Application of cellular automata to sewer network optimization problems

A Cellular Automata approach is introduced in this paper for the optimal design of sewer network problems. The solution of sewer network optimization problems requires the determination of pipe diameters and average pipe cover depths, minimizing the total cost of the sewer network subject to operational constraints. One constraint of the problem, namely, the maximum relative depth of flow, is first used to define the pipe diameters in terms of the pipe slope and, hence, the nodal elevation of the network. As a result, the sewer network optimization problem is redefined, in terms of the network nodal elevations, and the resulting problem is solved using a Cellular Automata (CA) approach. The nodes of the network are used as the CA cell, with the corresponding elevations as CA cell states. The updating rule of the proposed CA is then derived by requiring the stationary total penalized objective function of the problem, with respect to the cell state. The proposed method is used to solve two benchmark examples and the results are compared to those obtained by other methods. The results indicate that the proposed method is highly efficient compared to alternative methods, while producing comparable results.