Regularized Evolutionary Multitask Optimization: Learning to Intertask Transfer in Aligned Subspace

This article proposes a novel and computationally efficient explicit intertask information transfer strategy between optimization tasks by aligning the subspaces. In evolutionary multitasking, the tasks might have biases embedded in function landscapes and decision spaces, which often causes the threat of predominantly negative transfer. However, the complementary information among different tasks can give an enhanced performance of solving complicated problems when properly harnessed. In this article, we distill this insight by introducing an intertask knowledge transfer strategy implemented in the low-dimension subspaces via a learnable alignment matrix. Specifically, to unveil the significant features of the function landscapes, the task-specific low-dimension subspaces is established based on the distribution information of subpopulations possessed by tasks, respectively. Next, the alignment matrix between pairwise subspaces is learned by minimizing the discrepancies of the subspaces. Given the aligned subspaces by applying the alignment matrix to subspaces' base vectors, the individuals from different tasks are then projected into aligned subspaces and reproduce therein. Moreover, since this method only considers the leading eigenvectors, it turns out to be intrinsically regularized and noise-insensitive. Comprehensive experiments are conducted on the synthetic and practical benchmark problems so as to assess the efficacy of the proposed method. According to the experimental results, the proposed method exhibits a superior performance compared with existing evolutionary multitask optimization algorithms.