Optimal design of district metered areas based on improved particle swarm optimization method for water distribution systems Open Access

Water distribution systems (WDSs) are an important part of urban infrastructure and indispensable to the stable development of a city. The continuous increase in complexity and scale of WDSs further increases the difficulty of leakage management and control of the pipeline network. The partitioning of the WDS into district metered areas (DMAs) was proposed to control leakage (Burrows et al. 2000) and achieve the purpose of ‘divide and conquer’ effectively. DMA partition management can meet the water demand of users, reduce costs for enterprises, improve economic benefits, and enhance management efficiency (Araujo et al. 2006; Shafiee et al. 2016).

The water supply network can be represented as a simple graph from the perspective of topology and complex network theory, and graph partition algorithms can be used to partition the water supply network in studies on DMA partitioning (Di Nardo & Di Natale 2011; Perelman & Ostfeld 2011; Sela Perelman et al. 2015; Campbell et al. 2016a). The multilevel graph partitioning algorithm is a basic method based on graph theory (Campbell et al. 2016b). A graph partitioning algorithm based on multilevel recursive bisectioning (MLRB) is used to balance the number of users in each DMA partition and minimize the number of DMA partition boundary pipe segments after constructing the topology (Di Nardo et al. 2013, 2015, 2017). The partitioning results of the multilevel graph partitioning algorithm and spectral clustering algorithm are compared (Di Nardo et al. 2018) using an actual pipe network. The SWANP (Smart Water Network Partitioning) software was proposed to achieve automatic network partitioning based on the MLRB graph partitioning algorithm (Di Nardo et al. 2014, 2017, 2020).

Many researchers have recently carried out multi-objective optimization of the water supply network by adding objectives, considering economic factors, hydraulic factors, and other aspects of DMA partition design and operation (Hadka & Reed 2013; Brentan et al. 2017; Di Nardo et al. 2017; Zhang et al. 2017). The genetic algorithm was used to optimize the location of the flowmeter and maximize the total energy of the pipe network (Di Nardo et al. 2014). The simulated annealing algorithm considers scenarios such as future infrastructure with the total investment in the partition (Gomes et al. 2013). In addition, studies have also used iterative methods for the objective optimization of partitions (Giudicianni et al. 2018; Vasilic et al. 2020). Flowmeters have been installed based on the minimum energy dissipation path, and then the number and locations of flowmeters changed alternately to find the best solution (Di Nardo et al. 2020). However, the iterative method does not consider the combined effect of simultaneous closure of multiple pipes compared with the heuristic algorithm. Moreover, the previous studies demonstrated that the increase in the number of boundary pipes led to an explosive growth of the search space. In addition, since the initial solution is random, it is difficult to evolve a feasible solution that satisfies the minimum service head through many iterations. Third, the possibility of installing gate valves or flowmeters is the same for the boundary pipes and the importance of different boundary pipes is not considered in the iterative process, which could cause the poor optimization effect.

A novel two-step optimal method for designing DMAs in WDSs is proposed in this study. The clustering phase is accomplished using an improved METIS graph partition algorithm on the basis of node water demand and pipe length similarity between DMAs. The demand and pipe length are also considered in this study. Second, the dividing phase based on the multi-objective BPSO (Discrete Binary Particle Swarm Optimization algorithm) is put forward from both economic and hydraulic aspects in this work. The paper makes the following contributions to enhance the efficiency of the optimization. The most important pipes among the boundary pipes are selected according to the hydraulic characteristics and the flowmeters are installed on these pipes to reduce the solution vector space dimension of the BPSO. In addition, the improved BPSO is optimized from two aspects: the initial solution and the updated particle position. Specifically, the initial solution generation process is modified. Considering the characteristics of different boundary pipes, the particle position update formula in the iterative process is modified, and the crossover mechanism is introduced to update the particle position again. Two case networks of different scales will allow the demonstration and analysis of the overall DMA design strategy from a hydraulic perspective.

The bioinspired algorithm can solve the optimization problems and obtain better results in water distribution. At this stage, the paper is based on the classical bionic algorithm BPSO (Kennedy & Eberhart 1997), based on the behavior of a flock of birds to find food. The optimization problem contains binary decision variables by MOBPSO, with one decision variable for each boundary pipe corresponding to the installation location of a flowmeter or a closed gate valve. The following objectives are optimized in this stage from aspects of economic and hydraulic conditions: (1) number of flowmeters, (2) leakage reduction rate, and (3) improved pressure balance. The process of the three-objective dividing phase is presented as follows:

The purchase cost depends on the pipe diameter. The flowmeter quantity minimization does not take into account the purchase cost for two reasons. First, the subsequent management costs are higher than the initial cost (Laucelli et al. 2017). Second, the goal of the quantity minimization drives the search for quantity minimization for flowmeters installed on the pipes with higher flow rate.

Here, the reduction rate of the background leakage in WDS with respect to the original WDS configuration is proposed as the function. The maximization of the background leakage reduction obtained by the positioning of the closed valves is calculated by the extended cycle hydraulic simulation.

The traditional pressure balance within the DMA has been improved by adding the indicator to ensure that the node pressure is low while meeting the constraints. This will further save energy and prevent the occurrence of high pressure in local areas and reduce abnormal events, such as pipe bursts (Zhang et al. 2022). The water supply stability of the pipe network improves and the local excess water head is prevented when the objective is optimized. Pressure-driven analysis (Giustolisi et al. 2008; Giustolisi & Walski 2012) is necessary to run the hydraulic model.

In the dividing phase, the main improvements were made. In process 1, the important pipe is selected manually and the flowmeter is installed on it according to the hydraulic characteristics of the boundary pipe segment after clustering in the generated boundary pipe set. In process 2, this paper improves the BPSO used to determine the location of valves and flowmeters. The BPSO is difficult to solve initially during operation, and it is easy to search for solutions that do not satisfy the constraint conditions. Finally, in the optimization process, the location of valves or flowmeters on all pipe sections has the same probability. The improvements improve the computing efficiency and obtain good solutions.

In the process of preliminary identification of important pipes, this paper proposeds the following principles.

• (a)

  According to their flow rate, the boundary pipes are sorted from smallest to largest. A certain number of boundary pipes corresponding to smaller flow rate constitute the set s, and the remaining is set r. The state of closure is set on the pipes in the set s, and it is judged whether the previously mentioned constraint conditions are satisfied. If the constraint conditions are not satisfied, that is, there is a node smaller than the minimum service head, enter (b).

• (b)

  In the set s, the pipes with the highest flow rate are opened first, one boundary pipe at a time. If the pipe network satisfies the constraint condition, the pipe sections in the open state constitute the set r, then enter (d); otherwise, update the set s. The boundary pipe segment of the set s is increased by 1, and then proceed to step (b) until all nodes are greater than the minimum service head.

• (c)

  In the remaining boundary pipe segment set r, from the flow rate of the smallest, only one pipe segment is closed at a time, if there is less than the service head of the node, in the open state of the pipes combined for the combination of (b), enter step (d).

• (d)

  The pipe segment in the set r will remain open and flowmeter installed, and the remaining pipe segments remain closed.

The values of velocity are mapped to the interval 0 to 1. The s(·) is a sigmoid function. is the flow rate of the jth inlet pipe of the ith partition. is the total inflow of the ith partition, and is the number of inlet pipes in the jth partition.

The original algorithm considers the probability of installing a flowmeter to be the same for all boundary pipes, which is improved in this study. The pipe that bears a higher flow rate in the same partition is considered more likely to have a flowmeter installed, which is in line with the hydraulic characteristics of the pipe network.

According to the calculation results, CVD without node weights and with two weights are 0.450 and 0.293. To test the performance of the proposed method on partition, CVL without node weights and with two weights are 0.397 and 0.319.

Among 100 boundary pipes generated after 32 DMAs of the EXNET WDS, 23 pipes in Figure 7 are selected for the setting of flowmeters according to the specified criteria and are denoted in red. In the initial boundary pipe importance analysis, the pipes must be in the open state and have flowmeters installed. After eliminating the above 23 boundary pipes, the value of decision variables in the subsequent optimization process is reduced from 100 to 78, and the solution space is also reduced from the original to ⁠, which is only 1/8 of the original one. Therefore, this process greatly increases the probability of finding feasible solutions in each iteration of the particle swarm algorithm population.

A novel framework and optimization method is proposed in this study to simulate optimal DMA layouts. The optimization process can provide guidance to future studies on burst pipe detection and location based on DMAs. Compared with other partition methods, the proposed method demonstrates improvement in the following aspects of the dividing phase: pipe importance analysis, initial solution optimization, particle update position formula improvement, and crossover mechanism introduction. The improved multiobjective BPSO optimizes flowmeters (i.e., inlet pipes) and gate valve layouts from different objectives and enhances the efficiency of the dividing phase. The improvements solve the problem of not finding a solution that satisfies the constraints. The partition results can be effectively utilized for refined management of water supply, leakage reduction, and overall pressure reduction.

Finally, the proposed method can be used as a template for other DMA design purposes, such as elevation of nodes between DMAs. Additional objectives can be considered in the optimization process of boundary pipe segments, and trade-offs between these objectives can be explored to achieve a rational partition scheme and improve daily infrastructure management.

This work was supported by the National Natural Science Foundation of China (No. 52070167 and No. 52070165) and Zhejiang Provincial Natural Science Foundation of China (No. LHY22E080003).

All relevant data are available from an online repository or repositories: https://github.com/zhangxiangqiu/optimal_design_of_district_metered_areas.

The authors declare there is no conflict.