Improving the Efficiency of Limited-Memory Heuristic Search

Abstract

This paper describes a new admissible tree search algorithm called Iterative Threshold Search (ITS). ITS can be viewed as a much-simplified version of MA*[2], and a generalized version of MREC [15]. ITS's node selection and retraction (pruning) overhead is much less expensive than MA*'s. We also present the following results: 1. Every node generated by ITS is also generated by IDA*, even if ITS is given no more memory than IDA*. In addition, there are trees on which ITS generates O(N) nodes in comparison to O(N log N) nodes generated by IDA*, where N is the number of nodes eligible for generation by A*.<P>2. Experimental tests show that if the heuristic branching factor is low and the node- generation time is high (as in most practical problems), then ITS can provide significant savings in both number of node generations and running time.<P>3. Our experimental results also suggest that on the Traveling Salesman Problem, both IDA* and ITS are asymptotically optimal on the average if the costs between the cities are drawn from a fixed range. However, if the range of costs grows in proportion to the problem size, then IDA* is not asymptotically optimal. ITS's asymptotic complexity in the later case depends on the amount of memory available to it.