abstract

Low-Dimensional euclidean embedding for visualization of search spaces in combinatorial optimization

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Krzysztof MichalakAuthors Info & Claims

GECCO '19: Proceedings of the Genetic and Evolutionary Computation Conference Companion

Pages 27 - 28

https://doi.org/10.1145/3319619.3326761

Published: 13 July 2019 Publication History

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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 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.

References

[1]

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.

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[2]

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.

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[3]

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.

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[4]

L.J.P. van der Maaten. 2014. Accelerating t-SNE using Tree-Based Algorithms. Journal of Machine Learning Research 15 (2014), 3221--3245.

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Cited By

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Tran BLuong NLi XHandl J(2024)On the Investigation of Multimodal Evolutionary Algorithms Using Search Trajectory NetworksProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654050(32-40)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654050
Thomson SOchoa GVeerapen NMichalak KSilva SPaquete L(2023)Channel Configuration for Neural Architecture: Insights from the Search SpaceProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590386(1267-1275)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590386
Nolle LStahl FEl-Mihoub T(2023)On Explanations for Hybrid Artificial IntelligenceArtificial Intelligence XL10.1007/978-3-031-47994-6_1(3-15)Online publication date: 8-Nov-2023
https://doi.org/10.1007/978-3-031-47994-6_1

Index Terms

Low-Dimensional euclidean embedding for visualization of search spaces in combinatorial optimization
1. Computing methodologies
  1. Modeling and simulation
    1. Simulation types and techniques
      1. Scientific visualization
2. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial optimization
  2. Mathematical analysis
    1. Mathematical optimization
      1. Discrete optimization
        Optimization with randomized search heuristics
        Evolutionary algorithms

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Information

Published In

GECCO '19: Proceedings of the Genetic and Evolutionary Computation Conference Companion

July 2019

2161 pages

ISBN:9781450367486

DOI:10.1145/3319619

Editor:
Manuel López-Ibáñez
University of Manchester, UK
,
General Chairs:
Anne Auger
Inria and Ecole Polytechnique, France
,
Thomas Stützle
IRIDIA, Université libre de Bruxelles Belgium

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

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Published: 13 July 2019

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GECCO '19

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SIGEVO

GECCO '19: Genetic and Evolutionary Computation Conference

July 13 - 17, 2019

Prague, Czech Republic

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Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

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Tran BLuong NLi XHandl J(2024)On the Investigation of Multimodal Evolutionary Algorithms Using Search Trajectory NetworksProceedings of the Genetic and Evolutionary Computation Conference10.1145/3638529.3654050(32-40)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638529.3654050
Thomson SOchoa GVeerapen NMichalak KSilva SPaquete L(2023)Channel Configuration for Neural Architecture: Insights from the Search SpaceProceedings of the Genetic and Evolutionary Computation Conference10.1145/3583131.3590386(1267-1275)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583131.3590386
Nolle LStahl FEl-Mihoub T(2023)On Explanations for Hybrid Artificial IntelligenceArtificial Intelligence XL10.1007/978-3-031-47994-6_1(3-15)Online publication date: 8-Nov-2023
https://doi.org/10.1007/978-3-031-47994-6_1

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Visualizing Combinatorial Search Spaces with Low-Dimensional Euclidean Embedding

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Locally linear embedding based on correntropy measure for visualization and classification