Building a Heuristic for Greedy Search

2007

In many shortest-path problems of practical interest, insufficient time is available to find a provably optimal solution. In dynamic environments, for example, the expected value of a plan may decrease with the time required to find it. One can only hope to achieve an appropriate balance between search time and the resulting plan cost. Several algorithms have been proposed for this setting, including weighted A*, Anytime A*, and ARA*. These algorithms multiply the heuristic evaluation of a node, exaggerating the effect of the cost-to-go. We propose a more direct approach, called BUGSY, in which one explicitly estimates search-nodes-togo. One can then attempt to optimize the overall utility of the solution, expressed by the user as a function of search time and solution cost. Experiments in several problem domains, including motion planning and sequence alignment, demonstrate that this direct approach can surpass anytime algorithms without requiring performance profiling.

Proceedings of the …, 2009

Journal of Systems and Software, 2000

In this paper, we present general models for estimating time and space requirements of heuristic search algorithms. We also present an empirical study on a set of four well-known heuristic search algorithms. This study is useful in two ways. On one hand, it gives a general framework for comparing heuristic search algorithms from various respects including time, space, solution quality, and search eectiveness. On the other hand, it provides additional independent empirical results collected from dierent domains. These results can be used to strengthen other results obtained by other researchers in the area. Furthermore, the obtained results are machine independent in the sense that the CPU time is separated from the timing parameters. This enables us to give quantitative arguments on heuristic search algorithms for any architecture.

2008

Problem solvers have at their disposal many heuristics that may support effective search. The efficacy of these heuristics, however, varies with the problem class, and their mutual interactions may not be well understood. The long-term goal of our work is to learn how to select appropriately from among a large body of heuristics, and how to combine them into a weighted mixture that works well on a specific class of problems. During learning, search heuristics' weights are used to solve a problem and then updated based on their performance. This paper proposes and demonstrates a variety of ways to gauge and adapt search performance, and shows how their application can improve subsequent search performance.

Proceedings of the International Conference on Automated Planning and Scheduling

Satisficing heuristic search such as greedy best-first search (GBFS) suffers from local minima, regions where heuristic values are inaccurate and a good node has a worse heuristic value than other nodes. Search algorithms that incorporate exploration mechanisms in GBFS empirically reduce the search effort to solve difficult problems. Although some of these methods entirely ignore the guidance of a heuristic during their exploration phase, intuitively, a good heuristic should have some bound on its inaccuracy, and exploration mechanisms should exploit this bound. In this paper, we theoretically analyze what a good node is for satisficing heuristic search algorithms and show that the heuristic value of a good node has an upper bound if a heuristic satisfies a certain property. Then, we propose biased exploration mechanisms which select lower heuristic values with higher probabilities. In the experiments using synthetic graph search problems and classical planning benchmarks, we show t...

2009

Traditionally, heuristic search algorithms have relied on an estimate of the cost-to-go to speed up problem-solving. In many domains, operators have different costs and estimated cost-to-go is not the same as estimated search-distance-togo. We investigate further accelerating search by using a distance-to-go function. We evaluate two previous proposals: Dynamically weighted A * and A * ǫ. We present a revision to dynamically weighted A * which improves its performance substantially in domains where solutions are not at fixed depths. We show how to incorporate search distance to go estimates into weighted A * in order to improve its performance in pathfinding problems. We present a proof showing that weighted A * can ignore duplicate states, leading to large improvements in performance for pathfinding problems.

2009

Heuristic functions for single-agent search applications estimate the cost of the optimal solution. When multiple heuristics exist, taking their maximum is an effective way to combine them. A new technique is introduced for combining multiple heuristic values. Inspired by the evaluation functions used in two-player games, the different heuristics in a singleagent application are treated as features of the problem domain. An ANN is used to combine these features into a single heuristic value. This idea has been implemented for the sliding-tile puzzle and the 4-peg Towers of Hanoi, two classic single-agent search domains. Experimental results show that this technique can lead to a large reduction in the search effort at a small cost in the quality of the solution obtained. To show the applicability of our learning approach we have also implemented it on the game of chess as a benchmark of two players games. Our experimental results show that the proposed learning strategy is effective in winning against an opponent who offers its best survival defense using Nalimov database of best endgame moves.

Journal of The ACM - JACM, 1985

This paper reports several properties of heuristic best-first search strategies whose scoring functions ƒ depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h. It is shown that several known properties of A* retain their form (with the minmax of f playing the role of the optimal cost), which helps establish general tests of admissibility and general conditions for node expansion for these strategies. On the basis of this framework the computational optimality of A*, in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that A* uses, is examined. A hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered. Computational performances relative to these algorithms and domains are appraised. For each class-domain combination, we then identify the strongest typ...

Artificial Intelligence, 2002

This article surveys three techniques for enhancing heuristic game-tree search pioneered in the author's Othello program LOGISTELLO, which dominated the computer Othello scene for several years and won against the human World-champion 6-0 in 1997. First, a generalized linear evaluation model (GLEM) is described that combines conjunctions of Boolean features linearly. This approach allows an automatic, data driven exploration of the feature space. Combined with efficient least squares weight fitting, GLEM greatly eases the programmer's task of finding significant features and assigning weights to them. Second, the selective search heuristic PROBCUT and its enhancements are discussed. Based on evaluation correlations PROBCUT can prune probably irrelevant sub-trees with a prescribed confidence. Tournament results indicate a considerable playing strength improvement compared to full-width α-β search. Third, an opening book framework is presented that enables programs to improve upon previous play and to explore new opening lines by constructing and searching a game-tree based on evaluations of played variations. These general methods represent the state-of-the-art in computer Othello programming and begin to attract researchers in related fields.

Lecture Notes in Computer Science, 2011

The first Cross-domain Heuristic Search Challenge (CHeSC 2011) seeks to bring together practitioners from operational research, computer science and artificial intelligence who are interested in developing more generally applicable search methodologies. The challenge is to design a search algorithm that works well, not only across different instances of the same problem, but also across different problem domains. This article overviews the main features of this challenge.