Evolution for automatic assessment of the difficulty of sokoban boards

Many games have a collection of boards with the difficulty of an instance of the game determined by the starting configuration of the board. Correctly rating the difficulty of the boards is somewhat haphazard and required either a remarkable level of understanding of the game or a good deal of play-testing. In this study we explore evolutionary algorithms as a tool to automatically grade the difficulty of boards for a version of the game sokoban. Mean time-to-solution by an evolutionary algorithm and number of failures to solve a board are used as a surrogate for the difficulty of a board. Initial testing with a simple string-based representation, giving a sequence of moves for the sokoban agent, provided very little signal; it usually failed. Two other representations, based on a reactive linear genetic programming structure called an ISAc list, generated useful hardness-classification information for both hardness surrogates. These two representations differ in that one uses a randomly initialized population of ISAc lists while the other initializes populations with competent agents pre-trained on random collections of sokoban boards. The study encompasses four hardness surrogates: probability-of-failure and mean time-to-solution for each of these two representations. All four are found to generate similar information about board hardness, but probability-of-failure with pre-evolved agents is found to be faster to compute and to have a clearer meaning than the other three board-hardness surrogates.