A Memetic Algorithm based on Variational Autoencoder for Black-Box Discrete Optimization with Epistasis among Parameters
Aoi Kato, Kenta Kojima, Masahiro Nomura, Isao Ono
TL;DR
This work tackles black-box discrete optimization with epistasis, a setting where single-parameter mutations often fail to improve the objective. It proposes a memetic algorithm that combines variational autoencoder (VAE) based sampling with bit-flip local search to efficiently explore high-dimensional, epistatic spaces. Across NK landscape benchmarks, the method outperforms state-of-the-art VAE-EDA variants and linkage-learning EAs, demonstrating superior optimization performance with scalable computation. The approach leverages the VAE to model parameter dependencies and uses FIHC-based refinement to achieve high-quality, diverse solutions, suggesting practical benefits for problems like neural architecture search and model estimation. Future work includes dynamic tuning of the VAE offspring parameter and extending to continuous or mixed-integer domains.
Abstract
Black-box discrete optimization (BB-DO) problems arise in many real-world applications, such as neural architecture search and mathematical model estimation. A key challenge in BB-DO is epistasis among parameters where multiple variables must be modified simultaneously to effectively improve the objective function. Estimation of Distribution Algorithms (EDAs) provide a powerful framework for tackling BB-DO problems. In particular, an EDA leveraging a Variational Autoencoder (VAE) has demonstrated strong performance on relatively low-dimensional problems with epistasis while reducing computational cost. Meanwhile, evolutionary algorithms such as DSMGA-II and P3, which integrate bit-flip-based local search with linkage learning, have shown excellent performance on high-dimensional problems. In this study, we propose a new memetic algorithm that combines VAE-based sampling with local search. The proposed method inherits the strengths of both VAE-based EDAs and local search-based approaches: it effectively handles high-dimensional problems with epistasis among parameters without incurring excessive computational overhead. Experiments on NK landscapes -- a challenging benchmark for BB-DO involving epistasis among parameters -- demonstrate that our method outperforms state-of-the-art VAE-based EDA methods, as well as leading approaches such as P3 and DSMGA-II.