Recent progress in heuristic search: A case study of the four-peg towers of Hanoi problem

We integrate a number of new and recent advances in heuristic search, and apply them to the fourpeg Towers of Hanoi problem. These include frontier search, disk-based search, parallel processing, multiple, compressed, disjoint, and additive pattern database heuristics, and breadth-first heuristic search. New ideas include pattern database heuristics based on multiple goal states, a method to reduce coordination among multiple parallel threads, and a method for reducing the number of heuristic calculations. We perform the first complete breadth-first searches of the 21 and 22-disc fourpeg Towers of Hanoi problems, and extend the verification of "presumed optimal solutions" to this problem from 24 to 30 discs. Verification of the 31-disc problem is in progress.