Limited multistage stochastic programming for water distribution systems optimal operation

Least-cost operation of water distribution systems (WDS) is a well-known problem in water distribution systems optimization. The formulation of the problem started with deterministic modeling, and the problem was subsequently handled with more sophisticated stochastic models that incorporate uncertainties related to the problem's parameters. This work applied a recently developed algorithm entitled limited multistage stochastic programming (LMSP) to deal with the stochastic formulation of the least-cost operation of WDS and serves merely as a proof of concept on an illustrative network. The demand is considered as the uncertain parameter in the problem formulation. This algorithm reduces the complexity of the classical multistage stochastic programming (MSP) by adding constraints which result in a linear growth of the problem, as opposed to an exponential growth in the MSP problem. This is accomplished by clustering decision variables based on a postanalysis of the implicit stochastic program of the problem. The clusters allow reduction of the number of decision variables, thus reducing the complexity of the optimization problem. The LMSP is expected to increase the cost because of the additional constraints imposed on the problem; however, a trade-off exists between the computational complexity and the optimality of the objective value to the number of clusters considered. An illustrative example application is provided for demonstrating the suggested methodology abilities.