A combinatorial optimization scheme for parameter structure identification in ground water modeling

This research develops a methodology for parameter structure identification in ground water modeling. For a given set of observations, parameter structure identification seeks to identify the parameter dimension, its corresponding parameter pattern and values. Voronoi tessellation is used to parameterize the unknown distributed parameter into a number of zones. Accordingly, the parameter structure identification problem is equivalent to finding the number and locations as well as the values of the basis points associated with the Voronoi tessellation. A genetic algorithm (GA) is allied with a grid search method and a quasi-Newton algorithm to solve the inverse problem. GA is first used to search for the near-optimal parameter pattern and values. Next, a grid search method and a quasi-Newton algorithm iteratively improve the GA's estimates. Sensitivities of state variables to parameters are calculated by the sensitivity-equation method. MODFLOW and MT3DMS are employed to solve the coupled flow and transport model as well as the derived sensitivity equations. The optimal parameter dimension is determined using criteria based on parameter uncertainty and parameter structure discrimination. Numerical experiments are conducted to demonstrate the proposed methodology, in which the true transmissivity field is characterized by either a continuous distribution or a distribution that can be characterized by zones. We conclude that the optimized transmissivity zones capture the trend and distribution of the true transmissivity field.     

An integrated optimization algorithm for parameter structure identification in groundwater modeling

The inverse problem of parameter structure identification in a distributed parameter system remains challenging. Identifying a more complex parameter structure requires more data. There is also the problem of over-parameterization. In this study, we propose a modified Tabu search for parameter structure identification. We embed an adjoint state procedure in the search process to improve the efficiency of the Tabu search. We use Voronoi tessellation for automatic parameterization to reduce the dimension of the distributed parameter. Additionally, a coarse-fine grid technique is applied to further improve the effectiveness and efficiency of the proposed methodology. To avoid over-parameterization, at each level of parameter complexity we calculate the residual error for parameter fitting, the parameter uncertainty error and a modified Akaike Information Criterion. To demonstrate the proposed methodology, we conduct numerical experiments with synthetic data that simulate both discrete hydraulic conductivity zones and a continuous hydraulic conductivity distribution. Our results indicate that the Tabu search allied with the adjoint state method significantly improves computational efficiency and effectiveness in solving the inverse problem of parameter structure identification.     

An efficient approach for successively perturbed groundwater models

Global optimization methods such as simulated annealing, genetic algorithms and tabu search are being increasingly used to solve groundwater remediation design and parameter identification problems. While these methods enjoy some unique advantages over traditional gradient based methods, they typically require thousands to tens of thousands of forward simulation runs before reaching optimal or near-optimal solutions. Thus, one severe limitation associated with these global optimization methods is very long computation time. To mitigate this limitation, this paper presents a new approach for obtaining, repeatedly and efficiently, the solutions of a linear forward simulation model subject to successive perturbations. The proposed approach takes advantage of the fact that successive forward simulation runs, as required by a global optimization procedure, usually involve only slight changes in the coefficient matrices of the resultant linear equations. As a result, the new solution to a system of linear equations perturbed by the changes in aquifer properties and/or sinks/sources can be obtained as the sum of a non-perturbed base solution and the solution to the perturbed portion of the linear equations. The computational efficiency of the proposed approach arises from the fact that the perturbed solution can be derived directly without solving the linear equations again. A two-dimensional test problem with 20 by 30 nodes demonstrates that the proposed approach is much more efficient than repeatedly running the simulation model, by more than 15 times after a fixed number of model evaluations. The ratio of speedup increases with the number of model evaluations and also the size of simulation model. The main limitation of the proposed approach is the large amount of computer memory required to store the inverse matrix. Effective ways for limiting the storage requirement are briefly discussed.     

Multiobjective heuristic approaches to seismic design of steel frames with standard sections

Seismic design problem of a steel moment‐resisting frame is formulated as a multiobjective programming problem. The total structural (material) volume and the plastic dissipated energy at the collapse state against severe seismic motions are considered as performance measures. Geometrically nonlinear inelastic time‐history analysis is carried out against recorded ground motions that are incrementally scaled to reach the predefined collapse state. The frame members are chosen from the lists of the available standard sections. Simulated annealing (SA) and tabu search (TS), which are categorized as single‐point‐search heuristics, are applied to the multiobjective optimization problem. It is shown in the numerical examples that the frames that collapse with uniform interstorey drift ratios against various levels of ground motions can be obtained as a set of Pareto optimal solutions. Copyright © 2007 John Wiley & Sons, Ltd.     

Simultaneous determination of aquifer parameters and zone structures with fuzzy c-means clustering and meta-heuristic harmony search algorithm

This study proposes an inverse solution algorithm through which both the aquifer parameters and the zone structure of these parameters can be determined based on a given set of observations on piezometric heads. In the zone structure identification problem fuzzy c-means (FCM) clustering method is used. The association of the zone structure with the transmissivity distribution is accomplished through an optimization model. The meta-heuristic harmony search (HS) algorithm, which is conceptualized using the musical process of searching for a perfect state of harmony, is used as an optimization technique. The optimum parameter zone structure is identified based on three criteria which are the residual error, parameter uncertainty, and structure discrimination. A numerical example given in the literature is solved to demonstrate the performance of the proposed algorithm. Also, a sensitivity analysis is performed to test the performance of the HS algorithm for different sets of solution parameters. Results indicate that the proposed solution algorithm is an effective way in the simultaneous identification of aquifer parameters and their corresponding zone structures.     

Improving the efficiency of ant algorithms using adaptive refinement: Application to storm water network design

The ant algorithm is a new evolutionary optimization method proposed for the solution of discrete combinatorial optimization problems. Many engineering optimization problems involve decision variables of continuous nature. Application of the ant algorithm to the optimization of these continuous problems requires discretization of the continuous search space, thereby reducing the underlying continuous problem to a discrete optimization problem. The level of discretization of the continuous search space, however, could present some problems. Generally, coarse discretization of the continuous design variables could adversely affect the quality of the final solution while finer discretization would enlarge the scale of the problem leading to higher computation cost and, occasionally, to low quality solutions. An adaptive refinement procedure is introduced in this paper as a remedy for the problem just outlined. The method is based on the idea of limiting the originally wide search space to a smaller one once a locally converged solution is obtained. The smaller search space is designed to contain the locally optimum solution at its center. The resulting search space is discretized and a completely new search is conducted to find a better solution. The procedure is continued until no improvement can be made by further refinement. The method is applied to a benchmark problem in storm water network design discipline and the results are compared with those of existing methods. The method is shown to be very effective and efficient regarding the optimality of the solution, and the convergence characteristics of the resulting ant algorithm. Furthermore, the method proves itself capable of finding an optimal, or near-optimal solution, independent of the discretization level and the size of the colony used.     

Simulation/optimization modeling for robust pumping strategy design

A new simulation/optimization modeling approach is presented for addressing uncertain knowledge of aquifer parameters. The Robustness Enhancing Optimizer (REO) couples genetic algorithm and tabu search as optimizers and incorporates aquifer parameter sensitivity analysis to guide multiple-realization optimization. The REO maximizes strategy robustness for a pumping strategy that is optimal for a primary objective function (OF), such as cost. The more robust a strategy, the more likely it is to achieve management goals in the field, even if the physical system differs from the model. The REO is applied to trinitrotoluene and Royal Demolition Explosive plumes at Umatilla Chemical Depot in Oregon to develop robust least cost strategies. The REO efficiently develops robust pumping strategies while maintaining the optimal value of the primary OF-differing from the common situation in which a primary OF value degrades as strategy reliability increases. The REO is especially valuable where data to develop realistic probability density functions (PDFs) or statistically derived realizations are unavailable. Because they require much less field data, REO-developed strategies might not achieve as high a mathematical reliability as strategies developed using many realizations based upon real aquifer parameter PDFs. REO-developed strategies might or might not yield a better OF value in the field.     

Partially constrained ant colony optimization algorithm for the solution of constrained optimization problems: Application to storm water network design

This paper exploits the unique feature of the Ant Colony Optimization Algorithm (ACOA), namely incremental solution building mechanism, to develop partially constraint ACO algorithms for the solution of optimization problems with explicit constraints. The method is based on the provision of a tabu list for each ant at each decision point of the problem so that some constraints of the problem are satisfied. The application of the method to the problem of storm water network design is formulated and presented. The network nodes are considered as the decision points and the nodal elevations of the network are used as the decision variables of the optimization problem. Two partially constrained ACO algorithms are formulated and applied to a benchmark example of storm water network design and the results are compared with those of the original unconstrained algorithm and existing methods. In the first algorithm the positive slope constraints are satisfied explicitly and the rest are satisfied by using the penalty method while in the second one the satisfaction of constraints regarding the maximum ratio of flow depth to the diameter are also achieved explicitly via the tabu list. The method is shown to be very effective and efficient in locating the optimal solutions and in terms of the convergence characteristics of the resulting ACO algorithms. The proposed algorithms are also shown to be relatively insensitive to the initial colony used compared to the original algorithm. Furthermore, the method proves itself capable of finding an optimal or near-optimal solution, independent of the discretisation level and the size of the colony used.     

Reflection-constrained 2D and 3D non-hyperbolic moveout analysis using particle swarm optimization

The objective of moveout parameter inversion is to derive sets of parameter models that can be used for moveout correction and stacking at each common midpoint location to increase the signal-to-noise ratio of the data and to provide insights into the kinematic characteristics of the data amongst other things. In this paper, we introduce a data-driven user-constrained optimization scheme that utilizes manual picks at a point on each reflector within a common midpoint gather to constrain the search space in which an optimization procedure can search for the optimal parameter sets at each reflection. The picks are used to create boundary curves which can be derived approximately via an optimization technique or analytically via the derivation of an analytical bounds function. In this paper, we derive analytical forms of bounds functions for four different moveout cases. These are normal moveout, non-hyperbolic moveout, azimuthally dependent normal moveout and azimuthally dependent non-hyperbolic moveout. The optimization procedure utilized here to search for the optimal moveout parameters is the particle swarm optimization technique. However, any metaheuristic optimization procedure could be modified to account for the constraints introduced in this paper. The technique is tested on two-layer synthetic models based on three of the four moveout cases discussed in this paper. It is also applied to an elastic forward modelled synthetic model called the HESS model, and finally to real 2D land data from Alaska. The resultant stacks show a marked improvement in the signal-to-noise ratio compared to the raw stacks. The results for the normal moveout, non-hyperbolic moveout and azimuthally dependent normal moveout tests suggest that the method is viable for said models. Results demonstrate that our method offers potential as an alternative to conventional parameter picking and inversion schemes, particularly for some cases where the number of parameters in the moveout approximation is 2 or greater.     

基于多目标差分进化算法的结构物理参数辨识

优化算法在用于结构的物理参数辨识时,测量数据的不完备和噪声严重影响了参数的辨识精度.针对这一问题,为得到理想的辨识精度,将时程响应数据和频率数据定义为多目标函数,并利用多目标差分进化算法(DEMO)进行优化求解.在数值模拟中,利用10层剪切型框架结构和31个单元的桁架桥结构作为算例.计算结果表明,该多目标函数和DEMO...     

A parallel evolutionary strategy based simulation–optimization approach for solving groundwater source identification problems

Groundwater characterization involves the resolution of unknown system characteristics from observation data, and is often classified as an inverse problem. Inverse problems are difficult to solve due to natural ill-posedness and computational intractability. Here we adopt the use of a simulation–optimization approach that couples a numerical pollutant-transport simulation model with evolutionary search algorithms for solution of the inverse problem. In this approach, the numerical transport model is solved iteratively during the evolutionary search. This process can be computationally intensive since several hundreds to thousands of forward model evaluations are typically required for solution. Given the potential computational intractability of such a simulation–optimization approach, parallel computation is employed to ease and enable the solution of such problems. In this paper, several variations of a groundwater source identification problem is examined in terms of solution quality and computational performance. The computational experiments were performed on the TeraGrid cluster available at the National Center for Supercomputing Applications. The results demonstrate the performance of the parallel simulation–optimization approach in terms of solution quality and computational performance.     

Application of the gravity search algorithm to multi-reservoir operation optimization

Complexities in river discharge, variable rainfall regime, and drought severity merit the use of advanced optimization tools in multi-reservoir operation. The gravity search algorithm (GSA) is an evolutionary optimization algorithm based on the law of gravity and mass interactions. This paper explores the GSA's efficacy for solving benchmark functions, single reservoir, and four-reservoir operation optimization problems. The GSA's solutions are compared with those of the well-known genetic algorithm (GA) in three optimization problems. The results show that the GSA's results are closer to the optimal solutions than the GA's results in minimizing the benchmark functions. The average values of the objective function equal 1.218 and 1.746 with the GSA and GA, respectively, in solving the single-reservoir hydropower operation problem. The global solution equals 1.213 for this same problem. The GSA converged to 99.97% of the global solution in its average-performing history, while the GA converged to 97% of the global solution of the four-reservoir problem. Requiring fewer parameters for algorithmic implementation and reaching the optimal solution in fewer number of functional evaluations are additional advantages of the GSA over the GA. The results of the three optimization problems demonstrate a superior performance of the GSA for optimizing general mathematical problems and the operation of reservoir systems.     

Optimal pumping locations of skimming wells

Abstract

A real-life problem involving pumping of groundwater from a series of existing wells along a river flood plain underlain with geologically saline water is examined within a conceptual framework. Unplanned pumping results in upconing of saline water. Therefore, it is necessary to determine optimal locations of fixed capacity pumping wells in space and time from a set of pre-selected candidate wells that minimize total salinity concentration in space and time. The nonlinear, non-convex, combinatorial problem involving zero—one decision variables is solved in a simulation—optimization (S/O) framework. Optimization is accomplished by using simulated annealing (SA)—a search algorithm. The computational burden is primarily managed by replacing the numerical model with a surrogate simulator—artificial neural network (ANN). The computational burden is further reduced through intuitive algorithmic guidance. The model results suggest that the skimming wells must be operated from optimal locations such that they are staggered in space and time to obtain least saline water.     

An Elitist Multiobjective Tabu Search for Optimal Design of Groundwater Remediation Systems

This study presents a new multiobjective evolutionary algorithm (MOEA), the elitist multiobjective tabu search (EMOTS), and incorporates it with MODFLOW/MT3DMS to develop a groundwater simulation‐optimization (SO) framework based on modular design for optimal design of groundwater remediation systems using pump‐and‐treat (PAT) technique. The most notable improvement of EMOTS over the original multiple objective tabu search (MOTS) lies in the elitist strategy, selection strategy, and neighborhood move rule. The elitist strategy is to maintain all nondominated solutions within later search process for better converging to the true Pareto front. The elitism‐based selection operator is modified to choose two most remote solutions from current candidate list as seed solutions to increase the diversity of searching space. Moreover, neighborhood solutions are uniformly generated using the Latin hypercube sampling (LHS) in the bounded neighborhood space around each seed solution. To demonstrate the performance of the EMOTS, we consider a synthetic groundwater remediation example. Problem formulations consist of two objective functions with continuous decision variables of pumping rates while meeting water quality requirements. Especially, sensitivity analysis is evaluated through the synthetic case for determination of optimal combination of the heuristic parameters. Furthermore, the EMOTS is successfully applied to evaluate remediation options at the field site of the Massachusetts Military Reservation (MMR) in Cape Cod, Massachusetts. With both the hypothetical and the large‐scale field remediation sites, the EMOTS‐based SO framework is demonstrated to outperform the original MOTS in achieving the performance metrics of optimality and diversity of nondominated frontiers with desirable stability and robustness.     

波动方程反演的全局优化方法研究

复杂介质波动方程反演是地球物理研究中的重要问题,通常表述为特定目标函数最优化,难点是多参数、非线性和不适定性.局部和全局优化方法都不能实现快速全局优化.本文概述了地震波勘探反演问题的理论基础和研究进展,阐述了反演中优化问题的解决方法和面临的困难,并提出了一种确定性全局优化的新方法.通过在优化参数空间识别并划分局部优化解及其附近区域,只需有限次参数空间划分过程就能发现所有局部解（集合）;基于复杂目标函数多尺度结构分析,提出多尺度参数空间分区优化方法的研究方向.该方法收敛速度快,优化结果不依赖初始解的选取,是对非线性全局优化问题的一个新探索.     

Seismic Event Location: Nonlinear Inversion Using a Neighbourhood Algorithm

—?A recently developed direct search method for inversion, known as a neighbourhood algorithm (NA), is applied to the hypocentre location problem. Like some previous methods the algorithm uses randomised, or stochastic, sampling of a four-dimensional hypocentral parameter space, to search for solutions with acceptable data fit. Considerable flexibility is allowed in the choice of misfit measure.¶At each stage the hypocentral parameter space is partitioned into a series of convex polygons called Voronoi cells. Each cell surrounds a previously generated hypocentre for which the fit to the data has been determined. As the algorithm proceeds new hypocentres are randomly generated in the neighbourhood of those hypocentres with smaller data misfit. In this way all previous hypocentres guide the search, and the more promising regions of parameter space are preferentially sampled.¶The NA procedure makes use of just two tuning parameters. It is possible to choose their values so that the behaviour of the algorithm is similar to that of a contracting irregular grid in 4-D. This is the feature of the algorithm that we exploit for hypocentre location. In experiments with different events and data sources, the NA approach is able to achieve comparable or better levels of data fit than a range of alternative methods; linearised least-squares, genetic algorithms, simulated annealing and a contracting grid scheme. Moreover, convergence was achieved with a substantially reduced number of travel-time/slowness calculations compared with other nonlinear inversion techniques. Even when initial parameter bounds are very loose, the NA procedure produced robust convergence with acceptable levels of data fit.     

An evaluation of a class of practical optimization techniques for structural dynamics applications

This paper evaluates a class of practical optimization techniques for parameter identification of realistic structural dynamic systems. The techniques involve quasi-Newton methods together with an efficient procedure for estimating complicated error functions. The optimization procedures are verified through their application to several representative examples, including finite-element models of realistic structural systems. Extensive numerical and graphical results demonstrate the effects of various optimization algorithm parameters on the rate of convergence of the objective function, the parameter vector error norm and the gradient norm. Guidelines are presented as an aid for addressing several significant issues in the practical application of structural dynamics optimization procedures, such as sensitivity problems, uniqueness, initial value definition for the parameter vector, convergence rates, constraints, the effect of alternative cost function definitions, accuracy of alternative gradient evaluation procedures, alternative procedures for estimating the inverse of the Hessian matrix and the use of a quadratic approximation of the objective function.     

Placement of sensors/actuators on civil structures using genetic algorithms

The optimal design and placement of controllers at discrete locations is an important problem that will have impact on the control of civil engineering structures. Though algorithms exist for the placement of sensor/actuator systems on continuous structures, the placement of controllers on discrete civil structures is a very difficult problem. Because of the nature of civil structures, it is not possible to place sensors and actuators at any location in the structure. This usually creates a non‐linear constrained mixed integer problem that can be very difficult to solve. Using genetic algorithms in conjunction with gradient‐based optimization techniques will allow for the simultaneous placement and design of an effective structural control system. The introduction of algorithms based on genetic search procedures should increase the rate of convergence and thus reduce the computational time for solving the difficult control problem. The newly proposed method of simultaneously placing sensors/actuators will be compared to a commonly used method of sensors/actuators placement where sensors/actuators are placed sequentially. The savings in terms of energy requirements and cost will be discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Two-stage decision-making under uncertainty and stochasticity: Bayesian Programming

This paper develops a new method for decision-making under uncertainty. The method, Bayesian Programming (BP), addresses a class of two-stage decision problems with features that are common in environmental and water resources. BP is applicable to two-stage combinatorial problems characterized by uncertainty in unobservable parameters, only some of which is resolved upon observation of the outcome of the first-stage decision. The framework also naturally accommodates stochastic behavior, which has the effect of impeding uncertainty resolution. With the incorporation of systematic methods for decision search and Monte Carlo methods for Bayesian analysis, BP addresses limitations of other decision-analytic approaches for this class of problems, including conventional decision tree analysis and stochastic programming. The methodology is demonstrated with an illustrative problem of water quality pollution control. Its effectiveness for this problem is compared to alternative approaches, including a single-stage model in which expected costs are minimized and a deterministic model in which uncertain parameters are replaced by their mean values. A new term, the expected value of including uncertainty resolution, or EVIUR, is introduced and evaluated for the illustrative problem. It is a measure of the worth of incorporating the experimental value of decisions into an optimal decision-making framework. For the illustrative problem, the two-stage adaptive management framework extracted up to approximately 50% of the gains of perfect information. The strength and limitations of the method are discussed and conclusions are presented.