AI Magazine Volume 25 Number 2 (2004) (© AAAI) Articles Incremental Heuristic Search in AI Sven Koenig, Maxim Likhachev, Yaxin Liu, and David Furcy ■ Incremental search reuses information from previ- changes of their models of the world, for ex- ous searches to find solutions to a series of similar ample, because the actual situation turns out search problems potentially faster than is possible to be slightly different from the one initially by solving each search problem from scratch. This assumed or because the situation changes over is important because many AI systems have to adapt their plans continuously to changes in (their time. In these cases, the original plan might no knowledge of) the world. In this article, we give an longer apply or might no longer be good, and overview of incremental search, focusing on LIFE- one thus needs to replan for the new situation LONG PLANNING A*, and outline some of its possible (desJardins et al. 1999). Similarly, one needs to applications in AI. solve a series of similar search problems if one wants to perform a series of what-if analyses or if the costs of planning operators, their precon- ditions, or their effects change over time be- cause they are learned or refined. Overview In these situations, most search algorithms t is often important that searches be fast. AI replan from scratch, that is, solve the new has developed several ways of speeding up search problem independently of the old ones. Isearches by trading off the search time and However, this approach can be inefficient in the cost of the resulting path, which includes large domains with frequent changes and, using inadmissible heuristics (Pohl 1973, 1970) thus, limit the responsiveness of AI systems or and search with limited look ahead (Korf 1990; the number of what-if analyses that they can Ishida and Korf 1991; Koenig 2001), which is perform. Fortunately, the changes to the also called real-time or agent-centered search. search problems are usually small. A robot, for In this article, we discuss a different way of example, might have to replan when it detects speeding up searches, namely, incremental a previously unknown obstacle, a traffic rout- search. Incremental search is a search technique ing system might have to replan when it learns for continual planning (or, synonymously, re- about a new traffic jam, and a decision support planning, plan reuse, and lifelong planning) system for marine oil spill containment might that reuses information from previous searches have to replan when the wind direction to find solutions to a series of similar search changes. This property suggests that a com- problems potentially faster than is possible by plete recomputation of the best plan for the solving each search problem from scratch. Dif- new search problem is unnecessary because ferent from other ways of speeding up search- some of the previous search results can be es, it can guarantee to find the shortest paths. reused, which is what incremental search does. Notice that the terminology is unfortunately Incremental search solves dynamic shortest- somewhat problematic because the term incre- path problems, where shortest paths have to be mental search in computer science also refers to found repeatedly as the topology of a graph or both online search and search with limited its edge costs change (Ramalingam and Reps look ahead (Pemberton and Korf 1994). 1996b). The idea of incremental search is old. Most of the research on search has studied For example, an overview article about short- how to solve one-time search problems. How- est-path algorithms from 1984 already cites ever, many AI systems have to adapt their several incremental search algorithms, includ- plans continuously to changes in the world or ing several ones published in the late 1960s Copyright © 2004, American Association for Artificial Intelligence. All rights reserved. 0738-4602-2004 / $2.00 SUMMER 2004 99 Articles (Deo and Pang 1984). Since then, additional Uninformed Incremental Search incremental search algorithms have been sug- gested in the algorithms literature (Ausiello et We now discuss one particular way of solving al. 1991; Even and Gazit 1985; Even and fully dynamic shortest-path problems. As an Shiloach 1981; Feuerstein and Marchetti-Spac- example, we use route planning in known eight-connected gridworlds with cells whose camela 1993; Franciosa, Frigioni, and Giaccio traversability changes over time. They are ei- 2001; Frigioni, Marchetti-Spaccamela, and ther traversable (with cost one) or untraversa- Nanni 1996; Goto and Sangiovanni-Vincentel- ble. The route-planning problem is to repeatedly li 1978; Italiano 1988; Klein and Subramanian find a shortest path between two given cells of 1993; Lin and Chang 1990; Rohnert 1985; Spi- the gridworld, knowing both what the topolo- ra and Pan 1975) and, to a much lesser degree, gy of the gridworld is and which cells are cur- the AI literature (Al-Ansari 2001; Edelkamp rently traversable. It can be solved with con- 1998). They differ in their assumptions, for ex- ventional search, such as breadth-first search, ample, whether they solve single-source or all- by finding a shortest path every time some pairs shortest-path problems, which perfor- edge costs change. Conventional search typi- mance measure they use, when they update cally does not reuse information from previous the shortest paths, which kinds of graph searches. The following example, however, il- topologies and edge costs they apply to, and lustrates the potential advantage of reusing in- how the graph topology and edge costs are al- formation from previous searches. lowed to change over time (Frigioni, Marchetti- Consider the gridworlds shown in figure 1. Spaccamela, and Nanni 1998). If arbitrary se- The original gridworld is shown in figure 1a, quences of edge insertions, deletions, or weight and the changed gridworld is shown in figure changes are allowed, then the dynamic short- 1b. Only two blockages have moved, resulting est-path problems are called fully dynamic in four cells with changed blockage status. The shortest-path problems (Frigioni, Marchetti-Spac- figure shows the shortest paths in both cases under the assumption that every move has cost camela, and Nanni 2000). one. The shortest path changed because two The idea of incremental search has also been cells on the original shortest path became un- pursued in AI for problems other than path traversable. finding. For example, a variety of algorithms The length of a shortest path from the start have been developed for solving constraint-sat- cell to a cell is called its start distance. Once the isfaction problems (Dechter and Dechter 1988; start distances of all cells are known, one can eas- Verfaillie and Schiex 1994) or constraint logic ily trace back a shortest path from the start cell programming problems (Miguel and Shen to the goal cell by always greedily decreasing the 1999) where the constraints change over time. start distance, starting at the goal cell. The start In this article, however, we study incremental distances are shown in each traversable cell of search only in the context of dynamic shortest- the original and changed gridworlds (figures 1a path problems, where it has not been studied and 1b). Those cells whose start distances in the extensively in AI. changed gridworld (figure 1b) are different from We believe that four achievements are neces- the corresponding cells in the original grid- sary to make incremental search more popular world; they are shaded gray in figure 1b. Even in AI. First, one needs to devise more powerful though large parts of the shortest path have incremental search algorithms than those that changed, less than a quarter of the start distances currently exist. Second, one needs to study have changed. Thus, in such cases, there is a po- their properties more extensively, both analyt- tential advantage to recalculating only those ically and experimentally, to understand their start distances that have changed, which is an ar- gument for caching the start distances rather strengths and limitations better. Third, one than the shortest path itself. needs to demonstrate that they apply to AI ap- Caching the start distances is basically what plications and compare them to other search the incremental search algorithm DYNAMIC- algorithms for these applications to demon- SWSF-FP (Ramalingam and Reps 1996a) does.1 strate that they indeed have advantages over DYNAMICSWSF-FP was originally developed in them. Finally, the AI community needs to be the context of parsing theory and theoretical made more aware of incremental search. This computer science. It uses a clever way of iden- article addresses the last issue so that more re- tifying the start distances that have not searchers can address the first three. It describes changed and recalculates only the ones that one particular incremental search algorithm have changed. Consequently, it performs best and its potential applications and then discuss- in situations where only a small number of es its potential advantages and limitations. start distances change. 100 AI MAGAZINE Articles A. Original Eight-Connected Gridworld Sstart 1 2 3 4 5 6 7 8 9 1 192 3 4 5 6 7 8 2 292 3 4 5 6 7 8 3 4 4135 6 7 12 12 12 5 5137 11 11 12 6 6136 7 8 10 11 12 8 9 10 11 12 13 12 1110 9 9 11 13 12 1110 10 10 12 12 Sgoal B. Changed Eight-Connected Gridworld Sstart 1 2 3 4 5 6 7 8 9 1 192 3 4 5 6 7 8 2 292 3 4 5 6 7 8 3 9 4 4105 6 7 12 11 10 5 51111 11 11 6 6 6 7 8 10 11 12 12 7 8 9 10 11 12 13 9 8138 8 9 11 9 9129 9 9 Sgoal Figure 1.