Development and application of a master-slave parallel hybrid multi-objective evolutionary algorithm for groundwater remediation design

Two primary goals of a multi-objective evolutionary algorithm (MOEA) for solving multi-objective optimization problems are to find as many nondominated solutions as possible toward the true Pareto front and to maintain diversity of Pareto-optimal solutions along the tradeoff curves. However, few MOEAs can achieve these two goals concurrently. This study presents a new hybrid MOEA, the niched Pareto tabu search combined with a genetic algorithm (NPTSGA), in which the global search ability of niched Pareto tabu search (NPTS) is improved by the diversification of candidate solutions that arose from the evolving population of nondominated sorting genetic algorithm-II (NSGA-II). The NPTSGA coupled with a flow and transport model is developed for multi-objective optimal design of groundwater remediation systems. The proposed methodology is then applied to a large field-scale groundwater remediation system for cleanup of large trichloroethylene plume at the Massachusetts Military Reservation in Cape Cod, Massachusetts. Furthermore, a master-slave (MS) parallelization scheme based on the Message Passing Interface is incorporated into the NPTSGA to implement objective function evaluations in a distributed processor environment, which can greatly improve the efficiency of the NPTSGA in finding Pareto-optimal solutions to the real-world applications. This study shows that the MS parallel NPTSGA in comparison with the original NPTS and NSGA-II can balance the tradeoff between the diversity and optimality of solutions during the search process and is an efficient and effective tool for optimizing the multi-objective design of groundwater remediation systems under complicated hydrogeologic conditions.     

大连周水子海水入侵区地下水多目标优化管理模型

将改进后的遗传算法GA（添加了小生境、Pareto解集过滤器等模块）与变密度地下水流及溶质运移模拟程序SEAWAT-2000相耦合,新开发了变密度地下水多目标模拟优化程序MOSWTGA。将MOSWTGA应用于求解大连周水子地区以控制抽水井所在含水层不发生海水入侵为约束的地下水开采多目标优化管理模型,得到地下水最大开采量与海水入侵面积之间一系列Pareto近似最优解。研究成果不仅为实行合理的地下水资源配置提供了科学的实用模型,同时也为解决多个优化目标下的变密度地下水优化管理问题提供高效可靠的模拟优化工具,具有重要的潜在环境经济效益。     

NPGA-GW在地下水系统多目标优化管理中的应用

在地下水系统管理问题中,涉及到多个相互冲突的目标函数常常被简化为不同形式的单一目标函数来求解,这种通过单一目标函数的优化方法只能给出一个解,由此确定的方案有时会违背决策者的意愿。而通过多目标优化方法可以得到一系列供决策者权衡选择的解集。将地下水流模拟程序MODFLOW 和溶质运移模拟程序MT3DMS 相耦合,采用基于小生境技术的Pareto 遗传算法进行求解,开发了一个用于地下水系统多目标管理的应用程序NPGA-GW。并将该程序应用于一个二维地下水污染修复问题的多目标优化求解,结果表明,该程序能够在较短的时间内得到一系列Pareto 最优解,解的跨度足够决策者进行适当的选择,具有很好的应用前景。     

A Hybrid Multi‐Objective Evolutionary Algorithm for Optimal Groundwater Management under Variable Density Conditions

In this paper, a new hybrid multi-objective evolutionary algorithm (MOEA), the niched Pareto tabu search combined with a genetic algorithm (NPTSGA), is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search (TS) based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm (GA) with a TS based MOEA, the niched Pareto tabu search (NPTS), which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.     

控制海水入侵的地下水多目标模拟优化管理模型

为实现滨海含水层地下水开采-回灌方案优化、控制海水入侵面积和降低海水入侵损失等多重管理目标,建立了海水入侵条件下地下水多目标模拟优化管理模型SWT-NPTSGA。模拟模型采用基于变密度流的数值模拟程序SEAWAT来模拟海水入侵过程。优化模型采用小生境Pareto禁忌遗传混合算法NPTSGA来求解,该算法在保证多目标权衡解的收敛性和计算效率的前提下,能维护整个进化群体的全局多样性。将SWT-NPTSGA程序应用于一个理想滨海含水层地下水开采方案和人工回灌控制海水入侵的优化设计中,结果表明该管理模型能够同时处理最大化总抽水流量、最小化人工回灌总量和最小化海水入侵范围等3个目标函数之间的权衡关系。通过采用人工回灌海水入侵区的减灾策略,既能增加滨海地区的供水量,又可减少海水入侵的范围,由此进一步验证了模型的有效性和可靠性。     

基于INPGA的地下水污染治理多目标优化管理模型:Ⅱ——实例应用

简单算例研究表明改进的小生境Pareto遗传算法(INPGA)用于求解地下水系统的多目标优化管理模型时,求解过程简单,计算速度快,而且得到的Pareto解集跨度更为合理.本文以美国麻省军事保护区(Massachusetts Military Reservation,MMR)为实例,通过建立研究区复杂地下水污染治理的多目...     

基于Pareto强度进化算法的供水库群多目标优化调度

提出用Pareto强度进化算法解决供水库群的多目标优化调度问题,算法利用种群的进化过程模拟寻找非劣解集的过程,将供水库群多目标优化调度问题的解当作进化种群中的个体,按照解的Pareto强度值与密度进行适应度计算,利用种群中个体的进化操作获得非劣解,最终整个种群进化为非劣解集。实例分析结果表明,算法能实现多峰搜索,最终非劣解集的分布均匀,且收敛速度快,为解决供水库群多目标优化调度问题提供了一种有效的方法。     

基于INPGA的地下水污染治理多目标优化管理模型:Ⅰ——理论方法与算例验证

基于小生境技术的Pareto遗传算法(NPGA)是一种求解多目标问题的智能搜索方法,适用于优化多种非线性、不连续等复杂多目标问题.但该算法存在局部早熟收敛和收敛速度慢两个不足,在求解Pareto前沿上效果不佳.本文在NPGA的基础上,提出了改进NPGA方法(INPGA),通过Pareto解集过滤器、精英个体保留策略、邻...     

Impact of climate change on multi-objective management of seawater intrusion in coastal karst aquifers in Zhoushuizi district of Dalian City,China

Combined simulation-optimization modeling is an essential tool for coastal groundwater management. However, determining the appropriate simulation-optimization approach for specific seawater intrusion problems remains a significant challenge, especially for the real-world conditions associated with management of complex groundwater systems, competing management objectives, and global concerns of future climate change. In this study, a linked multi-objective simulation-optimization framework, the MOSWTGA (multi-objective optimal code, coupling SEAWAT and an improved genetic algorithm), was applied to a coastal groundwater system in Zhoushuizi district of Dalian City in northern China. The system has fractured karst aquifers and is modelled for the next 20 years (from 2010) under the moderate greenhouse gas concentration scenario RCP4.5 (representative concentration pathways) in the CNRM (Centre National de Recherches Météorologiques) and MIROC (Model for Interdisciplinary Research on Climate) climate modes derived from the Coupled Model Intercomparison Project Phase 5 (CMIP5). The MOSWTGA was developed by integrating the density-dependent groundwater flow and solute transport code SEAWAT with a genetic algorithm improved by adding the Pareto-dominated ranking module, Pareto solution set filter, and fitness sharing procedure. A set of near Pareto-optimal solutions of the trade-off between the maximum of the total pumping rate and the minimum of the extent of seawater intrusion was obtained. The study tried to provide a theoretical basis for real-world groundwater management under the given conditions.

     

两种智能算法在求解地下水管理模型中的对比

分别将禁忌搜索和遗传算法与地下水流模型MODFLOW和地下水溶质运移模型MT3DMS相耦合,并将其应用于求解地下水资源优化管理模型。在概述两种智能算法基本原理和地下水管理模型组成的基础上,结合两个理想的应用实例,从优化结果和计算效率两个方面对禁忌搜索和遗传算法进行了对比分析。在两个实例中,禁忌搜索分别以高于遗传算法10倍和27倍的计算效率得到了减少抽水流量约160 m³/d和节约治理成本约47万元的治理方案。结果表明,禁忌搜索在求解地下水管理模型中具有较好的应用前景。     

某氨氮污染地下水体抽出 -处理系统优化模拟研究

抽出 -处理系统设计多侧重于考虑修复初期的效率,在修复后期通常效率低下,产生拖尾现象,其优化的关键在于布设的井群系统能否高效抽出受污染的地下水体。利用溶质运移数值模拟可为井群布设和抽水方案优化提供依据。本研究旨在优化我国北方某化肥厂高浓度氨氮污染的地下水体的抽出 -处理修复系统,节约时间和成本。在水文地质调查及氨氮浓度监测的基础上,综合考虑井数、抽水天数和总抽水量三个变量,采用中轴线法与三角形法结合的布井方法,利用GMS软件反复试算,筛选出三种较优抽水方案并进一步模拟优化,最终从中选出最优抽水方案。结果,相比最初方案（方案1）,最优方案（方案3）将修复周期缩短了23个月,抽水总量减少了约31.9×104 m3,而抽水井数量仅增加了1口。该模型进行了稳定流水位拟合验证和4期非稳定流实测溶质浓度验证,较符合实际。结果表明,针对抽水井数量不足引起的拖尾问题,关键因素在于合理的井位布设与分阶段的抽水模式。在修复过程中,及时对地下水中污染物进行监测,并随着污染羽变化过程及时调整抽水方案,保证高浓度区一直有抽水井进行较大流量抽水,可有效提高修复效率并缩短修复周期。     

水文模型参数多目标率定及最优非劣解优选

针对概念性水文模型参数众多、相互制约,且多目标参数优化率定最优参数求解困难、易受决策者主观因素影响的问题,采用多目标优化算法对水文模型参数进行率定,得到模型参数最优非劣解集,在此基础上,引入最小最大后悔值决策理论,并结合Pareto支配基本理论,提出了一种多目标最优非劣解选取准则。以柘溪流域为研究对象,采用三目标MOSCDE优化率定新安江模型的参数,并与单目标SCE-UA优化结果进行对比分析。结果表明,提出的非劣解选取方法可以有效从大规模非劣解集中筛选出最优非劣解,大大缩短参数率定耗时。     

A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.     

Settlement of Shallow Foundations on Cohesionless Soils Based on SPT Value Using Multi-Objective Feature Selection

Accurate prediction of settlement for shallow footings on cohesionless soil is a complex geotechnical problem due to large uncertainties associated with soil. Prediction of the settlement of shallow footings on cohesionless soil is based on in situ tests as it is difficult to find out the properties of soil in the laboratory and standard penetration test (SPT) is the most often used in situ test. In data driven modelling, it is very difficult to choose the optimal input parameters, which will govern the model efficiency along with a better generalization. Feature subset selection involves minimization of both prediction error and the number of features, which are in general mutual conflicting objectives. In this study, a multi-objective optimization technique is used, where a non-dominated sorting genetic algorithm (NSGA II) is combined with a learning algorithm (neural network) to develop a prediction model based on SPT data based on the Pareto optimal front. Pareto optimal front gives the user freedom to choose a model in terms of accuracy and model complexity. It is also shown how NSGA II can be effectively applied to select the optimal parameters and besides minimizing the error rate. The developed model is compared with existing models in terms of different statistical criteria and found to be more efficient.     

Applying numerical modeling for designing strategies of effective groundwater remediation

Selection of effective groundwater remediation scenarios is a complex issue that requires understanding of contaminants’ transport processes. The effectiveness of cleanup measures may be verified by fate and transport numerical modeling. The goal of this work was to present the usefulness of fate and transport modeling for planning, verification and fulfillment of effective groundwater remediation methods. Selection methodology was developed, which is based on results of numerical flow and transport modeling. A field site located in south-east Poland was selected as a case study, in which groundwater contamination of trichloroethene and tetrachloroethene was detected. The results indicated that “pump and treat” was the most effective among the studied remediation methods, followed by permeable reactive barrier and in situ chemical oxidation. Natural attenuation-based remediation was demonstrated to be the least suitable, as it requires the longest time to reach predefined remediation goals, principally due to low sorption capacity and unfavorable hydrogeochemical conditions for biodegradation. Fate and transport numerical modeling allowed simulating different remediation strategies, and thus the decision-making process was facilitated.     

Simultaneous optimization of the performance of flotation circuits and their simplification using the jumping gene adaptations of genetic algorithm-II: More complex problems

The binary-coded elitist non-dominated sorting genetic algorithm with the modified jumping gene operator (NSGA-II-mJG) is used to obtain global optimal solutions of flotation circuits. Several single-objective and multi-objective optimization problems are solved using the interconnecting cell linkage parameters (fraction flow rates) and the mean cell residence times as the decision variables. In the single-objective problem, the overall recovery of the concentrate stream is maximized for a desired grade of the concentrate. Two two-objective optimization problems are then solved. In one, the number of non-linking streams and the overall recovery of the concentrate are maximized simultaneously. This gives several simple circuits in a systematic manner with only marginally lower recoveries. In the other two-objective optimization problem, the overall recovery of the concentrate is maximized while the total cell volume is minimized. A three-objective problem (maximization of the overall recovery of the concentrate, maximization of the number of non-linking streams and minimization of the total cell volume) is then solved. All the problems constrain the grade of the product to lie at a fixed value. Finally, a complex and computationally intensive four-objective optimization problem is solved. The solution of several practical optimization problems in this study helps develop useful insights into the optimal solutions.     

Optimization of artificial ground freezing in tunneling in the presence of seepage flow

Artificial ground freezing is an environmentally friendly technique to provide temporary excavation support and groundwater control during tunnel construction under difficult geological and hydrological ground conditions. Evidently, groundwater flow has a considerable influence on the freezing process. Large seepage flow may lead to large freezing times or even may prevent the formation of a closed frozen soil body. For safe and economic design of freezing operations, this paper presents a coupled thermo-hydraulic finite element model for freezing soils integrated within an optimization algorithm using the Ant Colony Optimization (ACO) technique to optimize ground freezing in tunneling by finding the optimal positions of the freeze pipe, considering seepage flow. The simulation model considers solid particles, liquid water and crystal ice as separate phases, and the mixture temperature and liquid pressure as primary field variables. Through two fundamental physical laws and corresponding state equations, the model captures the most relevant couplings between the phase transition associated with latent heat effect, and the liquid transport within the pores. The numerical model is validated by means of laboratory results considering different scenarios for seepage flow. As demonstrated in numerical simulations of ground freezing in tunneling in the presence of seepage flow connected with the ACO optimization algorithm, the optimized arrangement of the freeze pipes may lead to a substantial reduction of the freezing time and of energy costs.     

Comparison of surrogate models with different methods in groundwater remediation process

Surrogate modelling is an effective tool for reducing computational burden of simulation optimization. In this article, polynomial regression (PR), radial basis function artificial neural network (RBFANN), and kriging methods were compared for building surrogate models of a multiphase flow simulation model in a simplified nitrobenzene contaminated aquifer remediation problem. In the model accuracy analysis process, a 10-fold cross validation method was adopted to evaluate the approximation accuracy of the three surrogate models. The results demonstrated that: RBFANN surrogate model and kriging surrogate model had acceptable approximation accuracy, and further that kriging model’s approximation accuracy was slightly higher than RBFANN model. However, the PR model demonstrated unacceptably poor approximation accuracy. Therefore, the RBFANN and kriging surrogates were selected and used in the optimization process to identify the most cost-effective remediation strategy at a nitrobenzene-contaminated site. The optimal remediation costs obtained with the two surrogate-based optimization models were similar, and had similar computational burden. These two surrogate-based optimization models are efficient tools for optimal groundwater remediation strategy identification.     

地下水污染强度及渗透系数场的反演识别研究

在制定地下水污染修复方案时,污染源参数和渗透系数场是最重要的地下水数值模型参数,但前人研究多集中于单一类型参数的识别。文章中采用地下水污染物运移模型（MT3DMS）和数据同化方法（迭代局部更新集合平滑器,ILUES）构成地下水污染源识别的求解框架,并利用Karhunen-Loève展开技术实现渗透系数场的参数降维,最后通过同化水头与浓度数据实现地下水污染源强和渗透系数场的联合反演。结果表明：（1）ILUES算法能精确识别污染源参数和渗透系数场,并且具有很高的普适性;（2）精确表征渗透系数在空间上呈现出的非均质性,是预测污染物迁移路径、反演污染强度的关键;（3）ILUES算法参数影响着反演效果,综合考虑计算效率和计算精度等,可以得到算例的最佳样本集合大小（Ne=4000）和ILUES算法最佳参数组合（局部临近样本集合占比α=0.4,相对权重b=4）。但在实际工程案例中,如果对精度的要求不是过高,经验组合（α=0.1,b=1）更值得推荐。研究结果对于区域地下水资源调查、评价和管理等工作具有较强的实践意义,并可为后期地下水污染预测及地下水监测井网优化提供技术支撑。     

Optimizing groundwater development strategies by genetic algorithm: a case study for balancing the needs for agricultural irrigation and environmental protection in northern China

Gaoqing Plain is a major agriculture center of Shandong Province in northern China. Over the last 30 years, the diversion of Yellow River water for intensive irrigation in Gaoqing Plain has led to elevation of the water table and increased evaporation, and subsequently, a dramatic increase in salt content in soil and rapid degradation of crop productivity. Optimal strategies have been explored, that will balance the need to extract sufficient groundwater for irrigation (to ease the pressure on diverting Yellow River water) with the need to improve the local environment by appropriately lowering the water table. Two simulation-optimization models have been formulated and a genetic algorithm (GA) is applied to search for the optimal groundwater development strategies in Gaoqing Plain, while keeping the adverse environmental impacts in check. Compared with the trial-and-error approach of previous studies, the optimization results demonstrate that using an optimization model coupled with a GA search is both effective and efficient. The optimal solutions identified by the GA will provide Gaoqing Plain with the blueprints for developing sustainable groundwater abstraction plans to support local economic development and improve its environmental quality. Li Zheng is currently a visiting scientist in the Mathematical Modeling and Analysis Group, Los Alamos National Laboratory, New Mexico, USA.