A reliability-based optimization model for water-distribution systems has been developed. The model is aimed at the following goals: (1) Design of the pipe network including the number, location, and size of pumps and tanks; (2) design of the pumping system using a reliability-based procedure considering both hydraulic failures of the entire network and mechanical failure of the pumping system; and (3) determination of the optimal operation of the pumps. The optimization problem is a large mixed-integer, nonlinear programming problem that is solved using a heuristic algorithm consisting of a master problem and a subproblem. The master problem is a pure 0–1 integer programming model, and the subproblem is a large nonlinear programming model solved in an optimal control framework. The conservation of flow and energy constraints are solved implicitly for each iteration of the nonlinear optimization procedure using a hydraulic simulation model, and the reliability constraints are also solved implicitly using a reliability model. The nonlinear programming problem is solved using a generalized reduced gradient code.
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