Recent Progress in the Design and Analysis of Admissible Heuristic Functions

In the past several years, significant progress has been made in finding optimal solutions to combinatorial problems. In particular, random instances of both Rubik’s Cube, with over 10 19 states, and the 5 5 sliding-tile puzzle, with almost 10 states, have been solved optimally. This progress is not the result of better search algorithms, but more effective heuristic evaluation functions. In addition, we have learned how to accurately predict the running time of admissible heuristic search algorithms, as a function of the solution depth and the heuristic evaluation function. One corollary of this analysis is that an admissible heuristic function reduces the effective depth of search, rather than the effective branching factor.