure and h+ topology. This results in low-order polynomial time analysis methods, implemented in a tool we call TorchLight. Of the 12 domains where the absence of local minima has been proved, TorchLight gives strong success guarantees in 8 domains. Empirically, its analysis exhibits strong performance in a further 2 of these domains, plus in 4 more domains where local minima may exist but are rare. In this way, TorchLight can distinguish "easy" domains from "hard" ones. By summarizing structural reasons for analysis failure, TorchLight also provides diagnostic output indicating domain aspects that may cause local minima. Some recent works in conditional planning have proposed reachability heuristics to improve planner scalability, but many lack a formal description of the properties of their distance estimates. To place previous work in context and extend work on heuristics for conditional planning, we provide a formal basis for distance estimates between belief states. We give a definition for the distance between belief states that relies on aggregating underlying state distance measures. We give several techniques to aggregate state distances and their associated properties. Many existing heuristics exhibit a subset of the properties, but in order to provide a standardized comparison we present several generalizations of planning graph heuristics that are used in a single planner. We compliment our belief state distance estimate framework by also investigating efficient planning graph data structures that incorporate BDDs to compute the most effective heuristics. We developed two planners to serve as test-beds for our investigation. The first, CAltAlt, is a conformant regression planner that uses A* search. The second, POND, is a conditional progression planner that uses AO* search. We show the relative effectiveness of our heuristic techniques within these planners. We also compare the performance of these planners with several state of the art approaches in conditional planning. In the recent AIPS98 Planning Competition, the hsp planner, based on a forward state search and a domain-independent heuristic, showed that heuristic search planners can be competitive with state of the art Graphplan and Satisfiability planners. hsp solved more problems than the other planners but it often took more time or produced longer plans. The main bottleneck in hsp is the computation of the heuristic for every new state. This computation may take up to 85 of the processing time. In this paper, we present a solution to this problem that uses a simple change in the direction of the search. The new planner, that we call hspr, is based on the same ideas and heuristic as hsp , but searches backward from the goal rather than forward from the initial state. This allows hspr to compute the heuristic estimates only once. As a result, hspr can produce better plans, often in less time. For example, hspr solves each of the 30 logistics problems from Kautz and Selman in less than 3 seconds. This is two orders of magnitude faster than blackbox. At the same time, in almost all cases, the plans are substantially smaller. hspr is also more robust than hsp as it visits a larger number of states, makes deterministic decisions, and relies on a single adjustable parameter than can be fixed for most domains. hspr, however, is not better than hsp accross all domains and in particular, in the blocks world, hspr fails on some large instances that hsp can solve. We discuss also the relation between hspr and Graphplan, and argue that Graphplan can also be understood as a heuristic search planner with a precise heuristic function and search algorithm. Planning with numeric state variables has been a challenge for many years, and was a part of the 3rd International Planning Competition (IPC-3). Currently one of the most popular and successful algorithmic techniques in STRIPS planning is to guide search by a heuristic function, where the heuristic is based on relaxing the planning task by ignoring the delete lists of the available actions. We present a natural extension of "ignoring delete lists" to numeric state variables, preserving the relevant theoretical properties of the STRIPS relaxation under the condition that the numeric task at hand is "monotonic". We then identify a subset of the numeric IPC-3 competition language, "linear tasks", where monotonicity can be achieved by pre-processing. Based on that, we extend the algorithms used in the heuristic planning system FF to linear tasks. The resulting system Metric-FF is, according to the IPC-3 results which we discuss, one of the two currently most efficient numeric planners. In many planning situations, a planner is required to return a diverse set of plans satisfying the same goals which will be used by the external systems collectively. We take a domain-independent approach to solving this problem. We propose different domain independent distance functions among plans that can provide meaningful insights about the diversity in the plan set. We then describe how two representative state-of-the-art domain independent planning approaches - one based on compilation to CSP, and the other based on heuristic local search - can be adapted to produce diverse plans. We present empirical evidence demonstrating the effectiveness of our approaches. We present a new approach to learning for planning, where knowledge acquired while solving a given set of planning problems is used to plan faster in related, but new problem instances. We show that a deep neural network can be used to learn and represent a (GRP) that maps a problem instance and a state to an action, and that the learned GRPs efficiently solve large classes of challenging problem instances. In contrast to prior efforts in this direction, our approach significantly reduces the dependence of learning on handcrafted domain knowledge or feature selection. Instead, the GRP is trained from scratch using a set of successful execution traces. We show that our approach can also be used to automatically learn a heuristic function that can be used in directed search algorithms. We evaluate our approach using an extensive suite of experiments on two challenging planning problem domains and show that our approach facilitates learning complex decision making policies and powerful heuristic functions with minimal human input. Videos of our results are available at this http URL.