University of California Water Resources Center

This report develops a multicommodity flow model to optimize water distribution and water quality in a regional water supply system. Waters from different sources with different qualities are considered as distinct commodities, which concurrently share a single water distribution system. Volumetric water blend is used to represent water quality in the model. The model can accommodate two-way flow pipes, represented by undirected arcs, and the perfect mixing condition. Additionally, blending requirements are specified at certain control nodes within the system to ensure that downstream users receive the desired water quality. The optimization model is highly nonlinear and solved by a hybrid genetic algorithm (GA). We first use GA to globally search for the directions of all undirected arcs. We then use a generalized reduced gradient (GRG) algorithm, which is embedded in GA, to optimize the objective function for fitness evaluation. The proposed methodology was first tested and verified on a simplified hypothetical system and then applied to the regional water distribution system of the Metropolitan Water District of Southern California (MWD). The results obtained indicate that the optimization model can efficiently allocate waters from different sources with different qualities to satisfy the blending requirements, perfect mixing and two-way flow conditions.