Reliability-based optimization model for water distribution systems

This paper presents the basic framework for a model that can be used to determine the optimal (least-cost) design of a water distribution system subject to continuity, conservation of energy, nodal head bounds, and reliability constraints. Reliability is defined as the probability of satisfying nodal demands and pressure heads for various possible pipe failures (breaks) in the water distribution system. The overall model includes three that are linked: a steady-state simulation model, a reliability model, and an optimization model. The simulation model is used to implicitly solve the continuity and energy constraints and is used in the reliability model to define minimum cut sets. The reliability model, which is based on a minimum cut-set method, determines the values of system and nodal reliability. The optimization model is based on a generalized reduced-gradient method. Examples are used to illustrate the model.