Method for Optimal Design of Branched Networks on Flat Terrain

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Abstract
A computationally efficient two‐stage method for the optimal design of branched water distribution networks on flat terrain is proposed. In the initial stage, the Lagrange multiplier method is used to obtain continuous optimal pipe sizes and Lagrange multipliers analytically. It is not necessary here to solve a system of linear equations and only simple arithmetic operations are needed. For any method in which continuous diameters are evaluated, a heuristic procedure is used to round off the continuous diameter into discrete diameters. The present method, however, uses the analytical solution obtained in the first stage to select a restricted candidate list of commercially available pipe sizes for input to an LP model. When the proposed method is applied to branched networks of different sizes and complexities, it is observed to be computationally more efficient than the LP model. Moreover, the optimal solution obtained by the proposed method coincides with the optimal solution obtained by the LP model for all branched networks so far randomly generated.

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