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...     

梯级水电站多目标发电优化调度

以发电量和保证出力为目标建立梯级水电站的多目标发电优化调度模型,对三峡梯级中长期发电优化调度进行研究。针对传统方法求解多目标优化问题的局限,提出一种强度Pareto差分进化算法(Strength Pareto Differential Evolution,SPDE)用于求解梯级水电站的多目标发电优化调度问题。SPDE以差分进化算法(Differential Evolution,DE)为基础,采用SPEA2的适应度评价方法,并根据多目标优化的特点对DE的进化算子进行修正。同时,提出一种自适应柯西变异策略(Adaptive Cauchy Mutation,ACM)用于克服算法的早熟收敛问题。三峡梯级水电站实例研究结果表明,SPDE可同时考虑两个目标并有效处理复杂约束条件,一次运行即可得到一组在各目标分布均匀、分布范围广的非劣调度方案供决策者评价优选。     

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。     

地下水污染监测网多目标优化设计模型及进化求解

采用模拟-优化方法建立了一个用于地下水污染监测网设计的多目标优化模型,该模型包括最小化监测费用、污染物质量评估误差、污染羽一阶矩评估误差和二阶矩评估误差等4个目标函数,以充分揭示减少地下水污染监测费用与提高污染监测精度之间的权衡关系.将改进小生境Pareto遗传算法与地下水流模拟程序和污染物运移模拟程序相耦合用于求解地下水污染监测网多目标设计模型.算例研究表明,采用进化算法求解监测网的多目标模型,能真实地反映各个目标函数间的权衡关系,并且不用考虑传统方法中惩罚因子的影响.与单目标优化模型相比,多目标优化模型可在较短的时间内得到优化问题的一系列Pareto权衡解,以利于相应条件下决策者选择最为经济有效的地下水污染监测方案.     

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。     

参数空间变异性下地下水污染监测网多目标优化机制研究

基于野外实际含水层参数存在空间变异性的客观事实,研发概率Pareto遗传算法(Probabilistic Pareto genetic algorithm,PPGA),用于求解考虑含水层参数空间变异性下地下水污染监测网多目标优化设计问题。PPGA在ε-改进非劣支配遗传算法(epsilon-dominance non-dominated sorted genetic algorithm II,ε-NSGAII)的基础上通过添加概率择优排序和概率拥挤度技术,寻求考虑参数空间变异条件下地下水污染监测网模拟—优化耦合模型的Pareto最优解。将优化结果与蒙特卡洛(Monte Carlo,MC)模拟分析结果进行对比,验证优化结果的可靠性。算例求解结果表明:在求解考虑参数空间变异性条件下地下水污染监测网多目标优化设计问题时,PPGA优化所得Pareto最优解变异性小,可靠性高,可为决策者提供一系列稳定可靠的监测方案。     

大地电磁实码广义遗传反演算法研究

大地电磁反演问题通常表述为目标函数最优化,难点是多参数、非线性和不适定性,局部和全局方法都不能实现快速全局优化[4].针对局部线性方法易使解陷入局部极值,严重依赖初始模型,而传统的遗传算法在优化应用中存在局部搜索能力弱、早熟收敛等问题.这里引进一种求解一维大地电磁测深反演问题的实数编码广义遗传算法.该算法利用拟网格法初始种群和综合交叉策略,克服了早熟收敛现象,从而提高了遗传寻优的效率.理论模型反演与其它方法比较,结果说明遗传算法具有不依赖初始模型,不容易陷入局部极小,多点多路径概率搜索,以及隐合并行性等优点.     

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。     

Pareto强度指标遗传算法求解地下水模拟-优化模型

针对地下水模拟-优化模型约束优化的特点,本文结合最小代数代沟模型和Pareto强度指标概念,引入一种求解地下水模拟-优化模型的新型实数编码遗传算法,该算法将罚函数法求解约束优化问题的目标函数和违反约束条件的程度函数的权组合方式改为向量组合形式,从而将约束优化问题转化为两目标优化问题进行求解。通过经典地下水算例与其他优化方法的比较分析表明了新算法的可靠性、通用性和稳健性。     

基于多目标优化的大都市土地整治潜力区划决策研究——以上海市青浦区为例

以促进耕地集中连片为单一目标的传统土地整治区划工作,已无法满足国土空间生态修复与全域土地整治提出的可持续发展新要求。本文以上海市青浦区土地整备引导区为研究区域,基于多目标优化理论与Pareto最优算法,考虑空间结构、生态价值、环境影响、农业生产潜力等多维度目标,建立基于多目标优化的大都市土地整治潜力区划决策框架。基于权衡视角下的土地整治潜力区划方案显示,青浦区土地整备引导区内总面积近2922公顷(6397个图斑)的区域划入土地整治潜力极高区,占引导区总面积的43.72%。本文提出的多目标最优的大都市土地整治潜力区划决策方法,能较好地处理多目标权衡下的定量求解问题,可对我国区县级重大土地整治项目的规划部署提供技术支持和借鉴。     

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.     

A least squares approach for efficient and reliable short-term versus long-term optimization

The uncertainties related to long-term forecasts of oil prices impose significant financial risk on ventures of oil production. To minimize risk, oil companies are inclined to maximize profit over short-term horizons ranging from months to a few years. In contrast, conventional production optimization maximizes long-term profits over horizons that span more than a decade. To address this challenge, the oil literature has introduced short-term versus long-term optimization. Ideally, this problem is solved by a posteriori multi-objective optimization methods that generate an approximation to the Pareto front of optimal short-term and long-term trade-offs. However, such methods rely on a large number of reservoir simulations and scale poorly with the number of objectives subject to optimization. Consequently, the large-scale nature of production optimization severely limits applications to real-life scenarios. More practical alternatives include ad hoc hierarchical switching schemes. As a drawback, such methods lack robustness due to unclear convergence properties and do not naturally generalize to cases of more than two objectives. Also, as this paper shows, the hierarchical formulation may skew the balance between the objectives, leaving an unfulfilled potential to increase profits. To promote efficient and reliable short-term versus long-term optimization, this paper introduces a natural way to characterize desirable Pareto points and proposes a novel least squares (LS) method. Unlike hierarchical approaches, the method is guaranteed to converge to a Pareto optimal point. Also, the LS method is designed to properly balance multiple objectives, independently of Pareto front’s shape. As such, the method poses a practical alternative to a posteriori methods in situations where the frontier is intractable to generate.     

Pareto optimality solution of the multi-objective photogrammetric resection-intersection problem

Reconstruction of architectural structures from photographs has recently experienced intensive efforts in computer vision research. This is achieved through the solution of nonlinear least squares (NLS) problems to obtain accurate structure and motion estimates. In Photogrammetry, NLS contribute to the determination of the 3-dimensional (3D) terrain models from the images taken from photographs. The traditional NLS approach for solving the resection-intersection problem based on implicit formulation on the one hand suffers from the lack of provision by which the involved variables can be weighted. On the other hand, incorporation of explicit formulation expresses the objectives to be minimized in different forms, thus resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may conflict in a Pareto sense, namely, a small change in the parameters results in the increase of one objective and a decrease of the other, as is often the case in multi-objective problems. Such is often the case with error-in-all-variable (EIV) models, e.g., in the resection-intersection problem where such change in the parameters could be caused by errors in both image and reference coordinates. This study proposes the Pareto optimal approach as a possible improvement to the solution of the resection-intersection problem, where it provides simultaneous estimation of the coordinates and orientation parameters of the cameras in a two or multistation camera system on the basis of a properly weighted multi-objective function. This objective represents the weighted sum of the square of the direct explicit differences of the measured and computed ground as well as the image coordinates. The effectiveness of the proposed method is demonstrated by two camera calibration problems, where the internal and external orientation parameters are estimated on the basis of the collinearity equations, employing the data of a Manhattan-type test field as well as the data of an outdoor, real case experiment. In addition, an architectural structural reconstruction of the Merton college court in Oxford (UK) via estimation of camera matrices is also presented. Although these two problems are different, where the first case considers the error reduction of the image and spatial coordinates, while the second case considers the precision of the space coordinates, the Pareto optimality can handle both problems in a general and flexible way.     

Optimal design of groundwater remediation systems using a multi-objective fast harmony search algorithm

A new multi-objective optimization methodology is developed, whereby a multi-objective fast harmony search (MOFHS) is coupled with a groundwater flow and transport model to search for optimal design of groundwater remediation systems under general hydrogeological conditions. The MOFHS incorporates the niche technique into the previously improved fast harmony search and is enhanced by adding the Pareto solution set filter and an elite individual preservation strategy to guarantee uniformity and integrity of the Pareto front of multi-objective optimization problems. Also, the operation library of individual fitness is introduced to improve calculation speed. Moreover, the MOFHS is coupled with the commonly used flow and transport codes MODFLOW and MT3DMS, to search for optimal design of pump-and-treat systems, aiming at minimization of the remediation cost and minimization of the mass remaining in aquifers. Compared with three existing multi-objective optimization methods, including the improved niched Pareto genetic algorithm (INPGA), the non-dominated sorting genetic algorithm II (NSGAII), and the multi-objective harmony search (MOHS), the proposed methodology then demonstrated its applicability and efficiency through a two-dimensional hypothetical test problem and a three-dimensional field problem in Indiana (USA).     

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。     

Pareto’s law and sample size: a case study of China’s urban system 1984–2008

While Pareto’s law has been widely supported by empirical evidence in urban studies, past studies have focused on finding best fits for city rank-size distribution. A main concern with Pareto’s law is the truncation of sample selection, for which few studies have examined it directly. This study tests three existing threshold methods (number threshold, size threshold, and urban population percentage threshold) using China’s city system as a case study. In addition, this study proposes a new method based upon the percentage threshold of the total number of cities. A systematic analysis is applied to examine the relationship between Pareto exponent and sample size using different threshold methods. The results show that Pareto exponent is sensitive to sample size and the truncation point. Including only large cities is problematic because a slight change in the truncation point will yield quite different results of Pareto exponent. In addition, the new method, the percentage threshold of the total number of cities method, presents an advantage over previous methods, in that this method yields a consistent set of results over a wide range of thresholds. Finally, when using this new method with China’s city system, the Pareto exponent presents a turning point in 1996, representing China’s transition from a planned economy to a more market oriented economy during that period.     

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.