Pipe network system analysis using simulated annealing

Water pipe network systems are designed and operated to supply fresh water from the source (or treatment facility) to the customers. Based on the energy conservation or mass balance principle, a nonlinear equation set can be formulated to describe the relationship between the nodal head and pipe flow rate. In the past, Hardy-Cross method or Newton-type method was commonly used to solve the nonlinear equation set for obtaining the solutions, such as the nodal heads and flow rates. However, these two methods have the drawbacks that a non-convergent and/or a poor result may occur if improper initial guesses for the nodal heads or flow rates are made. In this article, a pipe network solver, PNSA, is developed to solve the nodal head and flow rate for a given network. The nonlinear equation set is first formulated as an unconstrained optimization problem, and then uses simulated annealing to solve the solutions of a pipe network system. The results obtained from PNSA with initial guesses generated by a random number generator show good match with those obtained from modified Powell's hybrid method and sparse matrix method.