An optimization system optimizes groups of providers for a given population of users. The optimization system includes various engines such as a source interface engine, selection engine, and group score engine. The source interface engine receives information to be used in constrained optimization from server computers and stores the information in databases. The selection engine selects groups of providers from a set of all available providers. The group score engine generates a score for each group of providers. The selection engine continues to iteratively select groups of providers to minimize the generated score. The selection engine can use hard constraints, for example, requiring that a certain type of provider be included in all selected groups, or soft constraints, for example, requiring that a certain number of providers be included based on a size of the given population.