Computational Studies on Dynamic Multi-objective Optimization with Feature Representation Transfer

Transfer learning-based dynamic multi-objective evolutionary algorithms (Tr-DMOEAs) represent one of the earliest feature-representation-transfer optimization approaches in dynamic multi-objective optimization. Our previous investigations into Tr-DMOEAs revealed transfer effectiveness on problems with drastic shifts in Pareto-optimal sets (PSs), and demonstrated the superiority of a linear kernel over the original Gaussian kernel. This paper conducts comprehensive comparative studies on knowledge transfer in Tr-DMOEA variants with a linear kernel. We firstly investigate how transfer works in Tr- DMOEA with a linear kernel. We then propose six new Tr- DMOEA variants with linear feature representations to study the impact of different components of knowledge transfer in Tr- DMOEA. Among them, two variants have different approaches to learning linear feature representations, and four variants use different source knowledge selection methods. We show that all these six variants have little impact on knowledge transfer in Tr-DMOEA (i.e., little impact on the dynamic optimization). Considering the computational cost of feature representation learning and its little impact on knowledge transfer in Tr- DMOEA, we then propose three other new Tr-DMOEA variants without learning feature representations to further investigate their impact on knowledge transfer. The three variants have different methods of selecting source knowledge, which are experimentally shown to have few impact on knowledge transfer in Tr-DMOEA either. Finally, we demonstrate the superiority of Tr-DMOEA variants without feature representation over those with it regarding solution quality and transfer efficiency. Our studies show that feature representation is not essential in transfer learning based dynamic optimization.