In the context of Industry 4.0, digital twin technology has emerged with rapid advancements as a powerful tool for visualizing and analyzing industrial assets. This technology has attracted considerable interest from researchers across diverse domains such as manufacturing, security, transportation, and gaming. The metaverse has emerged as a significant enabler in these domains, facilitating the integration of various technologies to create virtual replicas of physical assets. The utilization of 3D character animation, often referred to as avatars, is crucial for implementing the metaverse. Traditionally, costly motion capture technologies are employed for creating a realistic avatar system. To meet the needs of this evolving landscape, we have developed a modular framework tailored for asset digital twins as a more affordable alternative. This framework offers flexibility for the independent customization of individual system components. To validate our approach, we employ the English peg solitaire game as a use case, generating a solution tree using the breadth-first search algorithm. The results encompass both qualitative and quantitative findings of a data-driven 3D animation system utilizing motion primitives. The presented methodologies and infrastructure are adaptable and modular, making them applicable to asset digital twins across diverse business contexts. This case study lays the groundwork for pilot applications and can be tailored for education, health, or Industry 4.0 material development.
Morpion Solitaire is a popular single player game, performed with paper and pencil. Due to its large state space (on the order of the game of Go) traditional search algorithms, such as MCTS, have not been able to find good solutions. A later algorithm, Nested Rollout Policy Adaptation, was able to find a new record of 82 steps, albeit with large computational resources. After achieving this record, to the best of our knowledge, there has been no further progress reported, for about a decade. In this paper we take the recent impressive performance of deep self-learning reinforcement learning approaches from AlphaGo/AlphaZero as inspiration to design a searcher for Morpion Solitaire. A challenge of Morpion Solitaire is that the state space is sparse, there are few win/loss signals. Instead, we use an approach known as ranked reward to create a reinforcement learning self-play framework for Morpion Solitaire. This enables us to find medium-quality solutions with reasonable computational effort. Our record is a 67 steps solution, which is very close to the human best (68) without any other adaptation to the problem than using ranked reward. We list many further avenues for potential improvement.
The Immigration Game (invented by Don Woods in 1971) extends the solitaire Game of Life (invented by John Conway in 1970) to enable two-player competition. The Immigration Game can be used in a model of evolution by natural selection, where fitness is measured with competitions. The rules for the Game of Life belong to the family of semitotalistic rules, a family with 262,144 members. Woods' method for converting the Game of Life into a two-player game generalizes to 8,192 members of the family of semitotalistic rules. In this paper, we call the original Immigration Game the Life Immigration Game and we call the 8,192 generalizations Immigration Games (including the Life Immigration Game). The question we examine here is, what are the conditions for one of the 8,192 Immigration Games to be suitable for modeling open-ended evolution? Our focus here is specifically on conditions for the rules, as opposed to conditions for other aspects of the model of evolution. In previous work, it was conjectured that Turing-completeness of the rules for the Game of Life may have been necessary for the success of evolution using the Life Immigration Game. Here we present evidence that Turing-completeness is a sufficient condition on the rules of Immigration Games, but not a necessary condition. The evidence suggests that a necessary and sufficient condition on the rules of Immigration Games, for open-ended evolution, is that the rules should allow growth.
Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game effectively using constraint programming is hard. This abstract presents the game, contributes new generalized variants of the game suitable for benchmarking and testing, and describes a model for the presented variants. The question of the top possible score in the standard game is an open challenge.
Our ignorance of the winnability percentage of the solitaire card game `Klondike' has been described as "one of the embarrassments of applied mathematics". Klondike, the game in the Windows Solitaire program, is just one of many single-player card games, generically called 'patience' or 'solitaire' games, for which players have long wanted to know how likely a particular game is to be winnable. A number of different games have been studied empirically in the academic literature and by non-academic enthusiasts. Here we show that a single general purpose Artificial Intelligence program named `Solvitaire' can be used to determine the winnability percentage of 73 variants of 35 different single-player card games with a 95% confidence interval of +/- 0.1% or better. For example, we report the winnability of Klondike as 81.945%+/- 0.084% (in the `thoughtful' variant where the player knows the rank and suit of all cards), a 30-fold reduction in confidence interval over the best previous result. The vast majority of our results are either entirely new or represent significant improvements on previous knowledge.
Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board before solving the challenge. These setup rules greatly increase the number of possible challenges, but can often generate unsolvable or uninteresting challenges. To better understand the compromises involved in minimizing undesirable challenges, we examine three games where component design choices can influence the stochastic nature of the resulting challenge generation algorithms. We evaluate the effect of these components and algorithms on challenge solvability and challenge engagement. We find that algorithms which control randomness through entangling components based on sub-elements of the puzzle mechanics can generate interesting challenges with a high probability of being solvable.