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This abstract summarizes the results reported in the paper [3]. In this paper a method named Low-Dimensional Euclidean Embedding (LDEE) is proposed, which can be used for visualizing high-dimensional combinatorial spaces, for example search spaces of metaheuristic algorithms solving combinatorial optimization problems. The LDEE method transforms solutions of the optimization problem from the search space Ω to R^k (where in practice k = 2 or 3). Points embedded in R^k can be used, for example, to visualize populations in an evolutionary algorithm.

The paper shows how the assumptions underlying the the t-Distributed Stochastic Neighbor Embedding (t-SNE) method can be generalized to combinatorial (for example permutation) spaces. The LDEE method combines the generalized t-SNE method with a new Vacuum Embedding method proposed in this paper to perform the mapping Ω → R^k.