Optimization Study For The Cross-Section Of A Concrete Gravity Dam: Genetic Algorithm Model And Application

Concrete gravity dams have trapezoidal shape in their cross section and shall guarantee the global stability against acting loads like hydrostatic and uplift pressures through his gravitational actions (self-weight and others). This study focuses on the shape optimization of concrete gravity dams using genetic algorithms. In this case, the dam cross section area is considered as the objective function and the design variables are the geometric parameters of the gravity dam. The optimum cross-section of a concrete gravity dam is achieved by the Genetic Algorithm (GA) through a Matlab routine developed by the author. Sliding, overturning and floating verifications are implemented in the program. In order to assess the efficiency of the proposed methodology for gravity dams optimization, one application is presented adopting the concrete gravity dam of Belo Monte Hydropower Plant (HPP), considering normal loading condition and others assumptions presented.Peer Reviewe

A robust optimization approach for magnetic spacecraft attitude stabilization

Attitude stabilization of spacecraft using magnetorquers can be achieved by a proportional–derivative-like control algorithm. The gains of this algorithm are usually determined by using a trial-and-error approach within the large search space of the possible values of the gains. However, when finding the gains in this manner, only a small portion of the search space is actually explored. We propose here an innovative and systematic approach for finding the gains: they should be those that minimize the settling time of the attitude error. However, the settling time depends also on initial conditions. Consequently, gains that minimize the settling time for specific initial conditions cannot guarantee the minimum settling time under different initial conditions. Initial conditions are not known in advance. We overcome this obstacle by formulating a min–max problem whose solution provides robust gains, which are gains that minimize the settling time under the worst initial conditions, thus producing good average behavior. An additional difficulty is that the settling time cannot be expressed in analytical form as a function of gains and initial conditions. Hence, our approach uses some derivative-free optimization algorithms as building blocks. These algorithms work without the need to write the objective function analytically: they only need to compute it at a number of points. Results obtained in a case study are very promising

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables

A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favorably with that of NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search), a well-known derivative-free optimization package. It is also applicable to multilevel equilibrium- or constrained-type problems. Its easy-to-use interface provides a number of user-oriented features, such as checkpointing and restart, variable scaling, and early termination tools

Bilevel derivative-free optimization and its application to robust optimization

We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the problem structure to derive conditions (related to the global convergence theory of the underlying trust-region methods, as far as possible) under which the lower level can be solved inexactly and sample points can be reused for model building. In addition, we indicate numerically how effective these expedients can be. A number of other issues are also discussed, from the extension to linearly constrained problems to the use of surrogate models for the lower level response. One important application of our work appears in the robust optimization of simulation-based functions, which may arise due to implementation variables or uncertain parameters. The robust counterpart of an optimization problem without derivatives falls in the category of the bilevel problems under consideration here. We provide numerical illustrations of the application of our algorithmic framework to such robust optimization example

Advanced Optimization and Statistical Methods in Portfolio Optimization and Supply Chain Management

This dissertation is on advanced mathematical programming with applications in portfolio optimization and supply chain management. Specifically, this research started with modeling and solving large and complex optimization problems with cone constraints and discrete variables, and then expanded to include problems with multiple decision perspectives and nonlinear behavior. The original work and its extensions are motivated by real world business problems.The first contribution of this dissertation, is to algorithmic work for mixed-integer second-order cone programming problems (MISOCPs), which is of new interest to the research community. This dissertation is among the first ones in the field and seeks to develop a robust and effective approach to solving these problems. There is a variety of important application areas of this class of problems ranging from network reliability to data mining, and from finance to operations management.This dissertation also contributes to three applications that require the solution of complex optimization problems. The first two applications arise in portfolio optimization, and the third application is from supply chain management. In our first study, we consider both single- and multi-period portfolio optimization problems based on the Markowitz (1952) mean/variance framework. We have also included transaction costs, conditional value-at-risk (CVaR) constraints, and diversification constraints to approach more realistic scenarios that an investor should take into account when he is constructing his portfolio. Our second work proposes the empirical validation of posing the portfolio selection problem as a Bayesian decision problem dependent on mean, variance and skewness of future returns by comparing it with traditional mean/variance efficient portfolios. The last work seeks supply chain coordination under multi-product batch production and truck shipment scheduling under different shipping policies. These works present a thorough study of the following research foci: modeling and solution of large and complex optimization problems, and their applications in supply chain management and portfolio optimization.Ph.D., Business Administration -- Drexel University, 201

Multidelity methods for multidisciplinary system design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 211-220).Optimization of multidisciplinary systems is critical as slight performance improvements can provide significant benefits over the system's life. However, optimization of multidisciplinary systems is often plagued by computationally expensive simulations and the need to iteratively solve a complex coupling-relationship between subsystems. These challenges are typically severe enough as to prohibit formal system optimization. A solution is to use multi- fidelity optimization, where other lower-fidelity simulations may be used to approximate the behavior of the higher-fidelity simulation. Low-fidelity simulations are common in practice, for instance, simplifying the numerical simulations with additional physical assumptions or coarser discretizations, or creating direct metamodels such as response surfaces or reduced order models. This thesis offers solutions to two challenges in multidisciplinary system design optimization: developing optimization methods that use the high-fidelity analysis as little as possible but ensure convergence to a high-fidelity optimal design, and developing methods that exploit multifidelity information in order to parallelize the optimization of the system and reduce the time needed to find an optimal design. To find high-fidelity optimal designs, Bayesian model calibration is used to improve low- fidelity models and systematically reduce the use of high-fidelity simulation. The calibrated low-fidelity models are optimized and using appropriate calibration schemes convergence to a high-fidelity optimal design is established. These calibration schemes can exploit high- fidelity gradient information if available, but when not, convergence is still demonstrated for a gradient-free calibration scheme. The gradient-free calibration is novel in that it enables rigorous optimization of high-fidelity simulations that are black-boxes, may fail to provide a solution, contain some noise in the output, or are experimental. In addition, the Bayesian approach enables us to combine multiple low-fidelity simulations to best estimate the high- fidelity function without nesting. Example results show that for both aerodynamic and structural design problems this approach leads to about an 80% reduction in the number of high-fidelity evaluations compared with single-fidelity optimization methods. To enable parallelized multidisciplinary system optimization, two approaches are developed. The first approach treats the system design problem as a bilevel programming problem and enables each subsystem to be designed concurrently. The second approach optimizes surrogate models of each discipline that are all constructed in parallel. Both multidisciplinary approaches use multifidelity optimization and the gradient-free Bayesian model calibration technique, but will exploit gradients when they are available. The approaches are demonstrated on an aircraft wing design problem, and enable optimization of the system in reasonable time despite lack of sensitivity information and 19% of evaluations failing. For cases when comparable algorithms are available, these approaches reduce the time needed to find an optimal design by approximately 50%.by Andrew I. March.Ph.D

Mastering Uncertainty in Mechanical Engineering

This open access book reports on innovative methods, technologies and strategies for mastering uncertainty in technical systems. Despite the fact that current research on uncertainty is mainly focusing on uncertainty quantification and analysis, this book gives emphasis to innovative ways to master uncertainty in engineering design, production and product usage alike. It gathers authoritative contributions by more than 30 scientists reporting on years of research in the areas of engineering, applied mathematics and law, thus offering a timely, comprehensive and multidisciplinary account of theories and methods for quantifying data, model and structural uncertainty, and of fundamental strategies for mastering uncertainty. It covers key concepts such as robustness, flexibility and resilience in detail. All the described methods, technologies and strategies have been validated with the help of three technical systems, i.e. the Modular Active Spring-Damper System, the Active Air Spring and the 3D Servo Press, which have been in turn developed and tested during more than ten years of cooperative research. Overall, this book offers a timely, practice-oriented reference guide to graduate students, researchers and professionals dealing with uncertainty in the broad field of mechanical engineering