Heuristic Hill-Climbing as a Markov Process

Abstract

The purpose of this paper is twofold: on one hand, modelling the hill-climbing heuristic search algorithm as a stochastic process serves for deriving interesting properties about its expected performance; on the other hand, the probability that a hill-climbing search algorithm ever fails when approaching the target node (i.e., it does not find a descendant with a heuristic value strictly lower than the current one) can be considered as a pesimistic measure of the accuracy of the heuristic function guiding it. Thus, in this work, it is suggested to model heuristic hill-climbing search algorithms with Markov chains in order to fulfill these goals. Empirical results obtained in various sizes of the (n,m)-Puzzle domain prove that this model leads to very accurate predictions.