التصميم الأمثل للتخطيط لنظام شبكات الصرف الصحي

Optimum Design of Layout for Sewer Networks System

   To optimize the layout of a sewer network, the feasible layouts of the network are firstly generated from directed or undirected base graph. Then, the best layout design (minimum cost with good system performance) is identified from among the numerous possible configurations subjected to constraints.

   Genetic algorithms are often based on random beginnings, which are weak solutions. Therefore, the problem of how to provide good initial estimates for finding a solution that is automatically assigned is an ongoing research topic. For this purpose, this study proposes a new method hybrid Genetic Algorithm with Tree-Growing Algorithm (GA-TGA) technique, which uses a suitable growth algorithm, TGA, to avoid the problems associated with the configuring of the infeasible solutions. This will minimize the search space to provide a good initial population to implement the genetic algorithms.

   Optimisation modelling is performed with a MATLAB (R2014a) code. The performance of seven different selection methods (RWS, RRWS, LRS, TRS, SUS, TOS and RMS), two different crossover methods (Order Crossover (OX) and Crossing Operator-Based Cloning (CX)), and different population sizes (number of solutions) (50, 100, 200, 300 and 500), have been examined using the proposed model to determine their impact on convergence behavior of the optimisation. Tournament Selection method (TOS) and Order Crossover (OX) proved to be the most effective in relation to the optimal layout design. With these methods as well as direct base graph resulted in the formation of a feasible offspring population for the new generation, there is neither need to discard or repair infeasible solutions nor to apply penalty factors to the cost function.

   Two benchmark examples (calibration examples) of sewer networks are used to test the proposed model. In the first example the proposed model found the minimum solution (5062.8 units) after 31 iterations and took about (3-5) min. to solve the example. It is clear from compared with previous studies the proposed (GA-TGA) model reaches the final solution with a number of generations less than the other methods. The study concluded that the proposed method is computationally efficient in terms of speed and is ease to implementation with identical objective function values.

   Also, the cost savings achieved by the proposed model for the second example in comparison with the different design of models. It can be seen that the cost of the present model is 24.5% less from DDDP design model (Wen and Shih, 1983).

   In order to determine the applicability of the proposed model with the practical networks in the local region, it is examined with two real case studies located in Karbala Holy city, and compared the cost of the manual designs with the designs obtained from the present model for networks. The percentages of saving were (13.05 %) and (7.123 %) for the first and second case studies respectively.