Optimal urban sewer layout design using Steiner tree problems

This article introduces a novel method using mixed-integer linear programming for optimizing sewer layouts. The research concept was obtained from the obstacle-avoiding rectilinear Steiner minimal tree technique in integrated circuit routing design. The Steiner nodes serve as optional nodes to link each sewer discharge node and flow to sinks on an optimal sewer layout. Those nodes are utilized for minimizing the total cost required for constructing pipes. All the nonlinear constraints and the objective function are transformed into a simple linear format. The optimization model analysed three types of objective function conditions-solely considering the pipe cost, solely considering the ground-cutting cost, and combining both considerations-to illustrate the importance of considering all conditions to obtain an optimal sewer layout design. The proposed optimization model can save more than 38.83% of the cost required to realize the expert's manual sewer layout design.