Geographic experiments are a widely-used methodology for measuring incremental return on ad spend (iROAS) at scale, yet their design presents significant challenges. The unit count is small, heterogeneity is large, and the optimal Supergeo partitioning problem is NP-hard. We introduce Optimized Supergeo Design (OSD), a two-stage framework that renders Supergeo designs practical for large-scale markets. Principal Component Analysis (PCA) first reduces the covariate space to create interpretable geo-embeddings. A Mixed-Integer Linear Programming (MILP) solver then selects a partition that balances both baseline outcomes and pre-treatment covariates. We provide theoretical arguments that OSD's objective value is within (1+ε) of the global optimum under community-structure assumptions. Rigorous ablation analysis demonstrates that PCA-based clustering achieves statistical parity with unit-level randomization (7% higher RMSE, not statistically significant) while enabling operational benefits through coarser granularity. Crucially, OSD solves the scalability bottleneck: for N=210 markets, OSD completes in 0.22 seconds compared to weeks for exact methods -- a speedup of over 5 million times. In extensive simulations with up to 1,000 units, OSD achieves excellent covariate balance (SMD < 1%) and retains every media dollar, establishing a scalable framework that matches the statistical efficiency of randomization with the operational practicality of Supergeos.

翻译：地理实验是一种广泛用于大规模测量广告支出增量回报率（iROAS）的方法，但其设计面临显著挑战：单元数量少、异质性强，且最优超地理划分问题属于NP难问题。本文提出优化超地理设计（OSD），一个两阶段框架，使超地理设计能够适用于大规模市场。首先通过主成分分析（PCA）降维协变量空间，生成可解释的地理嵌入；随后利用混合整数线性规划（MILP）求解器选择一种能平衡基线结果与处理前协变量的划分方案。理论分析表明，在社区结构假设下，OSD的目标函数值在全局最优解的（1+ε）范围内。严格的消融实验证明，基于PCA的聚类方法在统计效能上与单元级随机化相当（均方根误差高7%，统计不显著），同时通过更粗的粒度实现了操作优势。关键的是，OSD解决了可扩展性瓶颈：对于N=210个市场，OSD仅需0.22秒即可完成，而精确方法需数周——加速超过500万倍。在多达1,000个单元的广泛模拟中，OSD实现了优异的协变量平衡（标准化均差<1%）并保留了全部媒体预算，从而建立了一个既匹配随机化统计效率、又具备超地理操作实用性的可扩展框架。