Transfer learning based surrogate assisted evolutionary bi-objective optimization for objectives with different evaluation times

Various multiobjective optimization algorithms have been proposed with a common assumption that the evaluation of each objective function takes the same period of time. Little attention has been paid to more general and realistic optimization scenarios where different objectives are evaluated by different computer simulations or physical experiments with different time complexities (latencies) and only a very limited number of function evaluations is allowed for the slow objective. In this work, we investigate benchmark scenarios with two objectives. We propose a transfer learning scheme within a surrogate-assisted evolutionary algorithm framework to augment the training data for the surrogate for the slow objective function by transferring knowledge from the fast one. Specifically, a hybrid domain adaptation method aligning the second-order statistics and marginal distributions across domains is introduced to generate promising samples in the decision space according to the search experience of the fast one. A Gaussian process model based co-training method is adopted to predict the value of the slow objective and those having a high confidence level are selected as the augmented synthetic training data, thereby enhancing the approximation quality of the surrogate of the slow objective. Our experimental results demonstrate that the proposed algorithm outperforms existing surrogate and non-surrogate-assisted delay-handling methods on a range of bi-objective optimization problems. The approach is also more robust to varying levels of latency and correlation between the objectives.