Multiobjective optimization-based design of stabilizing piles in earth slopes

Though the technology of using stabilizing piles to prevent landsliding is not new, the design of such piles with a meaningful optimization framework has been rarely reported. In this paper, a multiobjective optimization-based framework for design of stabilizing piles is presented, in which both reinforcement effectiveness and cost efficiency could be explicitly considered. The design parameters considered in the proposed design framework are the pile parameters, including pile diameter, spacing, length, and position, and the design objectives considered are the reinforcement effectiveness and cost efficiency. The design of stabilizing piles is then implemented as a multiobjective optimization problem. In that the desire to maximize the reinforcement effectiveness and that to maximize the cost efficiency are two conflicting objectives, the output of this multiobjective optimization will be a Pareto front that depicts a trade-off between these two design objectives. With the obtained Pareto front, an informed decision regarding the design of stabilizing piles is reached. The effectiveness and significance of the proposed multiobjective optimization-based design framework for stabilizing piles are demonstrated through two illustrative examples: one is the design of stabilizing piles in a one-layer earth slope and the other the design of stabilizing piles in a two-layer earth slope. Further, parametric analyses are conducted to investigate the influences of the pile design parameters on the stability of reinforced slopes.     

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。     

System analysis in calculation of cantilever retaining walls

The paper is concerned with the solution and determination of the optimum shape of a retaining wall modelled by the co-ordinates of a set of points which belongs to a certain permissible space. An optimum design method is formulated as a non-linear multiobjective optimization problem. The following two objective functions, which are mutually conflicting and non-commensurable with each other, are considered: (a) to minimize the total weight of the wall, (b) to maximize the structure stability. A set of Pareto optimum solutions is derived numerically by adopting a logical algorithm, and a Pereto optimum solution is obtained by investigating the trade-off relationships among design objectives.     

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.     

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.     

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.     

Inverse analysis for geomaterial parameter identification using Pareto multiobjective optimization

An inverse analysis method that combines the back propagation neural network (BPNN) and vector evaluated genetic algorithm (VEGA) was proposed to identify mechanical geomaterial parameters for a more accurate prediction of deformation. The BPNN is used to replace the time‐consuming numerical calculations, thus enhancing the efficiency of the inverse analysis. The VEGA is used to find the Pareto‐optimal solutions to multiobjective functions. Unlike traditional back‐analysis methods which are based on only 1 type of field measurement and a single objective function, this proposed method can consider multiple field observations simultaneously. The proposed method was applied to the Shapingba foundation pit excavation located in Chongqing city, China. Two types of measurements are considered in the method simultaneously: the displacements in the x‐direction (north orientation) and those in the y‐direction (east orientation). Five deformation modulus parameters for artificial backfill soil, silty clay, siltstone, sandstone, and mudstone were selected as the inversion parameters. Compared with the weighted sum approach, the proposed method was demonstrated as an efficient multi‐objective optimization tool for back calculating undetermined parameters. After performing a forward‐calculation using the optimized parameters obtained by the inverse analysis, the predicted results were well consistent with the practical deformation in magnitude and trend.     

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。     

Determination of lower and upper bounds of predicted production from history-matched models

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.     

油气勘探开发项目投资决策路径的设计

研究油气勘探开发项目投资决策路径的根本目的在于规避风险,以利润极大化为原则,兼顾社会目标,正确选择投资方向,合理安排投资规模,保证石油化工企业油气资源的持续安全供应和可持续发展,提高集团的竞争力.油气勘探开发项目具有明显的实物期权特性,传统的NPV方法已经不适应此类项目的评价与决策,本文结合中石化的实际,从企业目标和社会目标2个方面着手,提出了基于实物期权的油气勘探开发项目投资决策路径,从而丰富了项目投资决策的思路和方法.     

高阻尼因子对阻尼最小二乘法效果的影响和克服

阻尼最小二乘法（包括改进的阻尼最小二乘法,下同）是目前公认的求解无约束最优化问题最优秀的算法之一,在解决实际问题中发挥了重要作用。但它并不是完美无缺的。本文提出高阻尼因子对阻尼最小二乘法效果的影响就是它们存在的,但尚未引起充分重视的问题。这个问题关系到使阻尼最小二乘法收敛缓慢甚至完全失效。本文提出设立高截止阻尼因子λh,并给出它的计算方法。它标志:超过λh的一切阻尼因子所相应的阻尼最小二乘法改正向量的步长已小于该点最速下降法的最优步长。这时应采取最速下降法探索极小点才能获得好的效果。通过设立高截止阻尼因子,将阻尼最小二乘法与最速下降法有机地结合起来,从而克服高阻尼因子对阻尼最小二乘法效果所带来的不良影响,也是对阻尼最小二乘法的进一步完善和补充。 实践证明:本文提出的设置高截止阻尼因子的理论推导和计算方法是正确的,效果明显。     

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).     

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。     

流域水资源调度多目标时变偏好决策方法及应用

传统多目标决策方法难以刻画流域水资源系统调度周期内多目标互馈关系及需求动态变化, 可能导致关键时期特定目标保障不足。为弥补该缺陷, 提出多目标时变偏好决策方法。以金沙江下游为例, 分析发电与生态目标需求的时空变异性, 构建并求解两目标随时程变化的Pareto前沿簇, 量化各时期目标间竞争强度, 基于灵敏比的非支配关系, 定量识别各调度时期决策人的目标偏好, 形成偏向度决策支持集, 建立多目标时变决策模型。结果表明: 考虑时变偏好的决策方法, 其动态累积Pareto前沿可以支配传统静态Pareto前沿; 相较于传统方法, 研究区全年增发电量0.7亿kW·h, 全年和关键生态期生态效益分别提升8.06%和2.83%, 可以在保持发电效益的同时显著优化生态效益, 并提高关键时期生态需求的保障程度。     

Ensemble-based hierarchical multi-objective production optimization of smart wells

In an earlier study, two hierarchical multi-objective methods were suggested to include short-term targets in life-cycle production optimization. However, this earlier study has two limitations: (1) the adjoint formulation is used to obtain gradient information, requiring simulator source code access and an extensive implementation effort, and (2) one of the two proposed methods relies on the Hessian matrix which is obtained by a computationally expensive method. In order to overcome the first of these limitations, we used ensemble-based optimization (EnOpt). EnOpt does not require source code access and is relatively easy to implement. To address the second limitation, we used the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to obtain an approximation of the Hessian matrix. We performed experiments in which water flood was optimized in a geologically realistic multilayer sector model. The controls were inflow control valve settings at predefined time intervals. Undiscounted net present value (NPV) and highly discounted NPV were the long-term and short-term objective functions used. We obtained an increase of approximately 14 % in the secondary objective for a decrease of only 0.2–0.5 % in the primary objective. The study demonstrates that ensemble-based hierarchical multi-objective optimization can achieve results of practical value in a computationally efficient manner.     

Waterflooding optimization with the INSIM-FT data-driven model

In a recent paper, we developed a physics-based data-driven model referred to as INSIM-FT and showed that it can be used for history matching and future reservoir performance predictions even when no prior geological model is available. The model requires no prior knowledge of petrophysical properties. In this work, we explore the possibility of using INSIM-FT in place of a reservoir simulation model when estimating the well controls that optimize water flooding performance where we use the net present value (NPV) of life-cycle production as our cost (objective) function. The well controls are either the flowing bottom-hole pressure (BHP) or total liquid rates at injectors and producers on the time intervals which represent the prescribed control steps. The optimal well controls that maximize NPV are estimated with an ensemble-based optimization algorithm using the history-matched INSIM-FT model as the forward model. We compare the optimal NPV obtained using INSIM-FT as the forward model with the estimate of the optimal NPV obtained using the correct full-scale reservoir simulation model when performing waterflooding optimization.     

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。     

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.     

A unified formulation for generalized oilfield development optimization

Oilfield development involves several key decisions, including the number, type (injection/production), location, drilling schedule, and operating control trajectories of the wells. Without considering the coupling between these decision variables, any optimization problem formulation is bound to find suboptimal solutions. This paper presents a unified formulation for oilfield development optimization that seeks to simultaneously optimize these decision variables. We show that the source/sink term of the governing multiphase flow equations includes all the above decision variables. This insight leads to a novel and unified formulation of the field development optimization problem that considers the source/sink term in reservoir simulation equations as optimization decision variables. Therefore, a single optimization problem is formulated to simultaneously search for optimal decision variables by determining the complete dynamic form of the source/sink terms. The optimization objective function is the project net present value (NPV), which involves discounted revenue from oil production, operating costs (e.g. water injection and recycling), and capital costs (e.g., cost of drilling wells). A major difficulty after formulating the generalized field development optimization problem is finding an efficient solution approach. Since the total number of cells in a reservoir model far exceeds the number of cells that are intersected by wells, the source/sink terms tend to be sparse. In fact, the drilling cost in the NPV objective function serves as a sparsity-promoting penalty to minimize the number of wells while maximizing the NPV. Inspired by this insight, we solve the optimization problem using an efficient gradient-based method based on recent algorithmic developments in sparse reconstruction literature. The gradients of the NPV function with respect to the source/sink terms is readily computed using well-established adjoint methods. Numerical experiments are presented to evaluate the feasibility and performance of the generalized field development formulation for simultaneous optimization of the number, location, type, controls, and drilling schedule of the wells.