ExTrEMO: Transfer Evolutionary Multiobjective Optimization With Proof of Faster Convergence

Transfer multiobjective optimization promises sample-efficient discovery of near Pareto-optimal solutions to a target task by utilizing experiential priors from related source tasks. In this paper, we show that in domains where evaluation data is at a premium, e.g., in scientific and engineering disciplines involving time-consuming computer simulations or complex real-world experimentation, knowledge transfer through surrogate models can be pivotal in saving sample evaluation costs. While state-of-the-art algorithms (without transfer) typically assume budgets in the order of only a few hundred evaluations, we seek to explore how far we can get on even tighter budgets. The uniqueness of our proposed Expensive Transfer Evolutionary Multiobjective Optimizer (ExTrEMO) is that it can maximally utilize external information from hundreds of source datasets, including those that may be negatively correlated with the target task. This is achieved by melding evolutionary search with factorized transfer Gaussian process surrogates, capturing varied source-target correlations in potentially decentralized computation environments. We provide a regret bound analysis for ExTrEMO that translates to a theoretical proof of increasingly faster convergence as a result of multi-source transfers. The theory is experimentally verified on benchmark functions and toward accelerated design of biomedical microdevices. We release our code at https://github.com/LiuJ-2023/ExTrEMO.