We study the problem of designing optimal targeted mass screening of nonuniform populations. Mass screening is an essential tool that is widely utilized in a variety of settings, for example, preventing infertility through screening programs for sexually transmitted diseases, ensuring a safe blood supply for transfusion, and mitigating the transmission of infectious diseases. The objective of mass screening is to maximize the overall classification accuracy under limited budget. In this paper, we address this problem by proposing a proactive optimizationbased framework that factors in population heterogeneity, limited budget, different testing schemes, the availability of multiple assays, and imperfect assays. By analyzing the resulting optimization problem, we take advantage of the structure of the problem as a multidimensional fractional knapsack problem and identify an efficient globally convergent thresholdstyle solution scheme that fully characterizes an optimal solution across the entire budget spectrum. Using realworld data, we conduct a geographicbased nationwide case study on targeted COVID19 screening in the United States. Our results reveal that the identified screening strategies substantially outperform conventional practices by significantly lowering misclassifications while utilizing the same amount of budget. Moreover, our results provide valuable managerial insights with regard to the distribution of testing schemes, assays, and budget across different geographic regions.