Dimensionality Reduction Using Variational Autoencoders in Constrained Evolutionary Multiobjective Optimization

Constrained multi-objective optimization problems (CMOPs) involving linear equality constraints arise in many real applications. Linear equality constraints confine the feasible region to a low-dimensional manifold embedded in the original decision space, which poses significant difficulties for conventional constraint-handling mechanisms in evolutionary algorithms (EAs). To overcome this challenge, we propose a variational autoencoder (VAE)-assisted evolutionary framework, termed L-MOEA-VAE. The VAE learns a low-dimensional latent representation of the feasible region from the nondominated solutions collected during the evolutionary process. Offspring are generated in both the learned latent space and the original decision space, with a probability parameter that adaptively allocates the search effort between the two spaces. This probability is updated online based on the survival rate of VAE-generated offspring. Additionally, a projection-based repair operator is employed to map infeasible solutions back onto the feasible manifold. Experimental results on a set of benchmark multiobjective test problems with linear equality constraints demonstrate that the proposed framework achieves superior performance in terms of both convergence and diversity compared to several existing baseline or recent constrained multi-objective evolutionary algorithms.