How to Use Limited Memory in Heuristic Search

Abstract

Traditional best-first search for optimal solutions quickly runs out of space even for problem instances of moderate size, and linear-space search has unnecessarily long running times since it cannot make use of available memory. For using available memory effectively , we developed a new generic approach to heuristie search. It integrates various strategies and includes ideas from bidirectional search. Due to insights into different utilizations of available memory, it allows the search to use limited memory effectively. Instantiations of this approach for two different benchmark domains showed excellent results that are statistically significant improvements over previously reported results: for finding optimal solutions in the 15-Puzzle we achieved the fastest searches of all those using the Manhattan distance heuristic as the only knowledge source, and for a scheduling domain our approach can solve much more difficult problems than the best competitor. The most important lessons we learned from the experiments are first, that also in domains with symmetric graph topology selecting the right search direction can be very important, and second, that memory can-under certain conditions-be used much more effectively than by traditional best-first search. 1 Introduction Best-first search in the tradition of A* [Hart et a/., 1968] typically requires exponential space. Therefore, it quickly runs out of space even for problem instances of moderate size when searching for optimal solutions. In contrast, linear-space search like IDA* [Korf, 1985], RBFS [Korf, 1993] and DFBB [Lawl er and Wood, 1966] does not suffer from memory limitations. Typically, there is even much more memory available than needed by such algorithms. Since they cannot make use of such memory, however, their running time is unnecessarily long. One of the major problems of heuristic search is how to use available but limited memory effectively. Pure uni-directional approaches to utilizing limited memory still did not lead to convincing results [Chakrabarti et al, 1989; Ghosh et ai, 1994; Reinefeld and Marsland, 1994; Russell, 1992; Sen and Bagchi, 1989]. Therefore, we propose to consider in addition ideas from bidirectional search [Kaindl and Khorsand, 1994; Koll and Kaindl, 1993; Kwa, 1989; Pohl, 1971]. In this paper we integrate various unidirectional strategies and include ideas from bidirectional search in a generic approach to heuristic search. Due to insights into different utilizations of available memory, our approach allows the search to use limited memory effectively. First, we present our new generic approach to heuristic search that specifically focuses on using limited memory. Then we show how this approach can be appropriately instantiated for two very different domains with few and many distinct cost values, respectively. For both domains , we report experimental data that represent significant improvements over previously published results. Finally, we compare our approach more generally with related work. 2 A Generic Approach to Heuristic Search Using Limited Memory We developed a new generic approach to heuristic search that integrates various approaches and typically leads to hybrid combinations of search algorithms. One of the main ideas to address the memory problem is to combine linear-space search with conventional best-first search in a bidirectional style. Fig. 1 gives an overview and indicates how our new algorithms integrate ideas from various approaches in hybrid combinations-this will be discussed in detail below. First, we explain the generic approach generally. Its major steps are: 1. Assign the search directions and the available memory to the traditional best-first and the linear-space algorithm, respectively. 2. Perform traditional best-first search using some or even nearly all of the available memory. 3. Unless the best-first search has already found an optimal solution, use a linear-space algorithm in the reverse direction. Use the memory structure built up by the previous best-first search, possibly together with additional memory that is still available. Note, that the linear-space algorithm per se only requires little memory, but it can utilize additional mem-236 AUTOMATED REASONING