Graph-Grounded Optimization: Rao-Family Metaheuristics, Classical OR, and SLM-Driven Formulation over Knowledge Graphs
For researchers in optimization and AI, this work proposes a new paradigm for problem formulation that leverages structured knowledge graphs, but the empirical comparison is incremental and lacks clear performance improvements over existing methods.
The paper introduces graph-grounded optimization, where optimization problems are sourced from knowledge graphs via Cypher queries, and evaluates Rao-family metaheuristics against OR-tools on seven real-world problems. Results show no single Rao variant dominates, and OR-tools excels on small linear problems but fails on non-linear objectives.
We propose graph-grounded optimization: a paradigm in which the decision variables, constraints, and objective coefficients of a real-world optimization problem are sourced from a property knowledge graph (KG) via Cypher queries, rather than supplied as free-form natural-language text or static tabular input. We motivate the paradigm by surveying recent LLM/SLM-driven optimization systems -- OptiMUS, Chain-of-Experts, LLMOPT, OPRO, FunSearch, Eureka -- none of which consume property graphs as the primary input modality. We instantiate the paradigm in the open-source samyama-graph database and evaluate seven real-world public-domain KG-backed problems spanning drug repurposing (245K-node biomedical KG), clinical-trial site selection (7.78M-node trial registry), Indian supply-chain rerouting (5.34M-node OSM road graph), healthcare equity allocation (WHO/GAVI/IHME KG), economic-environmental grid dispatch, antimicrobial-resistance stewardship (NCBI AMRFinderPlus, 10.4K resistance genes), and wildfire evacuation routing (OSM Paradise, CA). We compare a portfolio of Rao-family metaheuristics (BMWR, Jaya, SAMP-Jaya, EHR-Jaya, Rao-1) against Google OR-tools (CP-SAT and GLOP) reference solvers. We find that (i) no single Rao variant dominates: BMWR wins on discrete-with-tradeoff and high-dim-with-hard-constraint problems while Rao-1 wins on continuous low-/mid-dim problems, empirically supporting a portfolio approach; (ii) OR-tools dominates on small linear/MILP-friendly sub-problems but cannot encode the non-linear objectives that emerge in several of the real-world settings; (iii) graph-grounded formulations surface data-quality issues (missing properties, degenerate aggregates) that purely text-formulated optimizations would silently mask