The Lemmings Puzzle: Computational Complexity of an Approach and Identification of Difficult Instances

Artificial Intelligence can be thought of as the study of machines that are capable of solving problems that require human level intelligence. It has frequently been concerned with game playing. In this thesis we shall focus on the areas of search and complexity, with respect to single-player games. These types of games are called puzzles. Puzzles have received research attention for some decades. Consequently, interesting insights into some of these puzzles, and into the approaches for solving them, have emerged. However, many of these puzzles have been neglected by the artificial intelligence research community. Therefore, we survey these puzzles in the hope that we can motivate research towards them so that further interesting insights might emerge in the future. We describe research on a puzzle called LEMMINGS that is derived from a game called Lemmings, which itself is in NP-Complete. We attempt to find the first successful approach for LEMMINGS. We report on a successful approach to a sub-problem called α-LEMMINGS, and an investigation into different initialisation schemes for the approach. We also report a similar approach for the general LEMMINGS problem, and an investigation in order to find the best parameters to use for this approach to LEMMINGS. Furthermore, we outline the time and space requirements for this approach. Previous work has shown that difficult problems, which are contained in the set of NP-Complete problems, are sometimes easy to solve in general. The existence of a small number of hard instances of these problems yields their high difficulty. Previous work has also shown where the difficult instances are located. We report on an investigation that aims to find difficult instances of LEMMINGS. Future investigations, for example algorithm testing on benchmark problems, might make use of our difficult LEMMINGS instances.