Three approaches to heuristic search in networks

Abstract

Three different approaches to heuristic search in networks are analyzed. In the first approach, as formulated initially by Hart, Nilsson, and Raphael, and later modified by Martelli, the basic idea is to choose for expansion that node for which the evaluation function has a minimum value. A second approach has recently been suggested by Nilsson. In this method, in contrast to the earlier one, a node that is expanded once is not expanded again; instead, a “propagation” of values takes place. The third approach is an adaptation for networks of an AND/OR graph “marking” algorithm, originally due to Martelli and Montanari. Five algorithms are presented. Algorithms A and C illustrate the first approach; PropA and PropC, the second one; and MarkA, the third one. The performances of these algorithms are compared for both admissible and inadmissible heuristics using the following two criteria: (i) cost of the solution found; (ii) time of execution in the worst case, as measured by the number of node expansions (A, C), or node “selections” (PropA, PropC), or arc “markings” (MarkA). The relative merits and demerits of the algorithms are summarized and indications are given regarding which algorithm to use in different situations.