Loop-by-Loop Cutting Algorithm to Generate Layouts for Urban Drainage Systems

Abstract

The design of urban drainage systems consists of solving two subproblems: (1) generating the layout and (2) sizing the sewers. The latter includes pipe diameters, installation depths, and pumping facilities, all of which are significantly influenced by the layout configuration. This work aims at introducing a method to solve the layout subproblem based on the graph theory. For a given city, all possible sewer lines and manholes are considered for the sewer network so that an undirected looped graph is initially formed. Next, an adaptive procedure entitled the loop-by-loop cutting algorithm is developed to create feasible sewer layouts from the base graph. Using this algorithm, all constraints of the sewer layout subproblem are systematically handled. By defining an objective function, the optimum layout is achieved by employing a simple genetic algorithm. After the sewer layout is determined, the specifications for pipes and pumps are designed by using a discrete differential dynamic programming model. A benchmark sewer system is also considered from the literature to be optimized. The results are discussed and compared with previous studies. It is concluded that the loop-by-loop cutting algorithm is especially useful for the design of urban drainage systems in flat areas. The method is also computationally efficient and easy to implement and add to optimization solvers.