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The evolutionary multitask optimization (EMTO) algorithm is a promising approach to solve many-task optimization problems (MaTOPs), in which similarity measurement and knowledge transfer (KT) are two key issues. Many existing EMTO algorithms estimate the similarity of population distribution to select a set of similar tasks and then perform KT by simply mixing individuals among the selected tasks. However, these methods may be less effective when the global optima of the tasks greatly differ from each other. Therefore, this article proposes to consider a new kind of similarity, namely, shift invariance, between tasks. The shift invariance is defined that the two tasks are similar after linear shift transformation on both the search space and the objective space. To identify and utilize the shift invariance between tasks, a two-stage transferable adaptive differential evolution (TRADE) algorithm is proposed. In the first evolution stage, a task representation strategy is proposed to represent each task by a vector that embeds the evolution information. Then, a task grouping strategy is proposed to group the similar (i.e., shift invariant) tasks into the same group while the dissimilar tasks into different groups. In the second evolution stage, a novel successful evolution experience transfer method is proposed to adaptively utilize the suitable parameters by transferring successful parameters among similar tasks within the same group. Comprehensive experiments are carried out on two representative MaTOP benchmarks with a total of 16 instances and a real-world application. The comparative results show that the proposed TRADE is superior to some state-of-the-art EMTO algorithms and single-task optimization algorithms.
Wu et al. (Wed,) studied this question.