Dynamic Programming Over a Graph Modeling Framework for the Optimal Design of Pipe Series in Sewer Systems

Abstract

The sewer network optimal hydraulic design, for a specific layout consisting of a series of pipes, is the combination of diameters and slopes along the series that satisfy all the hydraulic, commercial, and construction constraints, while minimizing the construction costs. This work explains an exact, exhaustive, and flexible framework to find the cost-optimal design of a series of sewer pipes using a DP-based optimization engine [1]. The hydraulic design problem is modeled as a Shortest Path Problem [2], where the underlying graph considers every feasible combination of diameter and slope for each pipe in the series. As a result, a shortest path on the graph encodes the optimal hydraulic design decision for the series of pipes. The proposed methodology ensures the global optimal solution from an economic point of view because the graph considers all possible alternatives and the Bellman-Ford [3] algorithm implicitly explores all of them. Without having to simplify hydraulic constraints, this methodology still obtains the optimal solution in a very short computational time using a standard desktop computer. To evaluate the performance of the methodology, several numerical examples are presented varying the pipe material, the topography, and the number of pipes in the series.