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

翻译：我们提出了“图基优化”这一范式：在此范式中，实际优化问题的决策变量、约束条件和目标系数通过Cypher查询从属性知识图谱中获取，而非以自由格式的自然语言文本或静态表格形式输入。为论证该范式的必要性，我们调研了近期基于LLM/SLM的优化系统——OptiMUS、Chain-of-Experts、LLMOPT、OPRO、FunSearch、Eureka——这些系统均未将属性图作为主要输入模态。我们在开源samyama-graph数据库中实例化了该范式，并评估了七个真实世界中基于知识图谱的公开领域问题，涵盖药物重定位（24.5万节点生物医学知识图谱）、临床试验场所选择（778万节点试验注册库）、印度供应链重新路由（534万节点OSM道路图）、医疗公平性分配（WHO/GAVI/IHME知识图谱）、经济-环境电网调度、抗菌药物耐药性管理（NCBI AMRFinderPlus，10.4万个耐药基因）以及野火疏散路由（OSM Paradise, CA）。我们将一组Rao族元启发式方法（BMWR、Jaya、SAMP-Jaya、EHR-Jaya、Rao-1）与Google OR-tools（CP-SAT和GLOP）参考求解器进行了比较。研究发现：(i) 没有单一的Rao变体占据主导地位：BMWR在离散-权衡问题和高维-硬约束问题上表现最佳，而Rao-1在连续低维/中维问题上胜出，从经验上支持了组合策略的采用；(ii) OR-tools在小型线性/适用于MILP的子问题上具有优势，但无法编码多个实际场景中出现的非线性目标；(iii) 基于图的公式化表述暴露了数据质量问题（如属性缺失、聚合退化），而纯文本公式化的优化则会悄然掩盖这些问题。