Visualizing Combinatorial Search Spaces with Low-Dimensional Euclidean Embedding

The low dimensional Euclidean embedding method (LDEE) allows visualizing combinatorial search spaces by mapping to the Euclidean space R k (with k = 2 or 3 in practice). The mapping of a combinatorial search space Ω to R k is obtained by first running the t-SNE (t-distributed stochastic neighbor embedding) algorithm with an appropriate probability distribution used for the space Ω (for example the Mallows distribution for permutation spaces). Subsequently, the vacuum embedding algorithm, proposed in this article, is used to ensure good visual separation of solutions in R k . The LDEE method maps solutions to a regular grid in R k , which can be used for plotting various kinds of information. Apart from solution evaluations or comparisons of multiple objectives, the proposed method can be used for analyzing the behavior of the population in population-based metaheuristics, the working of genetic operators, etc. This newsletter contribution summarizes a recent research article [1].