A feedback matrix based evolutionary multitasking algorithm for high-dimensional ROC convex hull maximization

Abstract

Multi-objective evolutionary algorithms have shown their competitiveness in solving ROC convex hull maximization. However, due to “the curse of dimensionality”, few of them focus on high-dimensional ROCCH maximization. Therefore, in this paper, a feedback matrix (FM)-based evolutionary multitasking algorithm, termed as FM-EMTA, is proposed. In FM-EMTA, to tackle “the curse of dimensionality”, a feature importance based low-dimensional task construction strategy is designed to transform the high-dimensional ROCCH maximization task into several low-dimensional tasks. Then, each low-dimensional task evolves with a population. To ensure that the low-dimensional task achieves a better ROCCH, an FM-based evolutionary multitasking operator is proposed. Specifically, for each low-dimensional task i, the element FM(i,j) in feedback matrix is defined to measure the degree that the low-dimensional task j could assist task i. Based on it, an FM-based assisted task selection operator and an FM-based knowledge transfer operator are developed to constitute the evolutionary multitasking operator, with which the useful knowledge is transferred among the low-dimensional tasks. After the evolution, the best ROCCHs obtained by the low-dimensional tasks are combined together to achieve the final ROCCH on the original high-dimensional task. Experiments on twelve high-dimensional datasets with different characteristics demonstrate the superiority of the proposed FM-EMTA over the state-of-the-arts in terms of the area under ROCCH, the hypervolume indicator and the running time.