Admissible heuristic

About: Admissible heuristic is a research topic. Over the lifetime, 197 publications have been published within this topic receiving 15329 citations. The topic is also known as: admissible heuristics.

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.

Engineering Note FluCaP: A Heuristic Search Planner for First-Order MDPs

Abstract: We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted to those states that are reachable from the initial state. We demonstrate the usefulness of the above techniques for solving FOMDPs with a system, referred to as FluCaP (formerly, FCPlanner), that entered the probabilistic track of the 2004 International Planning Competition (IPC’2004) and demonstrated an advantage over other planners on the problems represented in first-order terms.

Additive Pattern Database Heuristics

Abstract: We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective, while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem.

A fast pruning algorithm for optimal sequence alignment

Abstract: Sequence alignment is an important operation in computational biology. Both dynamic programming and A* heuristic search algorithms for optimal sequence alignment are discussed and evaluated Presented here are two new algorithms for optimal pairwise sequence alignment which outperform traditional methods on very large problem instances (hundreds of thousands of characters, for example). The technique combines the benefits of dynamic programming and A* heuristic search, with a minimal amount of additional overhead. The dynamic programming matrix is traversed along antidiagonals, bounding the computation to exclude portions of the matrix that cannot contain optimal paths. An admissible heuristic assists in pruning away unnecessary areas of the matrix, while preserving optimal solutions for any given scoring function. Since memory requirements are a major concern for large sequence alignment problems, it is shown how the standard algorithm (requiring quadratic space) can be reformulated as a divide and conquer algorithm (requiring only linear space, at the cost of some recomputuation).

External-memory pattern databases using structured duplicate detection

Abstract: A pattern database is a lookup table that stores an exact evaluation function for a relaxed search problem, which provides an admissible heuristic for the original search problem. In general, the larger the pattern database, the more accurate the heuristic function. We consider how to build large pattern databases that are stored in external memory, such as disk, and how to use an external-memory pattern database efficiently in heuristic search. To limit the number of slow disk I/O operations needed to construct and query an external-memory pattern data-base, we adapt an approach to external-memory graph search called structured duplicate detection that localizes memory references by leveraging an abstraction of the state space. We present results that show this approach increases the scalability of heuristic search by allowing larger and more accurate pattern database heuristics.