Cross-domain aspect-based sentiment analysis (ABSA) uses annotated samples from the source domain to help train ABSA tasks on the target domain. However, not all samples from the source domain are suitable for transfer training, and some samples may have negative transfer effects on the training of the transfer model, which requires sample screening. Existing cross-domain instance transfer methods consider a one-sided transfer basis, ignoring the synergistic effect between samples and affecting cross-domain generalisation performance. In order to solve the problems of insufficient domain-specific training samples and sample screening in cross-domain transfer for ABSA tasks, this study proposes a cross-domain ABSA method based on high-quality sample selection by combining high-reliability machine learning theories and domain adaptation methods in modelling with the open environment of multi-domain sentiment analysis. First, inter-domain and intra-domain high-quality sample selection metrics are designed to filter the source domain data at the domain level and the sample level in turn, which takes into account the advantages of the two sample selection granularities. Second, similarity metrics between source and target domains are comprehensively designed and efficiently calculated through a graph neural network. Finally, the scenarios of multi-source domain transfer are included in the discussion of cross-domain ABSA, and inter-domain joint adaptability scores are designed to select the multi-source domain combinations with high inter-domain synergies by balancing the overlap and difference of domain features. A cross-domain transfer task is designed on a benchmark dataset covering six domains, and experiments are conducted on three sub-tasks of ABSA to validate the effectiveness of the proposed method.