## Generalized best-first search strategies and the optimality of A* (1985)

Venue: | JOURNAL OF THE ACM |

Citations: | 161 - 12 self |

### BibTeX

@ARTICLE{Dechter85generalizedbest-first,

author = {Rina Dechter and Judea Pearl},

title = {Generalized best-first search strategies and the optimality of A*},

journal = {JOURNAL OF THE ACM},

year = {1985},

volume = {32},

number = {3},

pages = {505--536}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper reports several properties of heuristic best-first search strategies whose scoring functions f 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 offplaying 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 type of optimality that exists and the algorithm for achieving it. The main results of this paper relate to the class of algorithms that, like A*, return optimal solutions (i.e., admissible) when all cost estimates are optimistic (i.e., h 5 h*). On this class, A * is shown to be not optimal and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A * is indeed optimal. Additionally, A * is also shown to be optimal over a subset of the latter class containing all best-first algorithms that are guided by path-dependent evaluation functions.

### Citations

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(Show Context)
Citation Context ... two separate functions is excluded from our formulation of best first search.sGeneralized BF Search Strategies and the Optimality ofA* 507 By far, the most studied version of BF* is the algorithm A* =-=[6]-=-, which was developed for additive cost measures, that is, where the cost of a path is defined as the sum of the costs of its arcs. To match this cost measure, A* employs an additive evaluation functi... |

686 | Heuristics: intelligent search strategies for computer problem solving - Pearl - 1984 |

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46 |
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(Show Context)
Citation Context ...ith an optimal-cost path. q By way of demonstrating its utility, Corollary 1 can readily delineate the range of admissibility of Pohl’s weighted evaluation function fw = (1 - w)g + wh, 0 I w I 1 (see =-=[18]-=-). Here $(C) = (1 - w)C, which complies with (1) for w < 1. It remains to examine what values of w < 1 will force fw to attain its maximum at the end of some optimal path P* = s, . . . , y. Writing we... |

38 |
Searching for an Optimal Path in a Tree with Random Costs
- Karp, Pearl
- 1983
(Show Context)
Citation Context ...m of finding the cheapest root-to-leaf path in a uniform binary tree of height N, where each branch independently may have a cost of 1 or 0 with probability p and 1 - p, respectively. It can be shown =-=[9]-=- that for p > 1 and large N the optimal cost is very likely to be near LU*N where (Y* is a constant determined by p. Consequently, a natural evaluation function for A* would be f(n) = g(n) + a*[N - d(... |

32 |
The avoidance of (relative) catastrophe, heuristic competence, genuine dynamic weighting and computational issues in heuristic problem solving
- Pohl
- 1973
(Show Context)
Citation Context ...ti [ 11, although they used $(C) = C and restricted f to the form f = g + h. Theorem 2 can be useful in appraising the degree of suboptimality exhibited by nonadmissible algorithms. For example, Pohl =-=[20]-=- suggests a dynamic weighting scheme for the evaluation function J: In his approach the evaluation function f is given by [ 1 f(n) = g(n) + h(n) + 6 1 - %$ h(n), where d(n) is the depth of node n and ... |

31 | Studies in semi-admissible heuristics - Pearl, Kim - 1982 |

26 |
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(Show Context)
Citation Context ...and is, in fact, the basis of the branch-and-bound method [lo]. Second, we are often able to purge from T large sets of paths that are recognized at an early stage to be dominated by other paths in T =-=[8]-=-. This becomes particularly easy if the evaluation function fis order preserving, that is, if, for any two paths PI and P2, leading from s to n, and for any common extension P3 of those paths, the fol... |

23 |
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(Show Context)
Citation Context ...tions even when h > h*. A*, for example, provides such guarantees; the costs of the solutions returned by A* do not exceed C* + A where A is the highest error h*(n) - h(n) over all nodes in the graph =-=[5]-=-, and, moreover, A* still returns optimal solutions in many problem instances, that is, whenever A is zero along some optimal path. This motivates the definition of A,, the class of algorithms globall... |

18 | Search Algorithms Under Different Kinds of Heuristics - A Comparative Study - Bagchi, Mahanti - 1983 |

16 |
On the Optimality of
- Gelperin
- 1977
(Show Context)
Citation Context ...ity to visit those sections of the graph. Later in this section (see Figure 6), we demonstrate the existence of an algorithm B, which manages to outperform A* using this kind of information. Gelperin =-=[4]-=- has correctly pointed out that, in any discussion of the optimality of A*, one should also consider algorithms that adjust their h in accordance with the information gathered during the search. His a... |

9 | On the discovery and generation of certain heuristics - Pearl - 1983 |

1 |
The Art and Theory ofDynamic Programming
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- 1977
(Show Context)
Citation Context ...,,-, are lower than the maximal f value between ni and y (along PJ). path from ni to n where Li = maxbiJ(nk). In other words, there should exist a path P,,,-, along which .fW) 5 mE,d(nk) Vn’ E P,,-,. =-=(3)-=- Moreover, a suficient condition for expanding n is that (3) be satisfied with strict inequality. PROOF. Assume that n is expanded by BF* and let & be the shallowest OPEN node on Pf at time tn when n ... |

1 | A heuristic search algorithm with modifiable estimate - MRo - 1984 |