Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item On the Asymptotic Performance of IDA*(1995) Mahanti, Ambuj; Ghosh, Subrata; Nau, D.S.; Pal, A.K.; Kanal, L.N.; ISRSince best-first search algorithms such as A* require large amounts of memory, they sometimes cannot run to completion, even on problem instances of moderate size. This problem has led to the development of limited-memory search algorithms, of which the best known is IDA* [9, 10]. This paper presents the following results about IDA* and related algorithms: The analysis of asymptotic optimality for IDA* in [10] is incorrect. There are trees satisfying the asymptotic optimality conditions given in [10] for which IDA* is not asymptotically optimal.To correct the above problem, we state and prove necessary and sufficient for asymptotic optimality of IDA* on trees. On trees not satisfying our conditions, we show that no best-first limited- memory search algorithm can be asymptotically optimal.
On graphs, IDA* can perform quite poorly. In particular, there are graphs on which IDA* does (22N) node expansions where N is the number of nodes expanded by A*.
Item Improving the Efficiency of Limited-Memory Heuristic Search(1995) Ghosh, Subrata; Mahanti, Ambuj; Nau, D.S.; ISRThis 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*.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.
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.
Item Manufacturing Cell Formation by State-Space Search(1993) Ghosh, Subrata; Mahanti, Ambuj; Nagi, Rakesh; Nau, Dana; ISRThis paper addresses the problem of grouping machines in order to design cellular manufacturing cells, with an objective to minimize intercell flow. This problem is replaced to one of the major aims of group technology (GT): to decompose the manufacturing system into manufacturing cells that are as independent as possible.This problem is NP-hard. Thus, nonheuristic methods cannot address problems of typical industrial dimensions because they would require exorbitant amounts of computing time, while fast heuristic methods may suffer from sub-optimality.
We present a branch-and-bound state-space search algorithm that attempts to overcome both these deficiencies. One of the major strengths of this algorithm is its efficient branching and search strategy. In addition, the algorithm employs the efficient Inter-Cell Traffic Minimization Method to provide good upper bounds, and computes lower bounds based on a relaxation of merging.
Item PRA: Massively Parallel Heuristic Search(1991) Evett, Matthew; Hendler, James A.; Mahanti, Ambuj; Nau, D.; ISRIn this paper we describe a variant of A* search designed to run on the massively parallel, SIMD Connection Machine. The algorithm is designed to run in a limited memory by use of a retraction technique which allows nodes with poor heuristic values to be removed from the open list, until such time as they may need reexpansion, more promising paths having failed. Our algorithm, called PRA* (for Parallel Retraction A*), is designed to maximize use of the Connection Machine's memory and processors. In addition, the algorithm is guaranteed to return an optimal path when an admissable heuristic is used. Results comparing PRA* to Korf's IDA* for the fifteen-puzzle show significantly fewer node expansions for PRA*. In addition, empirical results show significant parallel speedups, indicative of the algorithm's design for high processor utilization.