Classification performance is significantly affected by dependencies between class variables in multi-dimensional classification. These dependencies are effectively modeled by classifier chain algorithms. However, their performance is constrained by issues such as label order selection and error propagation. To address these limitations, this paper introduces a decomposition and ranking-based classifier chain for multi-dimensional classification algorithm. Initially, the multi-dimensional classification problem is simplified into binary classification problems using a one-vs-one strategy, which reduces complexity. Subsequently, the label order is treated as a linear ordering problem and optimized with the genetic algorithm to determine the optimal sequence. Finally, a feature space control strategy is proposed to minimize the impact of early classification errors on subsequent classifiers. Experiments conducted on 10 real-world datasets demonstrate that the proposed algorithm outperforms the state-of-the-art methods while also exhibiting lower computational complexity.