Affine Transformation-Enhanced Multifactorial Optimization for Heterogeneous Problems

Evolutionary multitasking (EMT) is a newly emerging research topic in the community of evolutionary computation, which aims to improve the convergence characteristic across multiple distinct optimization tasks simultaneously by triggering knowledge transfer among them. Unfortunately, most of the existing EMT algorithms are only capable of boosting the optimization performance for homogeneous problems which explicitly share the same (or similar) fitness landscapes. Seldom efforts have been devoted to generalize the EMT for solving heterogeneous problems. A few preliminary studies employ domain adaptation techniques to enhance the transferability between two distinct tasks. However, almost all of these methods encounter a severe issue which is the so-called degradation of intertask mapping. Keeping this in mind, a novel rank loss function for acquiring a superior intertask mapping is proposed in this article. In particular, with an evolutionary-path-based representation model for optimization instance, an analytical solution of affine transformation for bridging the gap between two distinct problems is mathematically derived from the proposed rank loss function. It is worth mentioning that the proposed mapping-based transferability enhancement technique can be seamlessly embedded into an EMT paradigm. Finally, the efficacy of our proposed method against several state-of-the-art EMTs is verified experimentally on a number of synthetic multitasking and many-tasking benchmark problems, as well as a practical case study.