# A latent space-based estimation of distribution algorithm for large-scale global optimization

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## Abstract

Large-scale global optimization problems (LSGOs) have received considerable attention in the field of meta-heuristic algorithms. Estimation of distribution algorithms (EDAs) are a major branch of meta-heuristic algorithms. However, how to effectively build the probabilistic model for EDA in high dimensions is confronted with obstacle, making them less attractive due to the large computational requirements. To overcome the shortcomings of EDAs, this paper proposed a latent space-based EDA (LS-EDA), which transforms the multivariate probabilistic model of Gaussian-based EDA into its principal component latent subspace with lower dimensionality. LS-EDA can efficiently reduce the complexity of EDA while maintaining its probability model without losing key information to scale up its performance for LSGOs. When the original dimensions are projected to the latent subspace, those dimensions with larger projected value make more contribution to the optimization process. LS-EDA can also help recognize and understand the problem structure, especially for black-box optimization problems. Due to dimensionality reduction, its computational budget and population size can be effectively reduced while its performance is highly competitive in comparison with the state-of-the-art meta-heuristic algorithms for LSGOs. In order to understand the strengths and weaknesses of LS-EDA, we have carried out extensive computational studies. Our results revealed LS-EDA outperforms the others on the benchmark functions with overlap and nonseparate variables.

## Keywords

Probabilistic PCA Estimation of distribution algorithm (EDA) Maximum likelihood estimate (MLE)## Notes

### Acknowledgements

This study was funded by the NSF of China (Grant Numbers 61170305, 61672024), the NSF of USA (Grant Number CMMI-1162482) and the Key Research Program in Higher Education of Henan (Grant Number 17A520046).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

### Informed consent

Informed consent was obtained from all individual participants included in the study.

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