Semi-supervised clustering, a technique that combines semi-supervised learning and clustering, is widely employed in the field of machine learning. However, clustering itself poses challenges as it is an NP-hard and multi-objective problem. Consequently, meta-heuristic and multi-objective algorithms have shown greater success in addressing this problem. Nonetheless, these algorithms often encounter issues such as being trapped in local optima and requiring manual parameter adjustments. This research paper introduces an algorithm that tackles the problem of semi-supervised clustering by creating convex hulls of the initial labeled data within each cluster. It also incorporates the labeling of data enclosed within these convex hulls and the adaptive adjustment of parameters using a multi-objective cuckoo algorithm. To enhance the results, labeled data is utilized in the initialization and learning phases of the algorithm. The proposed approach is evaluated using 11 UCI datasets and five synthetic datasets in various experiments. The statistical and numerical analysis demonstrates that the proposed method outperforms the other six algorithms used for comparison. The experiments employ four evaluation criteria, namely ARI, Accuracy, NMI, and F-measure. The results show the superiority of the proposed method across the majority of the datasets.