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Heuristics as Markov chains

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Abstract

Comparing heuristics has been a major issue from the early days of heuristic search. From the very beginning, measures of the accuracy of heuristic functions were strongly based on the number of nodes generated, and they are often still based on it. In this work, an alternative approach is suggested: to model the accuracy of admissible heuristic functions as the probability of the heuristic hill-climbing search algorithm to find the goal state in a number of steps that equals the heuristic value of an arbitrary node. The resulting method serves to assess on the accuracy of both consistent and inconsistent heuristic functions. Comparisons with different sizes of the sliding-tile puzzle show that the model suggested predicts the accuracy of the heuristic function with a good precision. The resulting procedure is used to derive figures on the accuracy of a large number of heuristics for the 15-Puzzle with different variants of the search algorithm IDA∗.

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Authors and Affiliations

  1. Computer Science Department, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911, Leganés, Madrid, Spain

    Carlos Linares López

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  1. Carlos Linares López
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Correspondence to Carlos Linares López.

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Linares López, C. Heuristics as Markov chains. Ann Math Artif Intell 73, 275–309 (2015). https://doi.org/10.1007/s10472-014-9439-1

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