Eric A. Hansen

LAO: a heuristic search algorithm that finds solutions with loops

Classic heuristic search algorithms can find solutions that take the form of a simple path (A*), a tree, or an acyclic graph (AO*). In this paper, we describe a novel generalization of heuristic search, called LAO*, that can find solutions with loops. We show that LAO* can be used to solve Markov decision problems and that it shares the advantage heuristic search has over dynamic programming for other classes of problems. Given a start state, it can find an optimal solution without evaluating the entire state space.  2001 Elsevier Science B.V. All rights reserved.

Anytime heuristic search

We describe how to convert the heuristic search algorithm A* into an anytime algorithm that finds a sequence of improved solutions and eventually converges to an optimal solution. The approach we adopt uses weighted heuristic search to find an approximate solution quickly, and then continues the weighted search to find improved solutions as well as to improve a bound on the suboptimality of the current solution. When the time available to solve a search problem is limited or uncertain, this creates an anytime heuristic search algorithm that allows a flexible tradeoff between search time and solution quality. We analyze the properties of the resulting Anytime A* algorithm, and consider its performance in three domains; sliding-tile puzzles, STRIPS planning, and multiple sequence alignment. To illustrate the generality of this approach, we also describe how to transform the memory-efficient search algorithm Recursive Best-First Search (RBFS) into an anytime algorithm.

Monitoring and control of anytime algorithms: a dynamic programming approach

Anytime algorithms offer a tradeoff between solution quality and computation time that has proved useful in solving time-critical problems such as planning and scheduling, belief network evaluation, and information gathering. To exploit this tradeoff, a system must be able to decide when to stop deliberation and act on the currently available solution. This paper analyzes the characteristics of existing techniques for meta-level control of anytime algorithms and develops a new framework for monitoring and control. The new framework handles effectively the uncertainty associated with the algorithm’s performance profile, the uncertainty associated with the domain of operation, and the cost of monitoring progress. The result is an efficient non-myopic solution to the meta-level control problem for anytime algorithms.  2001 Elsevier Science B.V. All rights reserved.

A heuristic search approach to planning with continuous resources in stochastic domains

We consider the problem of optimal planning in stochastic domains with resource constraints, where the resources are continuous and the choice of action at each step depends on resource availability. We introduce the HAO* algorithm, a generalization of the AO* algorithm that performs search in a hybrid state space that is modeled using both discrete and continuous state variables, where the continuous variables represent monotonic resources. Like other heuristic search algorithms, HAO* leverages knowledge of the start state and an admissible heuristic to focus computational effort on those parts of the state space that could be reached from the start state by following an optimal policy. We show that this approach is especially effective when resource constraints limit how much of the state space is reachable. Experimental results demonstrate its effectiveness in the domain that motivates our research: automated planning for planetary exploration rovers.

Sweep A: space-efficient heuristic search in partially ordered graphs

We describe a novel heuristic search algorithm, called Sweep A*, that exploits the regular structure of partially ordered graphs to substantially reduce the memory requirements of search. We show that it outperforms previous search algorithms in optimally aligning multiple protein or DNA sequences, an important problem in bioinformatics. Sweep A* also promises to be effective for other search problems with similar structure.

Symbolic Heuristic Search Using Decision Diagrams

We show how to use symbolic model-checking techniques in heuristic search algorithms for both deterministic and decision-theoretic planning problems. A symbolic approach exploits state abstraction by using decision diagrams to compactly represent sets of states and operators on sets of states. In earlier work, symbolic model-checking techniques have been used to find plans that minimize the number of steps needed to reach a goal. Our approach generalizes this by showing how to find plans that minimize the expected cost of reaching a goal. For this generalization, we use algebraic decision diagrams instead of binary decision diagrams. In particular, we show that algebraic decision diagrams provide a compact representation of state evaluation functions. We describe symbolic generalizations of A* search for deterministic planning and of LAO* search for decision-theoretic planning problems formalized as Markov decision processes.We report experimental results and discuss issues for future work.

Monitoring anytime algorithms

Anytime algorithms offer a tradeoff between solution quality and computation time that has proved useful in applying artificial intelligence techniques to time-critical problems. To exploit this tradeoff, a system must be able to determine the best time to stop deliberation and act on the currently available solution. If there is uncertainty about how much solution quality will improve with computation time, or about how the problem state may change after the start of the algorithm, monitoring the algorithms progress and/or the problem state can make possible a better stopping decision and so improve the utility of the system. This paper analyzes the issues involved in run-time monitoring of anytime algorithms. It reviews previous work and casts the problem in a new framework from which some improved monitoring strategies emerge.

Layered Duplicate Detection in External-Memory Model Checking

This paper presents a disk-based explicit-state model checking algorithm that uses an approach called layered duplicate detection. In this approach, states encountered during a breadth-first traversal of the graph of the transition system are stored in memory according to the layer of the graph in which they are first encountered. With this layered organization of memory, transition locality is exploited by checking only the most recent layers for duplicates. In RAM, exploiting transition locality in this way saves time. In external memory, it saves space. In addition, a layered structure allows an easy method of counterexample reconstruction in disk-based model checking. We prove a worst-case linear bound on the redundant work performed by our approach. Experimental results indicate that average case redundant work is much better than the worst-case. The implemented model checker has been used to verify a transition system that required more than 275 GBs of disk storage.

Branch and bound based feature elimination for support vector machine based classification of hyperspectral images

Feature selection (FS) is a classical combinatorial problem in pattern recognition and data mining. It finds major importance in classification and regression scenarios. In this paper, a hybrid approach that combines branch-and-bound (BB) search with Bhattacharya distance based feature selection is presented for classifying hyperspectral data using Support Vector Machine (SVM) classifiers. The performance of this hybrid approach is compared to another hybrid approach that uses genetic algorithm (GA) based feature selection in place of BB. It is also compared to baseline SVMs with no feature reduction. Experimental results using hyperspectral data show that under small sample size situations, BB approach performs better than GA and SVM with no feature selection.

K-group A* for multiple sequence alignment with quasi-natural gap costs

Alignment of multiple protein or DNA sequences is an important problem in bioinformatics. Previous work has shown that the A* search algorithm can find optimal alignments for up to several sequences, and that a K-group generalization of A* can find approximate alignments for much larger numbers of sequences [T. Ikeda et al. (1999)]. In this paper, we describe the first implementation of K-group A* that uses quasinatural gap costs, the cost model used in practice by biologists. We also introduce a new method for computing gap-opening costs in profile alignment. Our results show that K-group A* can efficiently find optimal or close-to-optimal alignments for small groups of sequences, and, for large numbers of sequences, it can find higher-quality alignments than the widely-used CLUSTAL family of approximate alignment tools. This demonstrates the benefits of A* in aligning large numbers of sequences, as typically compared by biologists, and suggests that K-group A* could become a practical tool for multiple sequence alignment.