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"图基优化"这一范式：在该范式中，真实世界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，而非以自由形式的自然语言文本或静态表格输入提供。我们通过调研近期基于大语言模型/小语言模型的优化系统——OptiMUS、Chain-of-Experts、LLMOPT、OPRO、FunSearch、Eureka——来论证该范式的必要性，上述系统均未将属性图作为主要输入模态。我们在开源samyama-graph数据库中实例化该范式，并评估了七个真实世界公共领域知识图谱支撑的优化问题，涵盖药物重定位（24.5万节点生物医学知识图谱）、临床试验机构选址（778万节点试验注册知识图谱）、印度供应链重新路由（534万节点OSM道路图）、医疗资源公平分配（WHO/GAVI/IHME知识图谱）、经济环境电网调度、抗菌素耐药性管理（NCBI AMRFinderPlus，1.04万个耐药基因）以及野火疏散路径规划（加利福尼亚州帕拉代斯OSM图）。我们将拉奥族元启发式算法组合（BMWR、Jaya、SAMP-Jaya、EHR-Jaya、Rao-1）与Google OR-tools（CP-SAT和GLOP）参考求解器进行对比。研究发现：（i）无单一拉奥变体占据主导地位：BMWR在带折衷离散问题和高维硬约束问题上胜出，而Rao-1在连续低/中维问题上表现最优，从实证角度支持组合策略；（ii）OR-tools在小规模线性/适宜混合整数线性规划子问题上占优，但无法编码多个真实场景中出现的非线性目标函数；（iii）图基形式化会暴露数据质量问题（缺失属性、退化聚合），而纯文本形式化优化则会悄然掩盖这些问题。