A problem similarity approach to devising heuristics: first results

  • Authors:
  • John Gaschnig

  • Affiliations:
  • Artificial Intelligence Center, SRI International, Menlo Park, CA and Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA

  • Venue:
  • IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
  • Year:
  • 1979

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Abstract

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.