This paper presents an investigation on the usage of modern dimensionality reduction methods for classic combinatorial optimization problems. We propose the use of t-Distributed Stochastic Neighbor Embedding (t-SNE) method to visualize feasible regions on high-dimensional permutations, aiming to avoid the consequences of combinatorial explosion. The results of the study indicate that the proposed approach can provide valuable insights and improve the understanding of the solution space of high-dimensional permutations for the application of local search approaches.