Coupled Topology and Pipe Size Optimization of Water Distribution Systems

This paper describes a new multi-objective evolutionary optimization approach to the simultaneous layout and pipe size design of water distribution systems. Pressure-deficient and topologically infeasible solutions are fully incorporated in the genetic algorithm without recourse to constraint violation penalties or tournaments. The proposed approach is demonstrated by solving three benchmark problems taken from the literature. New optimal layouts and/or new feasible solutions that are cheaper than the best solutions in the literature were found for both branched and looped network configurations. Specifically, a new best solution was generated for each of the above-mentioned benchmark problems. In addition, the case of the looped design of a hitherto branched network in the literature was considered. Detailed results are included that show that the proposed approach achieves good solutions efficiently and consistently.     

Application of Several Meta-Heuristic Techniques to the Optimization of Real Looped Water Distribution Networks

The optimization of looped water distribution systems is a complex problem as the pipe flows are unknown variables. Although many researchers have reported algorithms for minimizing the network cost applying a large variety of techniques, such as linear programming, non-linear programming, global optimization methods and meta-heuristic approaches, a totally satisfactory and efficient method is not available as yet. Many works have assessed the performance of these techniques using small or medium-sized benchmark networks proposed in the literature, but few of them have tested these methods with large-scale real networks. The aim of this paper is to evaluate the performance of several meta-heuristic techniques: genetic algorithms, simulated annealing, tabu search, and iterated local search. These techniques were first validated and compared by applying them to a medium-sized benchmark network previously reported in the literature. They were then applied to a large irrigation water distribution network that has been proposed in a previous work to assess their performance in a practical application. All the methods tested performed adequately well, compared with the results found in previous works. Genetic algorithm was more efficient when dealing with a medium-sized network, but other methods outperformed it when dealing with a real complex one.     

用聚类算法及Hopfield神经网络布置环状管网

为了降低供水管网的工程投资,提出了一种环状给水管网优化设计的方法,把环状管网布置问题用K-Means算法分解成许多小规模的环状问题,对于每一个小规模的环状管网用Hopfiled连续型神经网络求解环状的最短距离,然后把各个基环当成一个点,再用Hopfield神经网络以较大的概率求出最优路径。对某小区58个供水点进行了供水管网实例计算,结果表明:该供水管网的质心间最短距离为2.893 7 km,能量函数为递减状态且最终的能量函数值为1.447,再连接相邻聚类中的最接近的两个点就形成供水管网的环状布置。     

Reliability and Tolerance Comparison in Water Supply Networks

Urban water supply is a high priority service and so looped networks are extensively used in order to considerably reduce the number of consumers affected by a failure. Looped networks may be redundant in connectivity and capacity. The concept of reliability has been introduced in an attempt to quantitatively measure the possibility of maintaining an adequate service for a given period. Numerous researchers have considered reliability as a measure of redundancy. This concept is usually implicit, but some researchers have even stated it explicitly. This paper shows why reliability cannot be considered a measure of redundancy given that branched networks can achieve high values of reliability and this would deny the fact that a looped network is more reliable than a branched network with a similar layout and size. To this end the paper discusses two quantitative indices for measuring expected network behavior: reliability and tolerance. These indices are calculated and a comparison is made between looped, branched, and mixed networks.     

Heuristic Optimization Model for the Optimal Layout and Pipe Design of Sewer Systems

The design of urban stormwater systems and sanitary sewer systems consists of solving two problems: generating a layout of the system and the pipe design which includes the crown elevations, slopes and commercial pipe sizes. A heuristic model for determining the optimal (minimum cost) layout and pipe design of a storm sewer network is presented. The hierarchical procedure combines a sewer layout model formulated as a mixed-integer nonlinear programming (MINLP) problem which is solved using the General Algebraic Modeling System (GAMS) and a simulated annealing optimization procedure for the pipe design of a generated layout was developed in Excel. The GAMS and simulated annealing models are interfaced through linkage of Excel and GAMS. The pipe design model is based upon the simulated annealing method to optimize the crown elevations and diameter of pipe segments in a storm sewer network using layouts generated using GAMS. A sample scenario demonstrates that using these methods may allow for significant costs saving while simultaneously reducing the time typically required to design and compare multiple storm sewer networks.     

Nodal Analysis of Urban Water Distribution Networks

There are three methods for analysing the flow and pressure distribution in looped water supply networks (the loop method, the node method, the pipe method), accounting for the chosen unknown hydraulic parameters. For all of these methods, the nonlinear system of equations can be solved using iterative procedures (Hardy–Cross, Newton–Raphson, linear theory). In the cases of the extension or the rehabilitation of distribution networks, the unknown parameters are the hydraulic heads at nodes, and the nodal method for network analysis is preferred. In this paper, a generalised classic model is developed for the nodal analysis of complex looped systems with non-standard network components and the solvability of new problems, along with the determination of the pressure state in the system. In addition, this paper exhibits a different approach to this problem by using the variational formulation method for the development of a new analysis model based on unconditioned optimisation techniques. This model has the advantage of using a specialised optimisation algorithm, which directly minimises an objective multivariable function without constraints, implemented in a computer program. The two proposed models are compared with the classic Hardy–Cross method, and the results indicated a good performance of these models. Finally, a study is performed regarding the implications of the long-term operation of the pipe network on energy consumption using these models. The new models can serve as guidelines to supplement existing procedures of network analysis.     

Performance Assessment of a Coupled Particle Swarm Optimization and Network Flow Programming Model for Optimum Water Allocation

Water resources allocation problems are mainly categorized in two classes of simulation and optimization. In most cases, optimization problems due to the number of variables, constraints and nonlinear feasible search space are known as a challenging subject in the literature. In this research, by coupling particle swarm optimization (PSO) algorithm and a network flow programming (NFP) based river basin simulation model, a PSO-NFP hybrid structure is constructed for optimum water allocation planning. In the PSO-NFP model, the NFP core roles as the fast inner simulation engine for finding optimum values for a large number of water discharges in the network links (rivers and canals) and nodes (reservoirs and demands) while the heuristic PSO algorithm forms the outer optimization cover to search for the optimum values of reservoirs capacities and their storage priorities. In order to assess the performance of the PSO-NFP model, three hypothetical test problems are defined, and their equivalent nonlinear mathematical programs are developed in LINGO and the results are compared. Finally, the PSO-NFP model is applied in solving a real river basin water allocation problem. Results indicate that the applied method of coupling PSO and NFP has an efficient ability for handling river basin-scale water resources optimization problems.     

Accuracy and Sensitivity Evaluation of TFR Method for Leak Detection in Multiple-Pipeline Water Supply Systems

The transient frequency response (TFR) based pipe leak detection method has been developed and applied to water pipeline systems with different connection complexities such as branched and looped pipe networks. Previous development and preliminary applications have demonstrated the advantages of high efficiency and non-intrusion for this TFR method. Despite of the successful validations through extensive numerical applications in the literature, this type of method has not yet been examined systematically for its inherent characteristics and application accuracy under different system and flow conditions. This paper investigates the influences of the analytical approximations and assumptions originated from the method development process and the impacts of different uncertainty factors in practical application systems on the accuracy and applicability of the TFR method. The influence factors considered for the analysis contain system properties, derivation approximations and data measurement, and the pipeline systems used for the investigation include simple branched and looped multi-pipe networks. The methods of analytical analysis and numerical simulations are adopted for the investigation. The accuracy and sensitivity of the TFR method is evaluated for different factors and system conditions in this study. The results and findings are useful to understand the validity range and sensitivity of the TFR-based method, so as to better apply this efficient and non-intrusive method in practical pipeline systems.     

Decomposition based Multi Objective Evolutionary Algorithms for Design of Large-Scale Water Distribution Networks

In last two decades, multiobjective evolutionary algorithms (MOEAs) have shown their merit for solving different optimization problems within the context of water resources and environmental engineering. MOEAs mainly use the concept of Pareto dominance for obtaining the trade-off solutions considering different criteria. A new alternative method for solving multiobjective problems is multiobjective evolutionary algorithm based on decomposition (MOEA/D) which uses scalarizing the objective functions. In this paper, decomposition strategies are developed for the large-scale water distribution network (WDN) design problems by integrating the concepts of harmony search (HS) and genetic algorithm (GA) within the MOEA/D framework. The proposed algorithms are then compared with two well-known non-dominance based MOEAs: NSGA2 and SPEA2 across four different WDN design problems. Experimental results show that MOEA/D outperform the Pareto dominance methods in terms of both non-domination and diversity criteria. MOEA/D-HS in particular could provide very high quality solutions with a uniform distribution along the Pareto front preserving the diversity and dominating the solutions of the other algorithms. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated large-scale WDN design problems.     

Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos

Genetic algorithms (GA) have been widely applied to solve water resources system optimization. With the increase of the complexity and the larger problem scale of water resources system, GAs are most frequently faced with the problems of premature convergence, slow iterations to reach the global optimal solution and getting stuck at a local optimum. A novel chaos genetic algorithm (CGA) based on the chaos optimization algorithm (COA) and genetic algorithm (GA), which makes use of the ergodicity and internal randomness of chaos iterations, is presented to overcome premature local optimum and increase the convergence speed of genetic algorithm. CGA integrates powerful global searching capability of the GA with that of powerful local searching capability of the COA. Two measures are adopted in order to improve the performance of the GA. The first one is the adoption of chaos optimization of the initialization to improve species quality and to maintain the population diversity. The second is the utilization of annealing chaotic mutation operation to replace standard mutation operator in order to avoid the search being trapped in local optimum. The Rosenbrock function and Schaffer function, which are complex and global optimum functions and often used as benchmarks for contemporary optimization algorithms for GAs and Evolutionary computation, are first employed to examine the performance of the GA and CGA. The test results indicate that CGA can improve convergence speed and solution accuracy. Furthermore, the developed model is applied for the monthly operation of a hydropower reservoir with a series of monthly inflow of 38 years. The results show that the long term average annual energy based CGA is the best and its convergent speed not only is faster than dynamic programming largely, but also overpasses the standard GA. Thus, the proposed approach is feasible and effective in optimal operations of complex reservoir systems.     

GA-ILP Method for Optimization of Water Distribution Networks

Optimization of water distribution networks has been of central importance for recent decades. Genetic Algorithms (GA) are the most famous metaheuristics widely used for this purpose with great success. However, the fact that GA basically requires a large number of computations, has led to investigate for faster solvers. In this research, a new approach is proposed in which a simple GA is linked with the Integer-Linear Programming (ILP) method resulting in a hybrid optimization scheme. Using the mathematical method of ILP, the search space is significantly reduced thereby a limited number of evaluations are required to achieve a good solution. The approach is applied to two benchmark pipe-networks in order to show its ability in terms of accuracy and speed. The results are then compared with the previous works. The obtained results indicate that the proposed model is computationally efficient, like classic methods, while is still very promising in finding the global optimum like the nature-inspired metaheuristics.     

应用LINGO求解水污染控制系统规划中的费用函数问题

利用LINGO软件,对新疆水磨河水污染控制系统规划的费用函数进行求解,获得全局最优解:以碳化生化需氧量为水质指标时的最低费用为1496.61万元,以氨氮为水质指标时最低费用为924.12万元,该计算结果均优于模拟退火法(SA)、动态规划(DP)和遗传算法(GA)得到的结果,表明LINGO软件在求解水污染控制系统规划中的费用函数问题具有一定的优越性。     

Design of Water Distribution Networks using a Pseudo-Genetic Algorithm and Sensitivity of Genetic Operators

Genetic algorithms (GA) are optimization techniques that are widely used in the design of water distribution networks. One of the main disadvantages of GA is positional bias, which degrades the quality of the solution. In this study, a modified pseudo-genetic algorithm (PGA) is presented. In a PGA, the coding of chromosomes is performed using integer coding; in a traditional GA, binary coding is utilized. Each decision variable is represented by only one gene. This variation entails a series of special characteristics in the definition of mutation and crossover operations. Some benchmark networks have been used to test the suitability of a PGA for designing water distribution networks. More than 50,000 simulations were conducted with different sets of parameters. A statistical analysis of the obtained solutions was also performed. Through this analysis, more suitable values of mutation and crossover probabilities were discovered for each case. The results demonstrate the validity of the method. Optimum solutions are not guaranteed in any heuristic method. Hence, the concept of a “good solution” is introduced. A good solution is a design solution that does not substantially exceed the optimal solution that is obtained from the simulations. This concept may be useful when the computational cost is critical. The main conclusion derived from this study is that a proper combination of population and crossover and mutation probabilities leads to a high probability that good solutions will be obtained.     

混合智能算法在引水冲污方案优选中的应用

考虑水质、经济和生态环境影响等因素,建立佛山水道的引水规划优化模型。利用河网水环境数学模型模拟多组引水冲污方案的水质,将输入输出数据作为样本用于人工训练神经网络;将训练好的网络嵌入遗传算法,形成混合智能算法,求解引水规划优化模型。结果表明,混合智能算法能够自动求出不同引水流量下的最优方案,精度较高,无需人工试算,运算速度快,不必对遗传算法与河网模型进行接口处理,具有普遍适用性,为求解耦合复杂模拟模型的优化问题提供了一种理想的工具。     

供水管网水力计算与优化调度

本文用图论理论和稀疏矩阵技术进行城市供水非线性管网的水力分析，以减少存贮量和计算时间，对仅有泵站水源的管网，用两级递阶优化法进行优化调度，用正交试验法解决一般管网改建或扩建问题，计算机仿真结果表明，管网系统优化调度有效好的效果效益。     

Hydraulic Analysis of Water Distribution Systems Based on Fixed Point Iteration Method

Water distribution systems with complex configurations are important urban facilities and the hydraulic analysis is essential for system design, optimization and management. Hydraulic analysis involves the procedure of calculating the hydraulic parameters of nodal pressure heads and pipe flow rates under steady-state condition. The equations governing the heads and flows are nonlinear and the most popular method for solving the equations is the Newton-Raphson method, which is the basis of existing hydraulic simulator (EPANET 2). In this paper, fixed point iteration method is proposed for hydraulic analysis after transformation of the original nonlinear equations. Compared to EPANET 2, the proposed method can analyze a water distribution system without differentiation for the convergence for some problems which cannot be solved by EPANET 2. Three test networks were analyzed by the proposed method and EPANET 2. It is proved that the proposed method could get the convergence after a series of iterations, even in cases that EPANET 2 fail. And the initial values of nodal pressure heads and the specified calculation accuracy are considered to have influences on the calculation procedure.     

重力单水源环状管网优化设计的遗传-线性规划算法

本文首先提出了基管段流量概念，并作为优化变量，建立环状管网流量优化分配的非线性规划模型；又以管道尺寸为优化变量，建立某一流量分配方案下管网优化设计的线性规划模型。在优化设计计算过程中，采用遗传算法求解非线性规划模型及单纯形法求解线性规划模型，两种优化算法交替计算，可确定环状管网优化设计方案。本文提出的方法，是一种有效地解决重力单水源环状管网优化设计的新方法。     

Automated Framework for Water Looped Network Equilibrium

In this paper, a novel algorithm is proposed for balancing water looped network in steady state through a fully automated general framework of hydraulic networks regardless of their topological complexity. The model is developed by combining the following two steps, firstly a set of independent loops are identified based on a graph theoretical analysis in a looped network. Further the second step is devoted to the equilibrium process by determining the flow rate distribution within the network ducts and the pressure in the delivery nodes. The above such equilibrium process gives rise to a system of non linear algebraic equations which are solved numerically using both Hardy Cross (HC) and Newton Raphson (NR) methods. In HC method, the flow correction term is modified and a generalized expression is given to consider various possibilities of independent loops selection. Some real networks topologies that were commonly used as benchmarks, for testing various independent loops selection algorithms, are taken as case studies to apply the general automatic framework for hydraulic network analysis. Such network analysis enhances proving the applicability as well as the effectiveness of the proposed approach. Also, during the equilibrium procedure, it is proved that NR method is capable of producing accurate results and it converges more rapidly comparing to the widely used HC method. Moreover, it is demonstrated that NR’s iterative process, contrary to HC’s one, converges to reliable results even with a choice of random initial flow rates which makes a NR algorithm quite simple to implement without affecting the accuracy of the results.     

A GA-HP Model for the Optimal Design of Sewer Networks

This paper illustrates the application of a new model combined Genetic Algorithm with Heuristic Programming (GA-HP) technique in order to establish the optimal design for sewer networks. The objective is to minimise the construction cost function, which is represented by the depth of excavation and pipe diameter. The proposed GA-HP model has achieved the optimum design task in two stages. Firstly, the Genetic Algorithm (GA) was applied to obtain the diameters of the pipes needed for the preliminary design of the network. Secondly, Heuristic Programming (HP) preliminary designs were used to obtain the optimal slope for those pipes and to determine other characteristics such as the velocity, relative depth of water, excavation depths and total cost of the network. A MATLAB code was used to perform the GA-HP optimisation modelling. The performance of three different selection methods, four different crossover methods and different population sizes is examined with the proposed model, to determine their impact on convergence behaviour. The proposed GA-HP model is tested using some benchmark examples of sewer networks from the literature. The results show that the GA-HP model is superior to all previous methods and may be more efficient in the design of large networks.     

城市河网连通循环净化系统构建及其关键技术

针对城市河网连通性欠佳、水环境质量下降及河网调控难度大等问题,提出基于活水循环耦合高效净化的城市河网水环境改善新模式,并提出河网整治过程中待解决的关键问题,即城市河网全局补水调控技术、定量化整装净化技术、精细化水环境模拟与信息互馈机制、信息集中与全局处理。在此基础上,阐述了新发展形式下城市河网连通活水循环净化系统的内涵与总体需求,提出了涵盖河网整治、河网水体净化、河网水流-水质模拟评价、水质在线监测等4个方面的系统架构,明确了城市河网水体动态连通调控-定量整装成套净化耦合技术、河网水体动态监测-精细化模拟耦合技术、城市河网水环境全局信息管理与全面互联等关键技术问题,给出了城市河网未来的规划治理方向。