Krzysztof Michalak
ABSTRACT
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 Rk (where in practice k = 2 or 3). Points embedded in Rk 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 → Rk.
- Shumeet Baluja and Rich Caruana. 1995. Removing the Genetics from the Standard Genetic Algorithm. In Machine Learning Proceedings 1995, Armand Prieditis and Stuart Russell (Eds.). Morgan Kaufmann, San Francisco, 38--46. Google Scholar
Digital Library
- Krzysztof Michalak. 2015. The Sim-EA Algorithm with Operator Autoadaptation for the Multiobjective Firefighter Problem. In Evolutionary Computation in Combinatorial Optimization, Gabriela Ochoa and Francisco Chicano (Eds.). LNCS, Vol. 9026. Springer, 184--196.Google Scholar
- K. Michalak. 2019. Low-Dimensional Euclidean Embedding for Visualization of Search Spaces in Combinatorial Optimization. IEEE Transactions on Evolutionary Computation 23, 2 (2019), 232--246.Google ScholarCross Ref
- L.J.P. van der Maaten. 2014. Accelerating t-SNE using Tree-Based Algorithms. Journal of Machine Learning Research 15 (2014), 3221--3245. Google ScholarDigital Library
Index Terms
- Low-Dimensional euclidean embedding for visualization of search spaces in combinatorial optimization
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