Optimization of sewer networks using the mixed-integer linear programming

This paper introduces a method for optimizing sewer networks using the mixed-integer linear programming (MILP) for a given layout. The objective function is defined as the sum of the costs for pipe purchase, pipe-laying, and manhole construction expressed in linear terms and subject to minimum and maximum allowable slopes, velocities, and relative depths for both minimum and maximum sewage discharge rates in each pipe. Additionally, provisions are made as constraints or conditions to ensure that a minimum pipe cover is required, that pipe diameters do not decrease in the flow direction, and that pipes maintain a steady elevation at each manhole. All the non-linear constraints are transformed into the linear format. Pipe slope, binary variables accounting for commercial pipe diameters and average implemented depths have also been considered as decision variables. Finally, the performance of the proposed optimization method is evaluated in a benchmark sewer network from the literature.