Domain-Dependent Single-Agent Search Enhancements

Al research has developed an extensive collect ion of methods to solve state-space problems. Using the challenging domain of Sokoban, this paper studies the effect of search enhancements on program performance. We show that the current state of the ar t in AT generally requires a large p rog ramming and research effort into domain-dependent: methods to solve even moderately complex problems in such di f f icul t domains. The appl icat ion of domain-specif ic knowledge to exploi t propert ies of the search space can result in large reductions in the size of the search tree, often several orders of magni tude per search enhancement. Understanding the effect of these enhancements on the search leads to a new taxonomy of search enhancements, and a new f ramework for developing single-agent search appl icat ions. Th is is used to i l lust rate the large gap between what is portrayed in the l i terature versus what is needed in practice. K e y w o r d s : single-agent search, I D A * , Sokoban 1 I n t r o d u c t i o n The AI research commun i t y has developed an impressive suite of techniques for solv ing state-space problems. These techniques range f rom general-purpose domain independent methods such as A * , to domain-specif ic enhancements. There is a strong movement toward develop ing domain independent methods to solve problems. Wh i l e these approaches require m in ima l effort to specify a problem to be solved, the performance of these solvers is often l im i t ed , exceeding available resources on even simple prob lem instances. Th is requires the development of domain-dependent methods tha t explo i t addit ional knowledge about the search space. These methods can great ly improve the efficiency of a search based prog r a m , as measured in the size of the search tree needed to solve a problem instance. Th is paper presents a study on solv ing chal lenging single-agent search problems for the domain of Sokoban. Sokoban is a one-player game and is of general interest as an instance of a robot mo t ion p lann ing problem [Dor and Zwiek, 1995]. Sokoban is analogous to the prob lem of having a robot in a warehouse move specified goods f rom their current locat ion to their f inal dest inat ion, sul>ject to the topology of the warehouse and any obstacles in the way. Sokoban has been shown to be NP-hard [Culberson, 1997; Dor and Zwick, 1995]. Previously we reported on our a t tempts to solve Sokoban problems using the standard single-agent search techniques available in the l i terature [Junghanns and Schaeffer, 1998c]. When these proved inadequate, solving only 10 of a 90-problcm test suite, new a lgor i thms had to be developed to improve search efficiency [Junghanns and Schaeffer, 1998b; 1998a]. Th is allowed 47 problems to be op t ima l l y solved, or nearly so. Add i t ional efforts have since increased this number to 52. The results here show the large gains achieved by adding appl icat ion-dependent knowledge to our program Rolling Stone. W i t h each enhancement, reduct ions of the search tree size by several orders of magn i tude are possible. Ana lyz ing all the addi t ions made to the Sokoban solver reveals tha t the most valuable search enhancements are based on search (both on-l ine and off-l ine) by improv ing the lower bound. We classify the search enhancements along several dimensions inc lud ing their generali ty, compu ta t i ona l mode l , completeness and admissib i l i ty . Not surpr is ingly, the more specific an enhancement is, the greater its impact on search performance. When presented in the l i te ra ture, single-agent search (usually I D A * ) consists of a few lines of code. Most textbooks do not discuss search enhancements, other than cycle detect ion. In real i ty, non t r i v ia l single-agent search problems require more extensive p rog ramming (and possibly research) effort. For example, achieving high performance at solv ing s l id ing t i le puzzles requires enhancements such as cycle detect ion, pa t te rn databases, move order ing and enhanced lower bound calculat ions [Culberson and Schaeffer, 1996]. In th is paper, we out l ine a new f ramework for developing high-performance single-agent search programs. Th is paper contains the fo l lowing cont r ibut ions: 1. A case study showing the evolu t ion of a Sokoban 570 COMPUTER GAME PLAYING Figure 1: Problem #1 of the Test Set solver's performance, beginning wi th a domainindependent solver and ending wi th a highly-tuned, application-dependent program. 2. A taxonomy of single-agent search enhancements. 3. A new framework for single-agent search, including search enhancements and their control functions.