Efficient Multi Objective Surrogate Optimization Of Computationally Expensive Models With Application To Watershed Model Calibration
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| Author | : Taimoor Akhtar |
| Publisher | : |
| Total Pages | : 520 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
This thesis introduces efficient algorithms for multi-objective optimization of computationally expensive simulation optimization problems. Implementation of efficient algorithms and their advantage of use for calibration of complex and deterministic watershed simulation models is also analyzed. GOMORS, a novel parallel multi-objective optimization algorithm involving surrogate modeling via Radial Basis Function approximation, is introduced in Chapter 2. GOMORS is an iterative search algorithm where a multiobjective search utilizing evolution, local search, multi method search and non-dominated sorting is done on the surrogate function to select numerous points for simultaneous expensive evaluations in each algorithm iteration. A novel procedure, "multi-rule selection", is introduced that simultaneously selects evaluation points (which can be computed in parallel) within an algorithm iteration through different metrics. Results are compared against ParEGO and the widely used NSGA-II on numerous test problems including a hypothetical groundwater PDE problem. The results indicate that GOMORS outperforms ParEGO and NSGA-II within a budget of 400 function evaluations. The superiority of performance of GOMORS is more evident for problems involving a large number of decision variables (15-25 decision variables). The second contribution (Chapter 3) to the thesis is a comparative analysis of algorithms for multi-objective calibration of complex watershed models. Since complex watershed models can be computationally expensive, we analyze and compare performance of various algorithms within a limited evaluation budget of 1000 evaluations. The primary aim of the analysis is to assess effectiveness of algorithms in identifying "meaningful trade-offs" for multi-objective watershed model calibration problems within a limited evaluation budget. A new metric, referred as the Distributed Cardinality index, is introduced for quantifying the relative effectiveness of different algorithms in identifying "meaningful tradeoffs". Our results indicate that GOMORS (the algorithm introduced in Chapter 2), outperforms various other algorithms, including ParEGO and AMALGAM, in computing good and meaningful trade-off solutions, within a limited simulation evaluation budget. The third and final contribution (see Chapter 4) to the thesis is MOPLS, a Multi-Objective Parallel Local Stochastic Search algorithm for efficient optimization of computationally expensive problems. MOPLS is an iterative algorithm which incorporates simultaneous local candidate search on response surface models within a synchronous parallel framework to select numerous evaluation points in each iteration. MOPLS was applied to various test problems and multi-objective watershed calibration problems with 4, 8 and 16 synchronous parallel processes and results were compared against GOMORS, ParEGO and AMALGAM. The results indicate that within a limited evaluation budget, MOPLS outperforms ParEGO and AMALGAM for computationally expensive watershed calibration problems, when comparison is made in function evaluations. When parallel speedup is taken into consideration and comparison is made in wall clock time, the results indicate that overall performance of MOPLS is better than GOMORS, ParEGO and AMALGAM.
| Author | : Ying Wan |
| Publisher | : |
| Total Pages | : 216 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
This research focuses on the development and implementation of e cient optimization algorithms that can solve a range of computationally expensive groundwater simulationoptimization problems. Because groundwater model evaluations are expensive, it is important to find accurate solutions with relatively few function evaluations. As a result, all the algorithms tested in this research are evaluated on a limited computation budget. The first contribution to the thesis is a comparative evaluation of a novel multi-objective optimization algorithm, GOMORS, to three other popular multi-objective optimization methods on applications to groundwater management problems within a limited number of objective function evaluations. GOMORS involves surrogate modeling via Radial Basis Function approximation and evolutionary strategies. The primary aim of the analysis is to assess the effectiveness of multi-objective algorithms in groundwater remediation management through multi-objective optimization within a limited evaluation budget. Three sets of dual objectives are evaluated. The objectives include minimization of cost, pollution mass remaining/pollution concentration, and cleanup time. Our results indicate that the overall performance of GOMORS is better than three other algorithms, AMALGAM, BORG and NSGA-II, in identifying good trade-off solutions. Furthermore, GOMORS incorporates modest parallelization to make it even more e cient. The next contribution is application of SO-MI, a surrogate model-based algorithm designed for computationally expensive nonlinear and multimodal mixed-integer black-box optimization problems, to solve groundwater remediation design problems (NL-MIP). SO-MI utilizes surrogate models to guide the search thus save the expensive function evaluation budget, and is able to find accurate solutions with relatively few function evaluations. We present numerical results to show the effectiveness and e ciency of SO-MI in comparison to Genetic Algorithm and NOMAD, which are two popular mixed-integer optimization algorithms. The results indicate that SO-MI is statistically better than GA and NOMAD in both study cases. Chapter 4 describes DYCORS-PEST, a novel method developed for high dimensional, computationally expensive, multimodal calibration problems when the computation budget is limited. This method integrates a local optimizer PEST into a global optimization framework DYCORS. The novelty of DYCORS-PEST is that it uses a memetic approach to improve the accuracy of the solution in which DYCORS selects the point at which the search switches to use of the local method PEST and when it switches back to the global phase. Since PEST is a very e cient and widely used local search algorithm for groundwater model calibration, incorporating PEST into DYCORS-PEST is a good enhancement for PEST and easy for PEST users to learn. DYCORS-PEST achieves the goal of solving the computationally expensive black-box problem by forming a response surface of the expensive function, thus reducing the number of required expensive function evaluations for finding accurate solutions. The key feature of the global search method in DYCORS-PEST is that the number of decision variables being perturbed is dynamically adjusted in each iteration in order to be more effective for higher dimensional problems. Application of DYCORS-PEST to two 28parameter groundwater calibration problems indicate this new method outperforms PEST by a large margin for high dimensional, computationally expensive, groundwater calibration problems.
| Author | : Xuesong Zhang |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
This study focuses on developing and evaluating efficient and effective parameter calibration and uncertainty methods for hydrologic modeling. Five single objective optimization algorithms and six multi-objective optimization algorithms were tested for automatic parameter calibration of the SWAT model. A new multi-objective optimization method (Multi-objective Particle Swarm and Optimization & Genetic Algorithms) that combines the strengths of different optimization algorithms was proposed. Based on the evaluation of the performances of different algorithms on three test cases, the new method consistently performed better than or close to the other algorithms. In order to save efforts of running the computationally intensive SWAT model, support vector machine (SVM) was used as a surrogate to approximate the behavior of SWAT. It was illustrated that combining SVM with Particle Swarm and Optimization can save efforts for parameter calibration of SWAT. Further, SVM was used as a surrogate to implement parameter uncertainty analysis fo SWAT. The results show that SVM helped save more than 50% of runs of the computationally intensive SWAT model The effect of model structure on the uncertainty estimation of streamflow simulation was examined through applying SWAT and Neural Network models. The 95% uncertainty intervals estimated by SWAT only include 20% of the observed data, while Neural Networks include more than 70%. This indicates the model structure is an important source of uncertainty of hydrologic modeling and needs to be evaluated carefully. Further exploitation of the effect of different treatments of the uncertainties of model structures on hydrologic modeling was conducted through applying four types of Bayesian Neural Networks. By considering uncertainty associated with model structure, the Bayesian Neural Networks can provide more reasonable quantification of the uncertainty of streamflow simulation. This study stresses the need for improving understanding and quantifying methods of different uncertainty sources for effective estimation of uncertainty of hydrologic simulation.
| Author | : Mahtab Kamali |
| Publisher | : |
| Total Pages | : 126 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
This thesis presents a new approach to calibration of hydrologic models using distributed computing framework. Distributed hydrologic models are known to be very computationally intensive and difficult to calibrate. To cope with the high computational cost of the process a Surrogate Model Optimization (SMO) technique that is built for distributed computing facilities is proposed. The proposed method along with two analogous SMO methods are employed to calibrate WATCLASS hydrologic model. This model has been developed in University of Waterloo and is now a part of Environment Canada MESH (Environment Canada community environmental modeling system called Modèlisation Environmentale Communautaire (MEC) for Surface Hydrology (SH)) systems. SMO has the advantage of being less sensitive to "curse of dimensionality" and very efficient for large scale and computationally expensive models. In this technique, a mathematical model is constructed based on a small set of simulated data from the original expensive model. SMO technique follows an iterative strategy which in each iteration the surrogate model map the region of optimum more precisely. A new comprehensive method based on a smooth regression model is proposed for calibration of WATCLASS. This method has at least two advantages over the previously proposed methods: a)it does not require a large number of training data, b) it does not have many model parameters and therefore its construction and validation process is not demanding. To evaluate the performance of the proposed SMO method, it has been applied to five well-known test functions and the results are compared to two other analogous SMO methods. Since the performance of all SMOs are promising, two instances of WATCLASS modeling Smoky River watershed are calibrated using these three adopted SMOs and the resultant Nash-Sutcliffe numbers are reported.
| Author | : Masoud Asadzadeh Esfahani |
| Publisher | : |
| Total Pages | : 133 |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
In the current water resources scientific literature, a wide variety of engineering design problems are solved in a simulation-optimization framework. These problems can have single or multiple objective functions and their decision variables can have discrete or continuous values. The majority of current literature in the field of water resources systems optimization report using heuristic global optimization algorithms, including evolutionary algorithms, with great success. These algorithms have multiple parameters that control their behavior both in terms of computational efficiency and the ability to find near globally optimal solutions. Values of these parameters are generally obtained by trial and error and are case study dependent. On the other hand, water resources simulation-optimization problems often have computationally intensive simulation models that can require seconds to hours for a single simulation. Furthermore, analysts may have limited computational budget to solve these problems, as such, the analyst may not be able to spend some of the computational budget to fine-tune the algorithm settings and parameter values. So, in general, algorithm parsimony in the number of parameters is an important factor in the applicability and performance of optimization algorithms for solving computationally intensive problems. A major contribution of this thesis is the development of a highly efficient, single objective, parsimonious optimization algorithm for solving problems with discrete decision variables. The algorithm is called Hybrid Discrete Dynamically Dimensioned Search, HD-DDS, and is designed based on Dynamically Dimensioned Search (DDS) that was developed by Tolson and Shoemaker (2007) for solving single objective hydrologic model calibration problems with continuous decision variables. The motivation for developing HD-DDS comes from the parsimony and high performance of original version of DDS. Similar to DDS, HD-DDS has a single parameter with a robust default value. HD-DDS is successfully applied to several benchmark water distribution system design problems where decision variables are pipe sizes among the available pipe size options. Results show that HD-DDS exhibits superior performance in specific comparisons to state-of-the-art optimization algorithms. The parsimony and efficiency of the original and discrete versions of DDS and their successful application to single objective water resources optimization problems with discrete and continuous decision variables motivated the development of a multi-objective optimization algorithm based on DDS. This algorithm is called Pareto Archived Dynamically Dimensioned Search (PA-DDS). The algorithm parsimony is a major factor in the design of PA-DDS. PA-DDS has a single parameter from its search engine DDS. In each iteration, PA-DDS selects one archived non-dominated solution and perturbs it to search for new solutions. The solution perturbation scheme of PA-DDS is similar to the original and discrete versions of DDS depending on whether the decision variable is discrete or continuous. So, PA-DDS can handle both types of decision variables. PA-DDS is applied to several benchmark mathematical problems, water distribution system design problems, and water resources model calibration problems with great success. It is shown that hypervolume contribution, HVC1, as defined in Knowles et al. (2003) is the superior selection metric for PA-DDS when solving multi-objective optimization problems with Pareto fronts that have a general (unknown) shape. However, one of the main contributions of this thesis is the development of a selection metric specifically designed for solving multi-objective optimization problems with a known or expected convex Pareto front such as water resources model calibration problems. The selection metric is called convex hull contribution (CHC) and makes the optimization algorithm sample solely from a subset of archived solutions that form the convex approximation of the Pareto front. Although CHC is generally applicable to any stochastic search optimization algorithm, it is applied to PA-DDS for solving six water resources calibration case studies with two or three objective functions.
| Author | : Qingyun Duan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 356 |
| Release | : 2003-01-10 |
| Genre | : Science |
| ISBN | : 087590355X |
Published by the American Geophysical Union as part of the Water Science and Application Series, Volume 6. During the past four decades, computer-based mathematical models of watershed hydrology have been widely used for a variety of applications including hydrologic forecasting, hydrologic design, and water resources management. These models are based on general mathematical descriptions of the watershed processes that transform natural forcing (e.g., rainfall over the landscape) into response (e.g., runoff in the rivers). The user of a watershed hydrology model must specify the model parameters before the model is able to properly simulate the watershed behavior.
| Author | : Abdulbaset Elha Saad |
| Publisher | : |
| Total Pages | : |
| Release | : 2018 |
| Genre | : |
| ISBN | : |
Rapid advances of computer modeling and simulation tools and computing hardware have turned Model Based Design (MBD) a more viable technology. However, using a computationally intensive, "black-box" form MBD software tool to carry out design optimization leads to a number of key challenges. The non-unimodal objective function and/or non-convex feasible search region of the implicit numerical simulations in the optimization problems are beyond the capability of conventional optimization algorithms. In addition, the computationally intensive simulations used to evaluate the objective and/or constraint functions during the MBD process also make conventional stochastic global optimization algorithms unusable due to their requirement of a huge number of objective and constraint function evaluations. Surrogate model, or metamodeling-based global optimization techniques have been introduced to address these issues. Various surrogate models, including kriging, radial basis functions (RBF), multivariate adaptive regression splines (MARS), and polynomial regression (PR), are built using limited samplings on the original objective/constraint functions to reduce needed computation in the search of global optimum. In many real-world design optimization applications, computationally expensive numerical simulation models are used as objective and/or constraint functions. To solve these problems, enormous fitness function evaluations are required during the evolution based search process when advanced Global Optimization algorithms, such as DIRECT search, Differential Evolution (DE), and Bat Algorithm (BA) are used. In this work, improvements have been made to three widely used global optimization algorithms, Divided Rectangles (DIRECT), Differential Evolution (DE), and Bat Algorithm (BA) by integrating appropriate surrogate modeling methods to increase the computation efficiency of these algorithms to support MBD. The superior performance of these new algorithms in comparison with their original counterparts are shown using commonly used optimization algorithm testing benchmark problems. Integration of the surrogate modeling methods have considerably improved the search efficiency of the DIRECT, DE, and BA algorithms with significant reduction on the Number of Function Evaluations (NFEs). The newly introduced algorithms are then applied to a complex engineering design optimization problem, the design optimization of floating wind turbine platform, to test its effectiveness in real-world applications. These newly improved algorithms were able to identify better design solutions using considerably lower NFEs on the computationally expensive performance simulation model of the design. The methods of integrating surrogate modeling to improve DIRECT, DE and BA global optimization searches and the resulting algorithms proved to be effective for solving complex and computationally intensive global optimization problems, and formed a foundation for future research in this area.
| Author | : Seyed Saman Razavi |
| Publisher | : |
| Total Pages | : 191 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
Environmental simulation models have been playing a key role in civil and environmental engineering decision making processes for decades. The utility of an environmental model depends on how well the model is structured and calibrated. Model calibration is typically in an automated form where the simulation model is linked to a search mechanism (e.g., an optimization algorithm) such that the search mechanism iteratively generates many parameter sets (e.g., thousands of parameter sets) and evaluates them through running the model in an attempt to minimize differences between observed data and corresponding model outputs. The challenge rises when the environmental model is computationally intensive to run (with run-times of minutes to hours, for example) as then any automatic calibration attempt would impose a large computational burden. Such a challenge may make the model users accept sub-optimal solutions and not achieve the best model performance. The objective of this thesis is to develop innovative strategies to circumvent the computational burden associated with automatic calibration of computationally intensive environmental models.
| Author | : Alexander Forrester |
| Publisher | : John Wiley & Sons |
| Total Pages | : 228 |
| Release | : 2008-09-15 |
| Genre | : Technology & Engineering |
| ISBN | : 0470770791 |
Surrogate models expedite the search for promising designs by standing in for expensive design evaluations or simulations. They provide a global model of some metric of a design (such as weight, aerodynamic drag, cost, etc.), which can then be optimized efficiently. Engineering Design via Surrogate Modelling is a self-contained guide to surrogate models and their use in engineering design. The fundamentals of building, selecting, validating, searching and refining a surrogate are presented in a manner accessible to novices in the field. Figures are used liberally to explain the key concepts and clearly show the differences between the various techniques, as well as to emphasize the intuitive nature of the conceptual and mathematical reasoning behind them. More advanced and recent concepts are each presented in stand-alone chapters, allowing the reader to concentrate on material pertinent to their current design problem, and concepts are clearly demonstrated using simple design problems. This collection of advanced concepts (visualization, constraint handling, coping with noisy data, gradient-enhanced modelling, multi-fidelity analysis and multiple objectives) represents an invaluable reference manual for engineers and researchers active in the area. Engineering Design via Surrogate Modelling is complemented by a suite of Matlab codes, allowing the reader to apply all the techniques presented to their own design problems. By applying statistical modelling to engineering design, this book bridges the wide gap between the engineering and statistics communities. It will appeal to postgraduates and researchers across the academic engineering design community as well as practising design engineers. Provides an inclusive and practical guide to using surrogates in engineering design. Presents the fundamentals of building, selecting, validating, searching and refining a surrogate model. Guides the reader through the practical implementation of a surrogate-based design process using a set of case studies from real engineering design challenges. Accompanied by a companion website featuring Matlab software at http://www.wiley.com/go/forrester
| Author | : Hoai An Le Thi |
| Publisher | : Springer |
| Total Pages | : 1164 |
| Release | : 2019-06-15 |
| Genre | : Technology & Engineering |
| ISBN | : 3030218031 |
This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.
