In the previous works, the author developed a method of optimal design for expansion of existing water distribution networks. The novel feature of this method is that it clarifies the trade-off relationship between enhancement of the supply stability (or reliability) and reduction of the construction cost. This paper generalizes the formulation so that it copes with the existence of a variety of hydraulic elements and introduces a combination of the penalty functions and the Newton method instead of the previous solution based on the generalized reduced gradient method so that the computational time is reduced and ill-conditioned problems are made solvable.
