An adaptive Gaussian process based manifold transfer learning to expensive dynamic multi-objective optimization

Abstract

Expensive dynamic multi-objective optimization problems (EDMOPs) is one kind of DMOPs where the objectives change over time and the function evaluations commonly involve computationally intensive simulations or costly physical experiments. Hence, the key to solve EDMOPs is to quickly and accurately track the time-varying Pareto optimal fronts under the limit of small number of function evaluations, in which how to augment enough training data to build informative surrogate models and manage the models during the search process. To overcome the issue, we propose a transfer learning based surrogate assisted evolutionary algorithm (TrSA-DMOEA) to efficiently solve EDMOPs. Specifically, when a change occurs, we propose a knee point-based manifold transfer learning method based on geodesic flow kernel, which exploits the knowledge from previous high-quality knee solutions to augment the training data for building Gaussian process models, thereby improving the computational complexity and the quality of solutions. Moreover, to efficiently find the optima with limited budget of function evaluations, a novel surrogate-assisted mechanism based on an adaptive acquisition function is introduced, which achieves a balance between convergence and diversity by adaptively adjusting the weights of the angle-penalized distance and average uncertainty at different search stages. By comparing with state-of-the-art algorithms on widely used test problems, the experimental results demonstrate that the proposed method outperforms others and is able to efficiently solve EDMOPs.