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Comp."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem formulation or is relying on a solver that automatically detects and handles symmetries. While modelers of a problem can handle various kinds of symmetries, automatic symmetry detection and handling for MINLP is mostly restricted to permutation symmetries. This article therefore develops techniques such that also black-box solvers can automatically detect and handle a broader class of symmetries. Inspired from geometric packing problems like the kissing number problem, we focus on reflection symmetries of MINLPs. We develop a generic and easily applicable framework to automatically detect reflection symmetries of MINLPs and more general mathematical programs. To handle this broader class of symmetries, we discuss generalizations of state-of-the-art methods for permutation symmetries, and develop dedicated symmetry handling methods for special reflection groups. Our symmetry detection framework has been implemented in the open-source solver\n                    <jats:sc>SCIP<\/jats:sc>\n                    and we provide a comprehensive discussion of the implementation. The article concludes with a detailed numerical evaluation of our symmetry handling methods when solving MINLPs.\n                  <\/jats:p>","DOI":"10.1007\/s12532-025-00289-9","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T10:12:14Z","timestamp":1752142334000},"page":"31-78","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Detecting and handling reflection symmetries in mixed-integer (nonlinear) programming and beyond"],"prefix":"10.1007","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5324-8996","authenticated-orcid":false,"given":"Christopher","family":"Hojny","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,10]]},"reference":[{"key":"289_CR1","doi-asserted-by":"publisher","unstructured":"Anders, M., Schweitzer, P.: Parallel computation of combinatorial symmetries. 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