A Problem Similarity Approach to Devising Heuristics: First Results

Here we describe an approach, based upon a notion of problem similarity, that can be used when attempting to devise a heuristic for a given search problem (of a sort represented by graphs). The proposed approach relies on a change in perspective: instead of seeking a heuristic directly for a given problem P1, one seeks Instead a problem P2 easier to solve than P1 and related to P1 in a certain way. The next step is to find an algorithm for finding paths in P2, then apply this algorithm in a certain way as a heuristic for P1. In general, the approach is to consider as candidates problems P2 that are "edge subgraphs" or "edge supergraphs" of the given problem P1. As a non-trivial application, we show that a certain restricted form of sorting problem (serving as P2) is an edge supergraph of the 8-puzzle graph (P1). A simple algorithm for solving this sorting problem is evident, and the number of swaps executed in solving an instance thereof is taken as a heuristic estimate of distance between corresponding points in the 8-puzzle graph. Using the At algorithm, we experimentally compare the performance of this "maxsort" heuristic for the 8-puzzle with others in the literature. Hence we present evidence of a role for exploiting certain similarities among problems to transfer a heuristic from one problem to another, from an "easier" problem to a "harder" one.

[1]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[2]  Alberto Martelli,et al.  On the Complexity of Admissible Search Algorithms , 1977, Artif. Intell..

[3]  J. Gaschnig.  Performance measurement and analysis of certain search algorithms. , 1979 .

[4]  Ira Pohl,et al.  Heuristic Search Viewed as Path Finding in a Graph , 1970, Artif. Intell..

[5]  James Doran,et al.  AN APPROACH TO AUTOMATIC PROBLEM -SOLVING , 1966 .

[6]  David Gelperin,et al.  The optimality of A , 1988 .

[7]  Nils J. Nilsson,et al.  Problem-solving methods in artificial intelligence , 1971, McGraw-Hill computer science series.

[8]  James R. Slagle,et al.  Experiments in automatic learning for a multipurpose hueristic program , 1971, CACM.

[9]  Wayne A. Wickelgren.  How to solve problems , 1974 .

[10]  J. Doran,et al.  Experiments with the Graph Traverser program , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  吴德恒,et al.  经Co , 1964 .

[12]  W. W. Bledsoe,et al.  Review of "Problem-Solving Methods in Artificial Intelligence by Nils J. Nilsson", McGraw-Hill Pub. , 1971, SGAR.

[13]  A. L. Samuel,et al.  Some studies in machine learning using the game of checkers. II: recent progress , 1967 .

[14]  Philip C. Jackson.  Introduction to Artificial Intelligence , 1985 .

[15]  L. Rowell Huesmann,et al.  The thinking computer : mind inside matter , 1977 .

[16]  Gordon J. Vanderbrug.  Problem representations and formal properties of heuristic search , 1976, Inf. Sci..

[17]  Arthur L. Samuel,et al.  Some Studies in Machine Learning Using the Game of Checkers , 1967, IBM J. Res. Dev..

[18]  John Gaschnig,et al.  Exactly How Good Are Heuristics?: Toward a Realistic Predictive Theory of Best-First Search , 1977, IJCAI.

[19]  Larry R. Harris,et al.  The Heuristic Search under Conditions of Error , 1974, Artif. Intell..