Fig. The concept of applicability domain (AD) and difficulties of multi-objective optimization incorporating multiple ADs. a, The concept of AD. The size of an AD occupied in the chemical space can be varied by changing the reliability level. b, One of the strategies for multi-objective optimization that incorporates ADs is to merge the ADs of multiple prediction models and regard them as a single AD. c, The inherent trade-off between the reliability level and size of an overlapping domain (highlighted in orange) of multiple ADs in the context of multi-objective optimization. d, Examples of success and failure cases in molecular design incorporating ADs of multiple prediction models. Depending on the setting of the molecular design, multi-objective optimization may succeed in the overlapping region of multiple ADs (upper case). However, the molecular design may fall outside the overlapping region (middle case) and the ADs may not overlap each other depending on the reliability levels of the ADs (bottom case). Setting the appropriate reliability levels of the ADs before designing is difficult.