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Designing such systems is a grand challenge: the combinatorial explosion of possible chemical compositions and spatial arrangements makes brute-force exploration infeasible, while many current generative approaches remain limited to isolated molecules. In this work, we introduce a hierarchical generative optimization framework that overcomes this barrier by coupling a genetic algorithm for configurational search with a generative model for molecular design. This closed-loop approach enables simultaneous refinement of geometry and composition, efficiently steering discovery toward systems with targeted functionality. As a proof of concept, we design catalytic environments for the Claisen rearrangement of p-tolyl ether by optimizing surrounding components around a fixed reference transition-state geometry. Despite this constraint during the search phase, post-hoc validation via Climbing-Image Nudged Elastic Band calculations, with the environment held fixed, indicates a reduction of the activation barrier by about 30%. Beyond this example, the framework applies to systems in which a well-defined central structure is stabilized by non-covalently interacting components, such as supramolecular hosts and local catalytic environments. \u00a0<\/jats:p>","DOI":"10.1186\/s13321-026-01313-3","type":"journal-article","created":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T23:44:20Z","timestamp":1791675860000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hierarchical generative modeling for the design of multi-component systems"],"prefix":"10.1186","volume":"18","author":[{"given":"Rhyan","family":"Barrett","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robin","family":"Curth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6531-0742","authenticated-orcid":false,"given":"Julia","family":"Westermayr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,11]]},"reference":[{"issue":"8","key":"1313_CR1","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1007\/s10822-013-9672-4","volume":"27","author":"PG Polishchuk","year":"2013","unstructured":"Polishchuk PG, Madzhidov TI, Varnek A (2013) Estimation of the size of drug-like chemical space based on gdb-17 data. 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