Multi-Objective Design Optimization of Branched Pipeline Systems with Analytical Assessment of Fire Flow Failure Probability

This paper develops a multi-objective optimization approach for incorporating the conditional probability of fire flow failure into the design of branched water networks. To this end, a new analytical probabilistic model was developed to quantify the conditional probability of fire flow failure in branched networks and incorporated into the non-dominated sorting genetic algorithm (NSGA-II). The optimization sought to minimize capital cost through pipe diameter and pump selection and to minimize the conditional probability of fire flow failure. The NSGA-II was applied to two branched networks to generate Pareto-optimal solutions. Results indicated a strategic allocation of pipe and pump capacity with limited fiscal resources and with a reduction in uncertainty of fire flow failure. Interestingly, optimization results for a real branched network supported the industry practice of using a minimum 150 mm distribution main sizing to provide fire flow protection.     

引江济淮工程（河南段）多目标水量优化调度

引江济淮工程（河南段）涉及河道、闸泵、管道和调蓄水库,约束条件复杂,常规的优化调度算法难以搜索可行解,求解效率低。选用受水区缺水率平均值最小、泵站总抽水量最小和受水区缺水率标准差最小作为目标函数,从供水保障、供水成本和公平性角度构建多目标水量优化调度模型。基于可行搜索思路,结合逆序演算和顺序演算过程对约束条件进行处理,引入决策系数,通过映射关系使搜索空间保持在可行域中,结合多目标非支配排序遗传算法（non-dominated sorting genetic algorithms,NSGA-II）进行求解,得到Pareto最优解集,并采用熵权法进行方案优选。结果表明,基于可行搜索的NSGA-II算法能够有效求解复杂调度系统的多目标优化问题,综合考虑多个目标的最优方案相对单目标方案更加合理,结果可为引江济淮工程（河南段）运行管理提供决策支撑。     

Multi Objective Optimization with a New Evolutionary Algorithm

Various objectives are mainly met through decision making in real world. Achieving desirable condition for all objectives simultaneously is a necessity for conflicting objectives. This concept is called multi objective optimization widely used nowadays. In this study, a new algorithm, comprehensive evolutionary algorithm (CEA), is developed based on general concepts of evolutionary algorithms that can be applied for single or multi objective problems with a fixed structure. CEA is validated through solving several mathematical multi objective problems and the obtained results are compared with the results of the non-dominated sorting genetic algorithm II (NSGA-II). Also, CEA is applied for solving a reservoir operation management problem. Comparisons show that CEA has a desirable performance in multi objective problems. The decision space is accurately assessed by CEA in considered problems and the obtained solutions’ set has a great extent in the objective space of each problem. Also, CEA obtains more number of solutions on the Pareto than NSGA-II for each considered problem. Although the total run time of CEA is longer than NSGA-II, solution set obtained by CEA is about 32, 4.4 and 1.6% closer to the optimum results in comparison with NSGA-II in the first, second and third mathematical problem, respectively. It shows the high reliability of CEA’s results in solving multi objective problems.     

泵站加压式树状供水管网优化设计研究

针对传统供水管网优化设计时未考虑整个管网的首末水头约束问题,提出了以管网系统年折算费用最小为目标函数,以水泵扬程和具有标准管径的干、支管管道长度为决策变量的泵站加压式树状供水管网优化设计数学模型。在该模型中,假定水泵扬程已知,将管网优化问题转化成管网投资线性子模型问题,并采用大系统分解-动态聚合方法对该子模型进行求解。研究结果表明,该方法寻优能力强,且计算时间短,计算结果精度较高,为泵站加压式树状供水管网系统优化设计提供了一种可行而有效的新方法。     

基于多目标优化模型的雨水管网改建

雨水管网是城市排涝工程体系的重要组成部分,如何科学经济地对现状雨水管网进行优化改建,是提升管网排水能力、缓解城市内涝的的关键问题之一。建立以降低造价和工程量以及提高排水能力为目标的管网改建多目标优化模型,以管径改建值作为变量,利用NSGA-II多目标优化算法求解;基于Java运行平台,将SWMM源代码嵌入寻优过程,实现程序自动调用水力学模拟软件,得到快速获取可行解的新途径;将新建模型应用于工程实例,应用结果表明,优化模型在保证工程合理性要求的前提下,可快速获得多个经济可行的组合改建方案。研究对于雨水管网改建工作等具有借鉴意义。     

Multiobjective Pump Scheduling Optimization Using Harmony Search Algorithm (HSA) and Polyphonic HSA

Harmony Search Algorithm (HSA) is a metaheuristic method that has attracted the scientific interest since its first presentation in 2001. It is a music inspired method, imitating the music creation process in order to find optimal solutions in complicated problems. HSA’s successful application on single – objective optimization problems has resulted to an increasing interest in the implementation of HSA towards multiobjective optimization. The authors have adjusted HSA in order to deal successfully with multi-criteria water management problems. This adjustment has resulted to the creation of Multiobjective – HSA (MO-HSA). In addition, they have designed the multiobjective variant Polyphonic-HSA (Poly-HSA), which is inspired by the independent development of different voices in music and borrows elements from Swarm Intelligence and the single-objective variant Global-Best HSA. In the first part of this paper, both methods are presented in detail. Moreover, the performance of the proposed Algorithms is evaluated using standard multiobjective test – functions. ZDT and DTLZ multiobjective tests have been chosen and indicators such as Hypervolume, C – metric and diversity metric – Δ have been used to measure the convergence to the optimal front and the diversity of the solutions obtained by the proposed methods. In the second part, MO-HSA and Poly-HSA have been introduced towards the optimization of a pump scheduling problem. The objectives considered are water supply, pumping cost, electric power peak demand and pump maintenance cost. Both methods converged to non-dominated fronts and provided excellent results which are presented in 3d figures, indicating that these methods can be effectively used in multiobjective water management problems.     

树状给水管网的优化

本文根据树状给水和网的特点，分别建立了重力和泵站加压树状管网优化计算的一规划模型，应用上述模型，可进行单水源树状管网的优化计算。     

Real-Time Operation of Pumping Systems for Urban Flood Mitigation: Single-Period vs. Multi-Period Optimization

To reduce flood risk in urban regions, it is important to optimize the performance of operational elements such as gates and pumps. This paper compares the performances of two approaches of multi-period and single-period simulation-optimization that are used to derive real-time control policies for operating urban drainage systems. The EPA storm water management model (SWMM), converting real-time rainfall data to surface runoff at network control points, i.e. pump stations, is linked to the particle swarm optimization (PSO) algorithm, evaluating the system operation performance measure (objective function) for different sets of control policies. A prototype network in a portion of the Seoul urban drainage system is used to investigate the efficiency of the proposed approaches. Results justify the high efficiency of multi-period optimization, leading to 32 and 29% average reductions in peak water level violations from a pre-defined permissible threshold at target points and the number of pump switches, respectively, in comparison with the online single-period optimization. The myopic policies derived by single-period optimization are not reliable, and in some cases, they even perform worse than ad-hoc policies applied by system operators based on their past experiences.     

整数规划的分支定界在水泵选型中的应用

以泵站系统效率最高为目标函数,以水泵台数为优化变量,以流量变化为约束条件,建立了水泵优化选型模型。采用整数规划的分支定界模型求解,运用该方法,既可以提高计算效率,又可以在较大解空间范围内获得最优水泵组合方案,使选型结果最优。     

Uncertainty Analysis of Transient Flow in Water Distribution Networks

For transient analysis of a pipe network, the unsteady flow governing equations should be solved to obtain the extreme pressure heads in the system, which may be faced with several uncertainties. To evaluate that to what extent the input uncertainties can affect the system responses, a simulation model based on the fuzzy sets theory is introduced. For this purpose, triangular fuzzy numbers are used to represent the input uncertainties. Then, to obtain the extreme pressure heads in each location of the network and at each level of uncertainty, four independent optimization problems are solved. In these problems, the nodal maximum and minimum pressure heads are the objective functions and the simulation parameters are the decision variables. Accordingly, for fuzzy analysis of a pipe network, a complicated many-objective optimization problem arises. To solve the problem efficiently a many-objective genetic algorithm is coupled to the transient simulation model. To speed up the analysis, a transient simulation model in the frequency domain is used. The proposed model is applied to a pipe network and the results are discussed. The model is found computationally fast and promising for real applications.     

Multi- Objective Optimal Design of on- Demand Pressurized Irrigation Networks

In the context of water as an economic good, from the use of water, one can derive a value, which can be affected by the reliability of supply. On-demand irrigation systems provide valuable water to skilled farmers who have the capacity to maximize economic value of water. In this study, simultaneous optimization of on-demand irrigation network layout and pipe sizes is considered taking into account both investment and annual energy costs. The optimization problem is formulated as a problem of searching for the upstream head value, which minimizes the total cost (investment and energy costs) of the system. The investment and annual energy costs are obtained in two separate phases. Max–Min ant system (MMAS) algorithm is used to obtain the minimum cost design considering layout and pipe diameters of the network simultaneously. Clement methodology is used to determine flow rates of pipelines at the peak period of irrigation requirements. The applicability of the proposed method is showed by re-designing a real world example from literature.     

Model for Optimal Operation of Water Distribution Pumps with Uncertain Demand Patterns

An optimization model is presented for pump operation based upon minimizing operation costs and indirectly the maintenance costs of pumps considering uncertainty of specified demand (load) curves. The purpose of this model is to determine pump operation to meet the uncertain demands as well as to satisfy the pressure requirements in the water distribution system. In addition, constraints on the number of pump (‘on-off’) switches are included as a surrogate to indirectly minimizing the maintenance costs. This model is a mixed integer nonlinear programming (MINLP) problem using a chance constraint formulation of the uncertain demand constraint. The optimization model was solved using the LocalSolver option in A Mathematical Programming Language (AMPL). The model was first applied to the operation of an example pumping system for an urban water distribution system (WDS) illustrating a reduction in operation costs using the optimization model. The optimization model with the chance-constraint for demand was applied for a range of demand satisfaction uncertainties. A decrease in the operation costs was observed with an increased uncertainty in demand satisfaction, which shows that the model further optimizes the operations considering the relaxed constraints. Model application could be extended to operations of pumping systems during emergencies and contingencies such as droughts, component failures etc.     

Multiobjective Optimal Design of Sewerage Rehabilitation by Using the Nondominated Sorting Genetic Algorithm-II

Application of multiobjective optimization in sewerage rehabilitation management is not widespread due to the limitation of data collection and complex optimization process. Thus, a few researches in literature focused on sewerage rehabilitation optimization, and only considered two-objective optimization usually between the service life and the direct cost instead of a social cost. A sewerage rehabilitation multiobjective optimization decision support system (SRMOS) was developed for sewerage rehabilitation management in this study. The nondominated sorting genetic algorithm-II was used to design a set of Pareto surfaces with desirable rehabilitation effectiveness at the lowest cost by providing optimal plans comprising a construction method and substitute material. The SRMOS was applied to a real sewerage system to provide tradeoff solutions for three conflicting objectives, which are minimizing rehabilitation cost, maximizing pipe service, and minimizing traffic disruption. Compared with the experts' manual estimation, the plan derived from the SRMOS enables saving nearly 20 % of the rehabilitation cost. The contours of the rehabilitation cost show the equivalent relation between the traffic disruption and service life of pipes. The results indicate that increasing the number of objectives can make up the drawback of cost hard to be quantified and can also facilitate deriving practical plans for reference in decision-making.     

基于模拟退火遗传算法的自压树状管网优化

将遗传算法全局优化和模拟退火的良好局部搜索能力有机结合,构造出一种退火遗传算法用于自压树状管网的优化设计方法。假定管网中每一管段最多只能由两种管径的管道组成,建立了以管网造价为目标函数,以管长、标准管径为决策变量的自压树状管网优化数学模型。采用基于不可行度的退火算法处理约束条件,应用遗传算法进行优化计算。仿真实例结果表明,该模型与算法在求解自压树状管网优化问题上,具有良好的优化性能和求解效率。     

Optimization on the VFDs’ Operation for Pump Units

The third Huaiyin pumping station in the South-to-North Water Diversion Project aims to solve the problem of lack of water. In order to save on electricity while satisfying the required flow demand, the operation optimization problem of the third Huaiyin pumping station is investigated, with a mathematical model set up to simulate the optimal daily operation, in which the pump units can have variable speed. After analyzing the characteristics of the mathematical model, an improved dynamic programming algorithm is presented to decrease the dimensions of the operation optimization problem and save electricity cost, which enables us to perform a practical engineering application. After discretization of the optimization problem has been achieved, the number of operational schedule sequences could be reduced and optimal scheduling could be achieved to save electricity costs by power constraint, classified enumeration constraint, feasible combination constraint and flow demand constraint. Through research and analysis of the working of the third Huaiyin pumping station, optimal operational scheduling of multiple pump units with variable speed operation using variable frequency drive (VFD) can lessen the electricity tariff significantly compared with dynamic programming with the successive approximation method and decomposition/aggregation-dynamic programming method. The operational electricity tariff is reduced by 7.71% by the improved dynamic programming algorithm in comparison with the benchmark scheduling. Simulation results demonstrate that the cost efficiency comes from variable speed operation with VFD and flow demand transfer from the time periods when a high electricity tariff applies to time periods of a low electricity tariff based on the time-of-use electricity tariff.

     

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.     

Multi-Directional Maximum-Entropy Approach to the Evolutionary Design Optimization of Water Distribution Systems

A new multi-directional search approach that aims at maximizing the flow entropy of water distribution systems is investigated. The aim is to develop an efficient and practical maximum entropy based approach. The resulting optimization problem has four objectives, and the merits of objective reduction in the computational solution of the problem are investigated also. The relationship between statistical flow entropy and hydraulic reliability/failure tolerance is not monotonic. Consequently, a large number of maximum flow entropy solutions must be investigated to strike a balance between cost and hydraulic reliability. A multi-objective evolutionary optimization model is developed that generates simultaneously a wide range of maximum entropy values along with clusters of maximum and near-maximum entropy solutions. Results for a benchmark network and a real network in the literature are included that demonstrate the effectiveness of the procedure.     

Penalty-Free Multi-Objective Evolutionary Approach to Optimization of Anytown Water Distribution Network

This paper describes the development and application of a new multi-objective evolutionary optimization approach for the design and upgrading of water distribution systems with multiple pumps and service reservoirs. The optimization model employs a pressure-driven analysis simulator that accounts for the minimum node pressure constraints and conservation of mass and energy. Pump scheduling, tank siting and tank design are integrated seamlessly in the optimization without introducing additional heuristic procedures. The computational solution of the optimization problem is entirely penalty-free, thanks to pressure-driven analysis and the inclusion of explicit criteria for tank depletion and replenishment. The model was applied to the Anytown network that is a benchmark optimization problem. Many new solutions were achieved that are cheaper and offer superior performance compared to previous solutions in the literature. Detailed and extensive simulations of the solutions achieved were carried out. Spatial and temporal variations in water quality were investigated by simulating the chlorine residual and disinfection by-products in addition to water age. The hydraulic requirements were satisfied; efficiency of pumps was consistently high; effective operation of the new and existing tanks was achieved; water quality was improved; and overall computational efficiency was high. The formulation is entirely generic.     

Evolving Effective Hydraulic Model for Municipal Water Systems

Constructing a robust hydraulic network model is vitally important, but a time-consuming task. Over last two decades, several approaches using optimization techniques have been developed for identifying model parameters. Although most of the methods can make the model agree with field observations, few are able to achieve a good level of accuracy in terms of determining the correct model parameters for a water distribution system. The previously developed methods appear to be lacking versatility for users to specify calibration tasks given real data for a real system. This paper proposes a comprehensive framework for evolving a hydraulic network model. Calibration tasks can be specified according to data availability and model application requirements. It allows an engineer to (1) flexibly choose any combination of the model parameters such as pipe roughness, junction demand and link (pipes, valves and pumps) operational status; (2) easily aggregate model parameters to reduce the problem dimension for expeditious calculation and (3) consistently specify boundary conditions and junction demand loadings that are corresponding to field data collection. A model calibration is then defined as an implicit nonlinear optimization problem, which is solved by employing a competent evolutionary algorithm. With this methodology, a modeler can be fully assisted to carry out not only a single parameter optimization run, but also a variety of calibration tasks in a progressive manner according to practical system conditions, thus it is possible to achieve a good model calibration with high level of confidence. The method has been applied to the model of a municipal water system to demonstrate the efficacy and robustness of the evolutionary modeling practices.     

南水北调中线天津段泵站输水方案水击等效管计算方法

通过研究了解水击条件下k条特性相同管道并联的等效计算模型，在特征线法的基础上，导出了用一条等效管代替并联管道的等效模型：等效管的直径和沿程阻力系数分别是实际管道直径和沿程阻力系数的√k倍，等效管的长度和水击波速等于任一实际管道的水击波速和长度；等效泵的机组惯性时间常数、扬程、出口阀门特性与实际泵相同，等效泵的Suter变换流量、力矩特性与实际泵相同，但等效泵的流量等于并联各泵流量之和。