Biological evolution has given rise to the vast diversity and complexity of the biosphere. Evolutionary computation has made great progress in capturing this creative potential. Here, we aim to create the next-generation evolutionary computation for designing new biomolecules, genomic constructs and microbial communities. Rather than solely aiming for improved performance, our aim is to develop algorithms capable of creating i) novel functionality, ii) capacity for improvements, iii) increasing complexity and iv) knowledge generation. We will develop the general computational framework, which we apply to a representative wet lab case within synthetic biology. This project will be in close collaboration with the Biocompute Lab at Bristol University, building on our joint research line "open-ended evolution for biodesign".