<p>Co-clustering is widely used for data analysis that independently reveals the clustering structures of rows and columns while also identifying their inter-relationships, which renders it more informative than conventional one-way clustering methods. Co-clustering is to not only cluster the samples and features of original data, but also mine the relationship between samples and features, and this is naturally a multi-objective problem. However, researchers frequently utilize the method of single-objective optimization to solve the co-clustering issue, while disregarding its multi-objective nature, and the side information in the original data is also ignored. To address these problems, we propose a self-supervised non-dominated sorted model for co-clustering (SNSC), which is represented by a group of multi-objective functions. The model not only perfectly aligns with the multi-objective nature of co-clustering tasks but also utilizes the supervised information in the original data. The objective function group consists of four objective functions acting on the original data and similarity matrix respectively. The heuristic initialization method with self-supervised properties is used in conjunction with the random initialization method, which improves the efficiency of the model and reduces the likelihood of converging to local optima. The overall model remains unsupervised, as all the supervised information is derived from the original data. Further, the algorithm for the SNSC model is designed by using the idea of the genetic algorithm, which is theoretically supported, and the complexity analysis of the algorithm is given. Finally, experiments on 12 datasets and 5 comparison algorithms show that the SNSC algorithm has significant advantages.</p>