Saturday 01 February 2025
The puzzle of higher-dimensional sliding puzzles has long been a fascinating challenge for computer scientists and mathematicians alike. In recent years, researchers have made significant progress in solving these puzzles using various algorithms, including evolutionary algorithms (EAs) and reinforcement learning (RL). A new study published this week explores the performance of EAs and RL on higher-dimensional sliding puzzles with varying face dimensions.
The researchers created a series of puzzles with different dimensions (d = 3, 4, and 5) and face dimensions (k = 1 to d −1). Each puzzle consisted of a hypercube with a specified number of uncoloured vertices (l), which were randomly assigned initial positions. The target configuration was defined as the desired final arrangement of the rings on the hypercube.
The EAs used in this study employed a mutation algorithm, where each agent’s configuration was modified by randomly selecting a face and moving one ring to an adjacent position. The RL approach used a search algorithm that explored the puzzle space by iteratively applying moves until reaching the target configuration or exhausting all possible combinations.
The results showed that both EAs and RL were able to solve the puzzles with varying degrees of success. For lower-dimensional puzzles (d = 3), the EAs outperformed RL, solving most puzzles within a reasonable number of generations. However, for higher-dimensional puzzles (d = 4 and 5), RL performed better, particularly when faced with more challenging configurations.
The study also highlighted the importance of face dimension (k) in determining puzzle difficulty. As k increased, the puzzles became increasingly harder to solve, with EAs struggling to find a solution for larger values of k. In contrast, RL was able to adapt to these changes and maintain its performance across different face dimensions.
One notable aspect of this study is the exploration of EA parameters and their impact on puzzle-solving performance. The researchers found that adjusting the mutation rate (c) significantly influenced the success rate and number of generations required to reach the target configuration. This highlights the importance of fine-tuning algorithmic parameters for optimal performance in complex problem domains.
The findings of this study have important implications for the development of more efficient and effective algorithms for solving higher-dimensional sliding puzzles. As researchers continue to push the boundaries of what is possible, these results demonstrate that EAs and RL can be powerful tools for tackling complex problems in computer science and mathematics.
Cite this article: “Higher-Dimensional Sliding Puzzles: A Comparative Study of Evolutionary Algorithms and Reinforcement Learning”, The Science Archive, 2025.
Higher-Dimensional Sliding Puzzles, Evolutionary Algorithms, Reinforcement Learning, Hypercubes, Face Dimensions, Mutation Algorithm, Search Algorithm, Puzzle Difficulty, Algorithmic Parameters, Computational Complexity.
