Download or read book Applications of Multi objective Mixed integer and Hybrid Global Optimization Algorithms for Computationally Expensive Groundwater Problems written by Ying Wan and published by . This book was released on 2015 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Developing Parsimonious and Efficient Algorithms for Water Resources Optimization Problems written by Masoud Asadzadeh Esfahani and published by . This book was released on 2012 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Deterministic Global Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2000 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified and insightful treatment of deterministic global optimization. It introduces theoretical and algorithmic advances that address the computation and characterization of global optima, determine valid lower and upper bounds on the global minima and maxima, and enclose all solutions of nonlinear constrained systems of equations. Among its special features, the book: Introduces the fundamentals of deterministic global optimization; Provides a thorough treatment of decomposition-based global optimization approaches for biconvex and bilinear problems; Covers global optimization methods for generalized geometric programming problems Presents in-depth global optimization algorithms for general twice continuously differentiable nonlinear problems; Provides a detailed treatment of global optimization methods for mixed-integer nonlinear problems; Develops global optimization approaches for the enclosure of all solutions of nonlinear constrained systems of equations; Includes many important applications from process design, synthesis, control, and operations, phase equilibrium, design under uncertainty, parameter estimation, azeotrope prediction, structure prediction in clusters and molecules, protein folding, and peptide docking. Audience: This book can be used as a textbook in graduate-level courses and as a desk reference for researchers in all branches of engineering and applied science, applied mathematics, industrial engineering, operations research, computer science, economics, computational chemistry and molecular biology.

Download or read book Constrained Global Optimization Algorithms and Applications written by Panos M. Pardalos and published by Springer. This book was released on 1987-07-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global optimization is concerned with the characterization and computation of global minima or maxima of nonlinear functions. Such problems are widespread in mathematical modeling of real world systems for a very broad range of applications. The applications include economies of scale, fixed charges, allocation and location problems, quadratic assignment and a number of other combinatorial optimization problems. More recently it has been shown that certain aspects of VLSI chip design and database problems can be formulated as constrained global optimization problems with a quadratic objective function. Although standard nonlinear programming algorithms will usually obtain a local minimum to the problem , such a local minimum will only be global when certain conditions are satisfied (such as f and K being convex).

Download or read book Frontiers in Global Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti mization", "State-of-the-Art in Global Optimization", and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.

Download or read book Mathematical Optimization of Water Networks written by Alexander Martin and published by Springer Science & Business Media. This book was released on 2012-06-30 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Water supply- and drainage systems and mixed water channel systems are networks whose high dynamic is determined and/or affected by consumer habits on drinking water on the one hand and by climate conditions, in particular rainfall, on the other hand. According to their size, water networks consist of hundreds or thousands of system elements. Moreover, different types of decisions (continuous and discrete) have to be taken in the water management. The networks have to be optimized in terms of topology and operation by targeting a variety of criteria. Criteria may for example be economic, social or ecological ones and may compete with each other. The development of complex model systems and their use for deriving optimal decisions in water management is taking place at a rapid pace. Simulation and optimization methods originating in Operations Research have been used for several decades; usually with very limited direct cooperation with applied mathematics. The research presented here aims at bridging this gap, thereby opening up space for synergies and innovation. It is directly applicable for relevant practical problems and has been carried out in cooperation with utility and dumping companies, infrastructure providers and planning offices. A close and direct connection to the practice of water management has been established by involving application-oriented know-how from the field of civil engineering. On the mathematical side all necessary disciplines were involved, including mixed-integer optimization, multi-objective and facility location optimization, numerics for cross-linked dynamic transportation systems and optimization as well as control of hybrid systems. Most of the presented research has been supported by the joint project „Discret-continuous optimization of dynamic water systems“ of the federal ministry of education and research (BMBF).

Download or read book Deterministic Global Optimization written by Christodoulos a Floudas and published by Springer. This book was released on 2014-01-15 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Comparison of Stochastic Radial Basis Function and PEST for Automatic Calibration of Computationally Expensive Groundwater Models with Application to Miyun Huai Shun Aquifer written by Ying Wan and published by . This book was released on 2013 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groundwater numerical models have been widely used as effective tools to analyze and manage water resources. However, the accuracy and reliability of a groundwater numerical model largely depends on model parameters calibration, which is extremely computationally expensive. Therefore, it is highly desirable that efficient optimization algorithms be applied to automatic calibration problems. In this study, we compare the performance of three optimization algorithms and propose a new hybrid method. The algorithms are applied to calibration of a model for part of Beijing water supply. We first outline the three algorithms and briefly describe our hybrid method. The first algorithm referred as PEST in this paper is the Gauss-Marquardt-Levenberg (GML) method including truncated singular value decomposition, which is widely applied in the field of model parameter calibration. As the second one, CMAES_P is a "PEST compatible" implementation of CMA-ES (Covariance Matrix Adaptation Evolution Strategy) global optimization algorithm. PEST derivative-based algorithm and CMAES_P are both encapsulated in the automated parameter optimization software PEST, which has advanced predictive analysis and regularization features to minimize user-specified objective functions. The third one, called Stochastic Radial Basis Function (Stochastic RBF) method, is developed by Regis and Shoemaker (2007), which utilizes radial basis function as the response surface model to approximate the expensive objective function. Our new hybrid method combines Stochastic RBF and PEST derivative-based algorithm, which provides PEST derivative-based algorithm with the starting points found by Stochastic RBF. This paper compares the performances of the aforementioned four algorithms for automatic parameter calibration of a groundwater model on three 28-parameter cases and two synthetic test function calibration problems. We employ the following characteristics as our comparison criteria on all the cases: (1) efficiency in giving good objective function for a given number of function evaluations; (2) performance for different statistical criteria; (3) variability of solutions in multiple trials; (4) improvements if more function evaluations are performed. On the basis of 20 trials, the results indicate that Stochastic RBF is best among the three and CMAES_P is superior to PEST. In addition, our hybrid method still failed to beat Stochastic RBF in highly computationally expensive nonlinear cases. To sum up, our results show that Stochastic RBF method is a more efficient alternative to PEST for automatic parameter calibration of computationally expensive groundwater models. ii.

Download or read book State of the Art in Global Optimization written by Christodoulos A. Floudas and published by Springer. This book was released on 2011-10-07 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.

Download or read book Global Optimization in Action written by János D. Pintér and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s). Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on the author's research, in cooperation (on applications) with a number of colleagues. Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

Download or read book Introduction to Optimization Analysis in Hydrosystem Engineering written by Ehsan Goodarzi and published by Springer Science & Business Media. This book was released on 2014-02-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basics of linear and nonlinear optimization analysis for both single and multi-objective problems in hydrosystem engineering. The book includes several examples with various levels of complexity in different fields of water resources engineering. The examples are solved step by step to assist the reader and to make it easier to understand the concepts. In addition, the latest tools and methods are presented to help students, researchers, engineers and water managers to properly conceptualize and formulate resource allocation problems, and to deal with the complexity of constraints in water demand and available supplies in an appropriate way.

Download or read book Developments in Global Optimization written by Immanuel M. Bomze and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented. Audience: All researchers and students working in mathematical programming.

Download or read book Global Optimization written by Angelika Michalski and published by Nova Science Publishers. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global optimisation is an important area of applied mathematics that has shown fast and growing development during the last few decades, and deals with the optimisation of a function or a set of functions according to some criteria. In this book the authors discuss the theory, developments and applications of global optimisation including: particle swarm optimisation with re-initialisation strategies for continuous global optimisation; particle swarm global optimisation for orbital manoeuvres; float-encoded genetic algorithms used for the inversion processing of well-logging data; particle collision algorithms; classifier-assisted frameworks for computationally expensive optimisation problems; and the cutting box strategy as an algorithmic framework for improving metaheuristics for continuous global optimisation.

Download or read book Swarm Intelligence and Evolutionary Computing for Single and Multi objective Optimization in Water Resource Systems written by Janga Reddy Manne and published by LAP Lambert Academic Publishing. This book was released on 2010 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional optimization methods are no longer adequate to solve complex real life problems, as most of them involve nonlinear, discontinuous, non- differentiable, nonconvex, multiobjective functions with mixed variables in their model formulation. Over the last few years, the use of nature inspired meta-heuristic algorithms for systems optimization has increased tremendously, and "swarm intelligence and evolutionary computing techniques" are rapidly emerging as powerful tools for solving practical problems. This book describes efficient computational techniques based on Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Differential Evolution (DE) principles for single and multiple criterion optimization; and hybrid soft-computing techniques such as PSO Neural Network (PSO-NN), Adaptive Network Fuzzy Inference System (ANFIS) for hydrologic forecasting and demonstrates their applications to case studies in reservoir systems operation. This book is intended for people who are willing to learn new technology to solve complex real life problems and especially useful to professional in water resources field.

Download or read book Metaheuristics in Water Geotechnical and Transport Engineering written by Xin-She Yang and published by Newnes. This book was released on 2012-12-31 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to an ever-decreasing supply in raw materials and stringent constraints on conventional energy sources, demand for lightweight, efficient and low cost structures has become crucially important in modern engineering design. This requires engineers to search for optimal and robust design options to address design problems that are often large in scale and highly nonlinear, making finding solutions challenging. In the past two decades, metaheuristic algorithms have shown promising power, efficiency and versatility in solving these difficult optimization problems. This book examines the latest developments of metaheuristics and their applications in water, geotechnical and transport engineering offering practical case studies as examples to demonstrate real world applications. Topics cover a range of areas within engineering, including reviews of optimization algorithms, artificial intelligence, cuckoo search, genetic programming, neural networks, multivariate adaptive regression, swarm intelligence, genetic algorithms, ant colony optimization, evolutionary multiobjective optimization with diverse applications in engineering such as behavior of materials, geotechnical design, flood control, water distribution and signal networks. This book can serve as a supplementary text for design courses and computation in engineering as well as a reference for researchers and engineers in metaheursitics, optimization in civil engineering and computational intelligence. Provides detailed descriptions of all major metaheuristic algorithms with a focus on practical implementation Develops new hybrid and advanced methods suitable for civil engineering problems at all levels Appropriate for researchers and advanced students to help to develop their work

Download or read book Mixed integer Nonlinear Optimization Methods for Pooling and Multiperiod Blending Problems written by Yifu Chen and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pooling and multiperiod blending problems are common in many industrial sectors, from oil refining to mining and wastewater management. Global optimization for such problems remains challenging due to the presence of bilinear terms. Binary variables may also be introduced to model certain operational constraints. To address the computational challenges, we develop mixed-integer nonlinear optimization methods for such problems. We first consider the multiperiod blending problem with minimizing cost objective. We develop a novel preprocessing algorithm to calculate lower bounds on stream flows. We define product dedicated flow variables to address product specific features involved in multiperiod blending problem. The bounds on stream flows and new product dedicated flow variables are then used to generate tightening constraints. For multiperiod blending problem with maximizing profit objective, we first propose a reformulation of the constraints involving bilinear terms using lifting. We introduce an algorithm that returns tight bounds on the lifted variables calculated by aggregating multiple constraints. We propose valid constraints derived from Reformulation-Linearization Technique that utilize the bounds on the lifted variables to further tighten the formulation. Finally, we develop tightening and solution methods based on nontrivial bounds on bilinear terms. We derive a family of valid linear constraints and further show that, when one of the nontrivial bounds is active, such constraints are tangent to one branch of the hyperbola that represents the bilinear term. We propose different preprocessing methods for generating strong constraints from the family and test them on the pooling problem.

Download or read book Optimal Calibration Uncertainty Assessment and Long term Monitoring Using Computationally Expensive Groundwater Models written by Pradeep Mugunthan and published by . This book was released on 2005 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: