Algebraic Structure Discovery for Real World Combinatorial Optimisation Problems: A General Framework from Abstract Algebra to Quotient Space Learning

Computer Science > Artificial Intelligence [Submitted on 10 Mar 2026] Algebraic Structure Discovery for Real World Combinatorial Optimisation Problems: A General Framework from Abstract Algebra to Quotient Space Learning Min Sun (1), Federica Storti (1), Valentina Martino (1), Miguel Gonzalez-Andrades (1), Tony Kam-Thong (1) ((1) F. Hoffmann-La Roche AG, Roche Pharma Research and Early Development) Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic structure, (ii) formalises operations, (iii) constructs quotient spaces that collapse redundant representations, and (iv) optimises directly over these reduced spaces. Across a broad family of rule-combination tasks (e.g., patient subgroup discovery and rule-based molecular screening), conjunctive rules form a monoid. Via a characteristic-vector encoding, we prove an isomorphism to the Boolean hypercube \{0,1\}^n with bitwise OR, so logical AND in rules becomes bitwise OR in the encoding. This yields a principled quotient-space formulation that groups functionally equivalent rules and guides structure-aware search. On real clinical data and synthetic benchmarks, quotient-space-aware genetic algorithms recover the global optimum in 48% to 77% of runs versus 35% to 37% for standard approaches, while maintaining diversity across equivalence classes. These results show that exposing and exploiting algebraic structure offers a simple, general route to more efficient combinatorial optimisation. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2604.04941 [cs.AI]   (or arXiv:2604.04941v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.04941 Focus to learn more Submission history From: Min Sun [view email] [v1] Tue, 10 Mar 2026 23:47:16 UTC (1,160 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)