Showing papers on "Admissible heuristic published in 2012"

MAXSAT heuristics for cost optimal planning

Abstract: The cost of an optimal delete relaxed plan, known as h+, is a powerful admissible heuristic but is in general intractable to compute In this paper we examine the problem of computing h+ by encoding it as a MAXSAT problem We develop a new encoding that utilizes constraint generation to supports the computation of a sequence of increasing lower bounds on h+ We show a close connection between the computations performed by a recent approach to solving MAXSAT and a hitting set approach recently proposed for computing h+ Using this connection we observe that our MAXSAT computation can be initialized with a set of landmarks computed via cheaper methods like LM-cut By judicious use of MAXSAT solving along with a technique of lazy heuristic evaluation we obtain speedups for finding optimal plans over LM-cut on a number of domains Our approach enables the exploitation of continued progress in MAXSAT solving, and also makes it possible to consider computing or approximating heuristics that are even more informed that h+ by, for example, adding some information about deletes back into the encoding

Scheduling FMS with alternative routings using Petri nets and near admissible heuristic search.

Abstract: This paper proposes and evaluates a near admissible heuristic search strategy and its application to a kind of flexible manufacturing system (FMS) scheduling in a Petri net framework. Petri nets can concisely model the strict precedence constraint, multiple kinds of resources, and concurrent activities. To cope with the complexities for scheduling of FMS with alternative routings, this paper proposes an admissible heuristic function based on the execution of P-timed Petri nets and presents an improved dynamic weighting A* strategy using the proposed heuristic function. The search scheme does not need to predict the depth of solution in advance and the quality of the search result is also controllable. Some numerical experiments are carried out to demonstrate usefulness of the algorithm.

An Improved Admissible Heuristic for Learning Optimal Bayesian Networks

Abstract: Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a relaxation of the learning problem such that each variable chooses optimal parents independently. As a result, the heuristic may contain many directed cycles and result in a loose bound. This paper introduces an improved admissible heuristic that tries to avoid directed cycles within small groups of variables. A sparse representation is also introduced to store only the unique optimal parent choices. Empirical results show that the new techniques significantly improved the efficiency and scalability of A* and BFBnB on most of datasets tested in this paper.

Probabilistic planning with non-linear utility functions and worst-case guarantees

Abstract: Markov Decision Processes are one of the most widely used frameworks to formulate probabilistic planning problems. Since planners are often risk-sensitive in high-stake situations, non-linear utility functions are often introduced to describe their preferences among all possible outcomes. Alternatively, risk-sensitive decision makers often require their plans to satisfy certain worst-case guarantees.We show how to combine these two approaches by considering problems where we maximize the expected utility of the total reward subject to worst-case constraints. We generalize several existing results on the structure of optimal policies to the constrained case, both for finite and infinite horizon problems. We provide a Dynamic Programming algorithm to compute the optimal policy, and we introduce an admissible heuristic to effectively prune the search space. Finally, we use a stochastic shortest path problem on large real-world road networks to demonstrate the practical applicability of our method.

Online speedup learning for optimal planning

Abstract: Domain-independent planning is one of the foundational areas in the field of Artificial Intelligence. A description of a planning task consists of an initial world state, a goal, and a set of actions for modifying the world state. The objective is to find a sequence of actions, that is, a plan, that transforms the initial world state into a goal state. In optimal planning, we are interested in finding not just a plan, but one of the cheapest plans. A prominent approach to optimal planning these days is heuristic state-space search, guided by admissible heuristic functions. Numerous admissible heuristics have been developed, each with its own strengths and weaknesses, and it is well known that there is no single "best" heuristic for optimal planning in general. Thus, which heuristic to choose for a given planning task is a difficult question. This difficulty can be avoided by combining several heuristics, but that requires computing numerous heuristic estimates at each state, and the tradeoff between the time spent doing so and the time saved by the combined advantages of the different heuristics might be high. We present a novel method that reduces the cost of combining admissible heuristics for optimal planning, while maintaining its benefits. Using an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for learning a classifier with that decision rule as the target concept, and employ the learned classifier to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms the standard method for combining several heuristics via their pointwise maximum.

Heuristic search of multiagent influence space

Abstract: Multiagent planning under uncertainty has seen important progress in recent years. Two techniques, in particular, have substantially advanced efficiency and scalability of planning. Multiagent heuristic search gains traction by pruning large portions of the joint policy space deemed suboptimal by heuristic bounds. Alternatively, influence-based abstraction reformulates the search space of joint policies into a smaller space of influences, which represent the probabilistic effects that agents' policies may exert on one another. These techniques have been used independently, but never together, to solve larger problems (for Dec-POMDPs and subclasses) than previously possible. In this paper, we take the logical albeit nontrivial next step of combining multiagent A* search and influence-based abstraction into a single algorithm. The mathematical foundation that we provide, such as partially-specified influence evaluation and admissible heuristic definition, enables an investigation into whether the two techniques bring complementary gains. Our empirical results indicate that A* can provide significant computational savings on top of those already afforded by influence-space search, thereby bringing a significant contribution to the field of multiagent planning under uncertainty.

How to relax a bisimulation

Abstract: Merge-and-shrink abstraction (M&S) is an approach for constructing admissible heuristic functions for cost-optimal planning. It enables the targeted design of abstractions, by allowing to choose individual pairs of (abstract) states to aggregate into one. A key question is how to actually make these choices, so as to obtain an informed heuristic at reasonable computational cost. Recent work has addressed this via the well-known notion of bisimulation. When aggregating only bisimilar states – essentially, states whose behavior is identical under every planning operator – M&S yields a perfect heuristic. However, bisimulations are typically exponentially large. Thus we must relax the bisimulation criterion, so that it applies to more state pairs, and yields smaller abstractions. We herein devise a fine-grained method for doing so. We restrict the bisimulation criterion to consider only a subset K of the planning operators. We show that, if K is chosen appropriately, then M&S still yields a perfect heuristic, while abstraction size may decrease exponentially. Designing practical approximations for K, we obtain M&S heuristics that are competitive with the state of the art.

An improved admissible heuristic for learning optimal Bayesian networks

Abstract: Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a relaxation of the learning problem such that each variable chooses optimal parents independently. As a result, the heuristic may contain many directed cycles and result in a loose bound. This paper introduces an improved admissible heuristic that tries to avoid directed cycles within small groups of variables. A sparse representation is also introduced to store only the unique optimal parent choices. Empirical results show that the new techniques significantly improved the efficiency and scalability of A* and BFBnB on most of datasets tested in this paper.

A Heuristic for Hybrid Planning with Preferences.

Abstract: In this paper, we introduce an admissible heuristic for hybrid planning with preferences. Hybrid planning is the fusion of hierarchical task network (HTN) planning with partial order causal link (POCL) planning. We consider preferences to be soft goals — facts one would like to see satisfied in a goal state, but which do not have to hold necessarily. Our heuristic estimates the best quality of any solution that can be developed from the current plan under consideration. It can thus be used by any branch-and-bound algorithm that performs search in the space of plans to prune suboptimal plans from the search space.

Guided Search for Deadlocks in Actor-Based Models

Abstract: Model checking is used to uncover errors by searching the state space of a model. Informed search algorithms use heuristic strategies with problem-specific knowledge to find solutions efficiently. Generally, such heuristics estimate the distance from a given state to a goal state. In this paper, we present seven heuristics for guiding search algorithms through the state-space of actor-based models to a deadlock. In many cases, our methods can find a deadlock more efficiently than uninformed searches. The A* search algorithm guarantees an optimal solution and returns the shortest counter-example when used with an admissible heuristic. These methods are supported by a tool that performs directed search for the deadlock property. The objective is to detect errors that might not be found by simulation or by conventional model checkers before reaching an upper bound or state-space explosion.

Analysing and Combining Partial Problem Solutions for Properly Informed Heuristic Generations

Abstract: Finding an optimal path to the fixed goal state of a problem instance lying in an enormous search space may be described in the framework of the conventional A * algorithm. However, the estimated distance to the goal state, so called h _ value , must be generated by an admissible heuristic such that it is not larger than but still as close as the unknown real distance to the goal. In this paper, we suggest a method of generating a heuristic with that property. After analyzing a number of devised partial problems, some are selected to be combined to produce a properly informed heuristic. In solving a complex problem with a fixed goal, some depth of fixed backward states is pre-stored. Those static backward states are also used for partial problem backward searches. For a given problem instance, the forward search is first performed for each of its partial problem. The dynamically generated space is combined with the static search space to produce the temporary search space, which is used to aid in the generation of each state heuristic for the course of problem solving. A novel method of constructing the temporary search space for each partial problem is suggested, in which each forward state found in the static backward space is back-propagated and propagated in the forward space. To show the effectiveness of our method, it has been massively experimented for instances of Rubik’s cube problem of some difficulty whose search space of states reachable from any given start state is known to cover 43*10 18 states, the number of which even an 64-bit unsigned integer cannot hold. Keywords: A * , admissible heuristic, partial problems, dynamic forward search, static backward search, Rubik’s cube