Many-Problem Surrogates for Transfer Evolutionary Multiobjective Optimization with Sparse Transfer Stacking

For expensive multiobjective optimization problems, there exists useful knowledge, e.g., the trained surrogate models, can be transferred to assist the optimization of a target optimization problem, which is termed as multiproblem surrogates. Stacking transfer is able to combine the pretrained source surrogate models and the preliminary target model with a meta-regression algorithm to transfer knowledge from source to target. However, when large-scale source models are involved in the many-problem scenarios, the less correlated sources may hurt the target performance, which is known as negative transfer. In this article, sparse representation of the coefficients of meta-regression is considered to automatically select the most relevant source models for largely avoiding negative transfer. In the proposed many-problem surrogates, the coefficients of the source and target models are assumed to be sparse under the non-negativity and sum-to-one constraints. Then, a sparse transfer stacking model is established with l(1) -norm of the coefficients. Next, the alternating direction method of multipliers is employed to solve the resulting constrained optimization problem by converting it into several much simpler problems. Most of the previous works assume that the costs for evaluation have no much difference and this assumption rarely holds in the real-world applications. In order to further reduce the total costs, an improved surrogate model with a cost-sensitive measure is designed to estimate the cost and select new solutions for real evaluation based on their estimated fitness, uncertainty and cost. Experimental results on synthetic and practical problems have demonstrated the superiority of the proposed many-problem surrogates.