Batched Data-Driven Evolutionary Multiobjective Optimization Based on Manifold Interpolation

Multiobjective optimization problems are ubiquitous in real-world science, engineering, and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of nondominated tradeoff solutions, where the expensive objective functions are approximated as a surrogate model. In this article, we propose a framework for implementing batched data-driven evolutionary multiobjective optimization (EMO). It is so general that any off-the-shelf EMO algorithms can be applied in a plug-in manner. There are two unique components: 1) based on the Karush–Kuhn–Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set and 2) a batch recommendation approach that reduces the computational time of the data-driven evolutionary optimization process by evaluating multiple samples at a time in parallel. Comparing against seven state-of-the-art surrogate-assisted evolutionary algorithms, experiments on 168 benchmark test problem instances with various properties and a real-world application on hyper-parameter optimization fully demonstrate the effectiveness and superiority of our proposed framework, which is featured with a faster convergence and a stronger resilience to various Pareto-optimal front shapes.