Genetic improvement uses artificial intelligence to automatically improve software with respect to non-functional properties (AI for SE). In this paper, we propose the use of existing software engineering best practice to enhance Genetic Improvement (SE for AI). We conjecture that existing Regression Test Selection (RTS) techniques (which have been proven to be efficient and effective) can and should be used as a core component of the GI search process for maximising its effectiveness. To assess our idea, we have carried out a thorough empirical study assessing the use of both dynamic and static RTS techniques with GI to improve seven real-world software programs. The results of our empirical evaluation show that incorporation of RTS within GI significantly speeds up the whole GI process, making it up to 78% faster on our benchmark set, being still able to produce valid software improvements. Our findings are significant in that they can save hours to days of computational time, and can facilitate the uptake of GI in an industrial setting, by significantly reducing the time for the developer to receive feedback from such an automated technique. Therefore, we recommend the use of RTS in future test-based automated software improvement work. Finally, we hope this successful application of SE for AI will encourage other researchers to investigate further applications in this area