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.
Previous work has been conducted to predict the performance of simpler real-time heuristic search algorithms. Citing important applications in planning (e.g., as part of the Heuristic Search Planner @cite_14 and the Fast-Forward Planner @cite_15 ), L o pez sought to model the efficiency of heuristic hill-climbing by modelling the algorithm as a Markov process @cite_33 . Using several sizes of the sliding tile puzzle, the model could reasonably predict the likelihood that a hill-climbing agent reaches a target state in a number of moves equal to the initial heuristic value. L o pez stated that this model is useful not only as a predictor of simple real-time search performance, but as a gauge of heuristic accuracy.
@cite_15 @cite_14 @cite_33
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The purpose of this paper is twofold: on one hand, modelling the hill-climbing heuristic search algorithm as a stochastic process serves for deriving interesting properties about its expected performance; on the other hand, the probability that a hill-climbing search algorithm ever fails when approaching the target node (i.e., it does not find a descendant with a heuristic value strictly lower than the current one) can be considered as a pesimistic measure of the accuracy of the heuristic function guiding it. Thus, in this work, it is suggested to model heuristic hill-climbing search algorithms with Markov chains in order to fulfill these goals. Empirical results obtained in various sizes of the (n,m)-Puzzle domain prove that this model leads to very accurate predictions. 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. 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. We discuss the relationships between three approaches to greedy heuristic search: best-first, hill-climbing, and beam search. We consider the design decisions within each family and point out their oft-overlooked similarities. We consider the following best-first searches: weighted A*, greedy search, ASeps, window A* and multi-state commitment k-weighted A*. For hill climbing algorithms, we consider enforced hill climbing and LSS-LRTA*. We also consider a variety of beam searches, including BULB and beam-stack search. We show how to best configure beam search in order to maximize robustness. An empirical analysis on six standard benchmarks reveals that beam search and best-first search have remarkably similar performance, and outperform hill-climbing approaches in terms of both time to solution and solution quality. Of these, beam search is preferable for very large problems and best first search is better on problems where the goal cannot be reached from all states. We analyze the behavior of hill-climbing algorithms for the minimum bisection problem on instances drawn from the “planted bisection” random graph model, G n,p,q , previously studied in [3, 4, 10, 11, 14, 9, 7]. This is one of the few problem distributions for which various popular heuristic methods, such as simulated annealing, have been proven to succeed. However, it has been open whether these sophisticated methods were necessary, or whether simpler heuristics would also work. Juels [14] made the first progress towards an answer by showing that simple hill-climbing does suffice for very wide separations between p and q. Here we give a more complete answer. A simple, polynomial-time, hill-climbing algorithm for this problem is given and shown to succeed in finding the planted bisection with high probability if p - q = O (n-½ln3n). For dense graphs, this matches the condition for optimality of the planted bisection to within a polylogarithmic factor. Furthermore, we show that a generic randomized hill-climbing algorithm succeeds in finding the planted bisection in polynomial time if p - q = O (n-¼ ln3 n), for any ∈ > 0. This algorithm, studied also by [14], is a degenerate case of both Metropolis and go-with-the-winners, and the range here properly includes those analyzed in [11, 9, 14]. So this result implies, extends, and unifies those from [11, 9, 14]. Thus, to get a provable distinction between simulated annealing and hill-climbing for natural problems will require considerable progress both on new positive results for SA and new negative results for hill-climbing methods. 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. Abstract Real-time heuristic search methods interleave planning and plan executions and plan only in the part of the domain around the current state of the agents. So far, real-time heuristic search methods have mostly been applied to deterministic planning tasks. In this article, we argue that real-time heuristic search methods can efficiently solve nondeterministic planning tasks. We introduce Min-Max Learning Real-Time A∗ (Min-Max LRTA∗), a real-time heuristic search method that generalizes Korf's LRTA∗ to nondeterministic domains, and apply it to robot-navigation tasks in mazes, where the robots know the maze but do not know their initial position and orientation (pose). These planning tasks can be modeled as planning tasks in nondeterministic domains whose states are sets of poses. We show that Min-Max LRTA∗ solves the robot-navigation tasks fast, converges quickly, and requires only a small amount of memory. 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. 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. 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. Efficient footstep planning for humanoid navigation through cluttered environments is still a challenging problem. Many obstacles create local minima in the search space, forcing heuristic planners such as A* to expand large areas. The goal of this work is to efficiently compute long, feasible footstep paths. For navigation, finding the optimal path initially is often not needed as it can be improved while walking. Thus, we propose anytime search-based planning using the anytime repairing A* (ARA*) and randomized A* (R*) planners. This allows to obtain efficient paths with provable suboptimality within short planning times. Opposed to completely randomized methods such as rapidly-exploring random trees (RRTs), these planners create paths that are goal-directed and guaranteed to be no more than a certain factor longer than the optimal solution. We thoroughly evaluated the planners in various scenarios using different heuristics. ARA* with the 2D Dijkstra heuristic yields fast and efficient solutions but its potential inadmissibility results in non-optimal paths for some scenarios. R*, on the other hand borrows ideas from RRTs, yields fast solutions, and is less dependent on a well-designed heuristic function. This allows it to avoid local minima and reduces the number of expanded states. Service-Oriented Architecture enables the composition of loosely coupled services provided with varying Quality of Service (QoS) levels. Given a composition, finding the set of services that optimizes some QoS attributes under given QoS constraints has been shown to be NP-hard. Therefore, heuristic algorithms are widely used, finding acceptable solutions in polynomial time. Still the time complexity of such algorithms can be prohibitive for real-time use, especially if the algorithms are required to run until they find near-optimal solutions. Thus, we propose a heuristic approach based on Hill-Climbing that makes effective use of an initial bias computed with Linear Programming, and works on a reduced search space. In our evaluation, we show that our approach finds near-optimal solutions and achieves a low time complexity. 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 this paper, we address the problem of navigation among movable obstacles (NAMO): a practical extension to navigation for humanoids and other dexterous mobile robots. The robot is permitted to reconfigure the environment by moving obstacles and clearing free space for a path. Simpler problems have been shown to be P-SPACE hard. For real-world scenarios with large numbers of movable obstacles, complete motion planning techniques are largely intractable. This paper presents a resolution complete planner for a subclass of NAMO problems. Our planner takes advantage of the navigational structure through state-space decomposition and heuristic search. The planning complexity is reduced to the difficulty of the specific navigation task, rather than the dimensionality of the multi-object domain. We demonstrate real-time results for spaces that contain large numbers of movable obstacles. We also present a practical framework for single-agent search that can be used in algorithmic reasoning about this domain. This paper deals with the problem of classical planning for multiple cooperative agents who have private information about their local state and capabilities they do not want to reveal. Two main approaches have recently been proposed to solve this type of prob- lem - one is based on reduction to distributed constraint satisfaction, and the other on partial-order planning techniques. In classical single-agent planning, constraint-based and partial-order planning techniques are currently dominated by heuristic forward search. The question arises whether it is possible to formulate a distributed heuristic forward search algorithm for privacy-preserving classical multi-agent planning. Our work provides a positive answer to this question in the form of a general approach to distributed state-space search in which each agent performs only the part of the state expansion relevant to it. The resulting algorithms are simple and efficient - outperforming previous algorithms by orders of magnitude - while offering similar flexibility to that of forward-search algorithms for single-agent planning. Furthermore, one particular variant of our general approach yields a distributed version of the a* algorithm that is the first cost-optimal distributed algorithm for privacy-preserving planning. 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. 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. This paper deals with planning domains that appear in computer games, especially when modeling intelligent virtual agents. Some of these domains contain only actions with no negative effects and are thus treated as easy from the planning perspective. We propose two new techniques to solve the problems in these planning domains, a heuristic search algorithm ANA* and a constraint-based planner RelaxPlan, and we compare them with the state-of-the-art planners, that were successful in IPC, using planning domains motivated by computer games. Fast-forward (FF) was the most successful automatic planner in the Fifth International Conference on Artificial Intelligence Planning and Scheduling (AIPS '00) planning systems competition. Like the well-known hsp system, FF relies on forward search in the state space, guided by a heuristic that estimates goal distances by ignoring delete lists. It differs from HSP in a number of important details. This article describes the algorithmic techniques used in FF in comparison to hsp and evaluates their benefits in terms of run-time and solution-length behavior. In this paper we present greedy methods for selecting a subset of heuristic functions for guiding A* search. Our methods are able to optimize various objective functions while selecting a subset from a pool of up to thousands of heuristics. Specifically, our methods minimize approximations of A*'s search tree size, and approximations of A*'s running time. We show empirically that our methods can outperform state-of-the-art planners for deterministic optimal planning.