چكيده به لاتين
One of the most important infrastructures for collecting surface runoff in urban areas is storm sewer networks. Due to high construction and operation cost of these networks, many researchers have tried to provide effective and efficient methods to reduce the costs. Pipe and excavation costs are a major part of the sewer networks construction costs. Any attempt to reduce the pipe and excavation costs would, therefore, lead to a huge saving. Excavation is a function of pipe nodal elevations and pipe costs is a function of pipe diameters. These two setoff decision variables are in conflict requiring an optimal balance if an optimal design is required. In many cases, economic limitations have made it almost impossible to design a network able to drain the whole volume of stormwater without flooding. Therefore, in these cases, the designer may allow for a limited amount of flood with specific return period. Since authorities may invest different amounts of finances for the design of such infrastructures and they may have different attitudes and consideration about the risks of flooding, it is vital to address the design of storm sewer network using multi-objective optimization. In single objective optimization, reducing the total cost of the network is the main goal of the designer. Whereas, when addressing the problem using multi-objective optimization, total cost and the flood volume can be considered as the main objectives. Here we review the different methods employed by various researchers and present a Cellular Automata method for both single and multi-objective design o sewer networks. New updating rules were introduced to eliminate the deficits of using a parameter named flow ratio. These new rules allow the Cellular Automata Algorithm to minimize the total cost, as well as, reducing the runtime. It also solves the problem of periodic answers emerged in the previous versions of cellular automata. Furthermore, a Parallel Cellular Automata approach was introduced and applied to two test examples. The superiority and the speed of this algorithm was compared with a well known multi-objective optimization algorithm, NSGA-II. The proposed method is able to present desirable set of feasible solutions while running the program for only one time. Two different versions of Parallel Cellular Automata Algorithm named PCA1 and PCA2 were employed in in which PCA1 uses a the probability function of Simulated Annealing Algorithm and PCA2 uses two-part convergence for exchanging the answers between two parallel CAs. A two-phase CA is used as the optimization tool while the EPA’s stormwater management model (SWMM) is used as the simulator. A splitting method is first used to redefine the sewer network design problem in terms of two sub-problems with pipe diameters and nodal elevations of each pipe as decision variables which are iteratively solved using CA methods. Starting with smart values according to the maximum rank of each pipe were chosen for pipe diameters and checked values for pipe nodal elevations, the pipe diameters of the network are assumed fixed in the first stage and the pipe nodal elevations are updated using CA method with the network nodes as the cells and the corresponding pipe nodal elevations as the cell states. The cell states are repeatedly updated by an ad-hoc local rule derived based on the engineering judgment. In the second stage, the pipe nodal elevations obtained from the first stage are assumed fixed and the pipes diameters are updated just one time using another CA. The pipes are considered as the CA cells and the pipe diameters as the cell states. The local update rule of the second CA is also derived in an ad-hoc manner based on engineering judgments. The whole process of updating the pipe nodal elevations and pipe diameters is iterated until the convergence is achieved. Then the genetic algorithm is used to design storm sewer network for comparing proposed CA method with heuristic algorithms. The NSGA-II method considers the nodal cover depth and pipe diameters as decision variables. A hybrid NSGAII-PCA is defined for comparing the answers and to prove the efficiency of the PCA. The results show that the both CA and PCA method with mentioned arrangements are more efficient and effective than alternative methods for the optimal design of storm sewer networks.
