Tomas Rokicki proved that it could be solved in a maximum of twenty-five iterations, improving on the work of Kunkle and Cooperman, while the minimum number of iterations needed can be as high as eighteen.  
Richard Korf developed the IDA* [I-D-A-Star] algorithm to solve this problem, and Herbert Kociemba improved upon Thistlethwaite's algorithm for solving it.  Tomas Rokicki proved that it could be solved in a maximum of twenty-five iterations, improving on the work of Kunkle and Cooperman, while the minimum number of iterations needed can be as high as eighteen.  The existence of a "God's Algorithm" for this problem has not been conclusively proven.  For 10 points, what is this problem, which involves several iterations of face-turns in an attempt to get each of six faces to display the same color?
Richard Korf developed the IDA* [I-D-A-Star] algorithm to solve this problem, and Herbert Kociemba improved upon Thistlethwaite's algorithm for solving it.  
(solving the) {Rubik's Cube} (for any random position)