Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients

In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed, and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem

Stopping rules effect on a derivative-free filter multistart algorithm for multilocal programming

Fundação para a Ciência e a Tecnologia (FCT

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Efficient Optimization and Robust Value Quantification of Enhanced Oil Recovery Strategies

With an increasing demand for hydrocarbon reservoir produces such as oil, etc., and difficulties in finding green oil fields, the use of Enhanced Oil Recovery (EOR) methods such as polymer, Smart water, and solvent flooding for further development of existing fields can not be overemphasized. For reservoir profitability and reduced environmental impact, it is crucial to consider appropriate well control settings of EOR methods for given reservoir characterization. Moreover, finding appropriate well settings requires solving a constrained optimization problem with suitable numerical solution methods. Conventionally, the solution method requires many iterations involving several computationally demanding function evaluations before convergence to the appropriate near optimum. The major subject of this thesis is to develop an efficient and accurate solution method for constrained optimization problems associated with EOR methods for their value quantifications and ranking in the face of reservoir uncertainties. The first contribution of the thesis develops a solution method based on the inexact line search method (with Ensemble Based Optimization (EnOpt) for approximate gradient computation) for robust constrained optimization problems associated with polymer, Smart water, and solvent flooding. Here, the objective function is the expectation of the Net Present Value (NPV) function over given geological realizations. For a given set of well settings, the NPV function is defined based on the EOR simulation model, which follows from an appropriate extension of the black-oil model. The developed solution method is used to find the economic benefits and also the ranking of EOR methods for different oil reservoirs developed to mimic North Sea reservoirs. Performing the entire optimization routine in a transformed domain along with truncations has been a common practice for handling simple linear constraints in reservoir optimization. Aside from the fact that this method has a negative impact on the quality of gradient computation, it is complicated to use for non-linear constraints. The second contribution of this thesis proposes a technique based on the exterior penalty method for handling general linear and non-linear constraints in reservoir optimization problems to improve gradient computation quality by the EnOpt method for efficient and improved optimization algorithm. Because of the computationally expensive NPV function due to the costly reservoir simulation of EOR methods, the solution method for the underlying EOR optimization problem becomes inefficient, especially for large reservoir problems. To speedup the overall computation of the solution method, this thesis introduces a novel full order model (FOM)-based certified adaptive machine learning optimization procedures to locally approximate the expensive NPV function. A supervised feedforward deep neural network (DNN) algorithm is employed to locally create surrogate model. In the FOM-based optimization algorithm of this study, several FOM NPV function evaluations are required by the EnOpt method to approximate the gradient function at each (outer) iteration until convergence. To limit the number FOM-based evaluations, we consider building surrogate models locally to replace the FOM based NPV function at each outer iteration and proceed with an inner optimization routine until convergence. We adapt the surrogate model using some FOM-based criterion where necessary until convergence. The demonstration of methodology for polymer optimization problem on a benchmark model results in an improved optimum and found to be more efficient compared to using the full order model optimization procedures

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

COMPUTATIONAL ADVANCES IN CONTINUUM TOPOLOGY OPTIMIZATION ALGORITHMS

Topology optimization is a fascinating area of research with numerous unsolved computational challenges. In this thesis, the author aims to advance the research on improving the computational efficiency of common topology algorithms for practical real life problems. Beside the research contributions in this thesis, the introduction (chapter 1) is written to cover much of the theory behind the algorithms and formulations used in topology optimization including some details that often get ignored in most papers and texts in the field of topology optimization. A lot of the details presented in the introduction is scattered in multiple resources between computational mechanics books, optimization theory books and papers, and topology optimization literature. This makes it difficult for people starting to learn topology optimization to easily cover the theory needed to do advanced research in the field. An attempt is made to give a reasonably comprehensive coverage of the theory of the finite element method with an emphasis on linear elasticity as well as the theory behind common nonlinear programming algorithms used in topology optimization. Additionally, a presentation of all the common paradigms for decision-making under uncertainty is presented. Topology optimization under uncertainty is a field of research with many unsolved computational problems. This presentation will hopefully help more researchers get started in this field of research more easily. In chapter 2, the first research contribution of this thesis is presented. In par- ticular, a flexible and theoretically sound way to adapt penalties in the continuation solid isotropic material with penalization (CSIMP) method is proposed which gives significant speedups in the experiments run. Four common test problems from literature, three 2D and one 3D, are used to test the efficacy of the penalty adap- tation with different parameter settings. The main factors affecting the efficacy of the penalty adaptation in the CSIMP algorithm in reducing the number of fi- nite element analysis (FEA) simulations needed to converge to the final solution are identified. The experimental results demonstrate a significant reduction in the number of FEA simulations required to reach the optimal solution in the decreasing tolerance CSIMP algorithm, with exponentially decaying tolerance, with little to no detriment in the objective value and the other metrics used. Finally, a mathematical and experimental treatment of the effect of the minimum pseudo-density parameter on the convergence of the CSIMP algorithm is given with some recommendations for choosing a suitable value. These results appear in the Computer Methods in Applied Mechanics and Engineering journal (Tarek & Ray 2020). In chapter 3, the problem of handling load uncertainty efficiently in compliance- based topology optimization problems is tackled. A comprehensive review of all the literature on handling uncertainty in compliance-based problems is presented. And a number of exact methods are proposed to handle load uncertainty in compliance- based topology optimization problems where the uncertainty is described in the form of a set of finitely many loading scenarios. This includes mean compliance minimization or constraining the mean compliance, minimizing or constraining a weighted sum of the mean and standard deviation of the load compliances as well as minimizing or constraining the maximum load compliance for all the loading scenarios. By detecting and exploiting low rank structures in the loading scenar- ios, significant performance improvements are achieved using some novel methods. The computational complexities of the algorithms proposed are demonstrated and experiments are run to verify the efficacy of the proposed algorithms at reducing the computational cost of these classes of topology optimization problems. The meth- ods presented here are fundamentally data-driven in the sense that no probability distributions or continuous domains are assumed for the loading scenarios. This sets this work apart from most of the literature in the domain of stochastic and robust topology optimization where a distribution or domain is assumed. Additionally, the methods proposed here are shown to be particularly suitable with the augmented Lagrangian algorithm when dealing with maximum compliance constraints. This work appears in the Structural and Multidisciplinary Optimization journal. In chapter 4, approximate methods for handling many loading scenarios with a high rank loading matrix are developed. In particular, approximation schemes for the mean compliance and a class of scalar-valued functions of the load compliances are developed. The approximation schemes are based on a reformulation of the function approximated as a trace or diagonal estimation problem, opening the door to using many of the available methods for trace or diagonal estimation. The approximation methods are tested on a number of standard 2D and 3D benchmark problems using low and high rank loading scenarios to solve mean compliance minimization as well as minimizing the weighted sum of the mean compliance and its standard deviation. Significant speedups are achieved compared to the exact methods when the rank of the load matrix is high. This work is submitted to the Structural and Multidisciplinary Optimization journal as of the time of the writing of this thesis. In chapter 5, a summary of all the findings in this thesis and some potential future work for the author here or for aspiring researchers in topology optimization is presented

On the controllability of fermentation systems

This thesis concerns the controllability of fermentation processes. Fermentation processes are often described by unstructured process models. A control system can be used to reduce the effect of the uncertainties and disturbances. A process is called controllable if a control system satisfying suitably defined control objectives can be found. Controllability measures based on linear process models are identified. The idealised control objective for perfect control allows fast evaluation of the controllability measures. These measures are applied to compare different designs of a continuous fermentation process by identifying the controllability properties of the process design. The operational mode of fed batch fermentations is inherently dynamic. General control system design methods are not readily applicable to such systems. This work presents an approach for the design of robust controllers suitable for these processes. The control objective is to satisfy a set of robustness constraints for a given set of model uncertainties and disturbances. The optimal operation and design problems are combined into a single optimal control problem. The controller design is integrated into the process design problem formulation. In this way the control system and the process are designed simultaneously. Different problem formulations are investigated. The proposed approach is demonstrated on complex fermentation models. The resulting operating strategies are controllable with respect to the aims of control

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics