Progressive auto-encoding for domain adaptation in evolutionary multi-task optimization

In recent years, evolutionary multi-task optimization (EMTO) has emerged as an effective paradigm for solving multiple optimization tasks simultaneously by leveraging knowledge transfer across tasks. The domain adaptation technique plays an important role in EMTO, as it helps align search spaces to support knowledge transfer among tasks. However, most existing domain adaptation methods rely on static pre-training or periodic re-matched mechanism, which do not adapt well to the dynamic change in evolving populations. In this paper, we propose a progressive auto-encoding (PAE) technique that enables continuous domain adaptation throughout the EMTO process. The PAE incorporates two complementary adaptation strategies: i) segmented PAE, which employs staged training of auto-encoders to achieve effective domain alignment across different optimization phases, and ii) smooth PAE, which utilizes eliminated solutions from the evolutionary process to facilitate more gradual and refined domain adaptation. We integrate the PAE into both single-objective and multi-objective multi-task evolutionary algorithms, yielding MTEA-PAE and MO-MTEA-PAE, respectively. Comprehensive experiments conducted on six benchmark suites and five real-world applications validate the effectiveness of our proposed PAE technique in enhancing domain adaptation capabilities within EMTO.