Bayesian Co-evolutionary Optimization based entropy search for high-dimensional many-objective optimization

Hongli Bian, Jie Tian, Jialiang Yu, Han Yu

Abstract: Bayesian evolutionary optimization algorithms have been widely employed to solve expensive many-objective optimization problems. However, the existing approaches are generally designed for low-dimensional problems. In high-dimensional problems, the accuracy of the prediction decreases. And the acquisition function becomes ineffective. The combination of these challenges renders existing approaches unsuitable for selecting potential individual solutions for high-dimensional many-objective optimization problems. To address these limitations, we propose a novel Entropy Search-based Bayesian Co-Evolutionary Optimization approach (ESB-CEO). With the co-evolutionary algorithm as the basic optimizer, it executes an adaptive acquisition function combining the Lp<math><msub is="true"><mrow is="true"><mi is="true">L</mi></mrow><mrow is="true"><mi is="true">p</mi></mrow></msub></math>-norm and information entropy to efficiently solve computationally expensive many-objective optimization problems. Individual solutions that have a significant effect on different search stages can be effectively identified, which improves the convergence and diversity of the algorithm. Extensive experimental results based on a set of expensive multi/many-objective test problems demonstrate that the proposed approach significantly outperforms five state-of-the-art surrogate-assisted evolutionary algorithms.