Can the SGWO Handle Sewer Network Design?

The importance of caring for the environment and sustainability is not concealed to anyone, and thus, understanding and handling the challenges of sustainable development is a must. One of the main steps in moving towards sustainability is the efficient design and operation of infrastructure systems. Sewer networks are one of the most important components of water resources management infrastructure. These networks are costly to construct and maintain, and most of the expenses are due to piping and excavation costs. Hence, these systems' optimum design is essential to reduce the cost and increase these systems' efficiency. Our paper published in ASCE Journal of Pipeline Systems Engineering and Practice, is focused on the application of a new meta-heuristic algorithm to solve this optimization problem.

The optimization of sewer network design is a demanding and constrained problem. In the optimum design of sewage network systems, different approaches may be used: a) optimizing the hydraulic components, such as pipe sizes, slopes, and flow rates, and b) optimizing the network's architecture. In formulating the optimization problem, these approaches can be used alone or in conjunction.

Classic optimization methods such as non-linear programming or dynamic programming have been utilized by researchers. But usually, these networks possess lots of manholes and pipes and the non-linearity of the problem at larger scales disables the aforementioned methods to be able to solve large-scale problems. This is where the technology helps us and the metaheuristic optimization algorithms can come in handy. Although these algorithms do not guarantee the global optimum, they can be improved and adjusted to reach the best answer possible. After all, reaching a near-optimum answer is better than overdesigning.

I have discussed the hybrid SGWO algorithm in previous posts (here). This algorithm performed extremely well in reservoir operation optimization, which although might not possess as much mathematical complexity as the sewer networks design, but they are much alike in the huge size and a high number of decision variables. Thus, the question was that, can this algorithm exhibit a good performance dealing with these problems? The answer turned out to be “YES!”

Fig. 1 - Network Layout of Problems 1 and 2

The first two networks are hypothetical networks purposed by Moeini and Afshar (2013) and the third network is a real-world example of a sewer network designed to be constructed in Hamedan, Iran. For problems 1 and 2, as shown in Fig. 1, the networks are two quadrangle zones with dimensions of 200m by 200m and 800m by 800m respectively. the first test example consists of 9 nodes and 12 pipes, while the second test example has 81 nodes and 144 pipes. The arrows indicate the flow direction, and all pipes for all networks are of an equal length of 100 meters. The 3rd problem illustrated in Fig. 2 has 215 pipes and 214 nodes, and each pipe is of a particular length with a particular design discharge. After choosing each algorithm's best configuration, each of the aforementioned optimization problems was solved by each algorithm. Each algorithm was implemented in 20 independent runs. For performance analysis, three different sewer networks were chosen to be designed using five algorithms: SGWO, GWO, SCE-UA, SFLA, and PSO.

Fig. 2 - Network Layout of Problem 3

It was derived from the results that dividing and shuffling the population in the optimization process of the SGWO improves the information exchange among the members and thus, improving the final obtained result.

Fig. 3 - Convergence Curves of the SGWO Algorithm

Also, the results indicated that although tuning of the SGWO can be more difficult than the GWO algorithm since it has more parameters, it improves the results in optimum objective values considerably, especially while handling large-scale problems. The minimum objective function for problems 2 and 3 was improved by 18.84% and 7.88%, respectively, by the SGWO algorithm. This improvement happens while the SGWO requires fewer function evaluations since it requires 43724 and 293584 for problems 2 and 3, respectively than the GWO algorithm, which indicates the high computing efficiency of the SGWO algorithm. Furthermore, the SGWO algorithm showed up to 59% less standard deviation in 20 runs on each problem than which indicates the higher reliability and robustness of the proposed algorithm.