Construction of Evaluation Functions for the Fifteen Puzzle by Learning Random Trials

Abstract

In this paper, we propose an evaluation function for the fifteen puzzle using a neural network learning random trials of moves of the puzzle. Using the IDA* algorithm with the evaluation function, we were able to solve problems of the fifteen puzzle with about one-6,600th times as less search nodes as the well-known Manhattan distance based evaluation function in average. Comparing to our evaluation function to non-admissible evaluation function whose values are products of Manhattan evaluation function and a constant between 1.3 and 1.7, the computation time were reduced to one-fifth to one-hundredth. We used data sets generated by random trials of moves from the goal pattern of the fifteen puzzle. In addition to the data sets, we chose some patterns whose distance from the goal state is 20 or 22, and which emerges frequently in the trial sequences, and we generated random sequences from the patterns. Adding those sets to the original random sequences and giving the sets to the neural network for learning, we were able to make the evaluation function more effective.