This book explores mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. The book gathers 81 contributions submitted to the 20th European Conference on Mathematics for Industry, ECMI 2018, which was held in Budapest, Hungary in June 2018. The application areas include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation. In turn, the mathematical technologies discussed include: Combinatorial Optimization, Cooperative Games, Delay Differential Equations, Finite Elements, Hamilton-Jacobi Equations, Impulsive Control, Information Theory and Statistics, Inverse Problems, Machine Learning, Point Processes, Reaction-Diffusion Equations, Risk Processes, Scheduling Theory, Semidefinite Programming, Stochastic Approximation, Spatial Processes, System Identification, and Wavelets. The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.

This book covers an introduction to convex optimization, one of the powerful and tractable optimization problems that can be efficiently solved on a computer. The goal of the book is tohelp develop a sense of what convex optimization is, and how it can be used in a widening array of practical contexts with a particular emphasis on machine learning.The first part of the book covers core concepts of convex sets, convex functions, and related basic definitions that serve understanding convex optimization and its corresponding models. The second part deals with one very useful theory, called duality, which enables us to: (1) gain algorithmic insights; and (2) obtain an approximate solution to non-convex optimization problems which are often difficult to solve. The last part focuses on modern applications in machine learning and deep learning.A defining feature of this book is that it succinctly relates the "story" of how convex optimization plays a role, via historical examples and trending machine learning applications. Another key feature is that it includes programming implementation of a variety of machine learning algorithms inspired by optimization fundamentals, together with a brief tutorial of the used programming tools. The implementation is based on Python, CVXPY, and TensorFlow. This book does not follow a traditional textbook-style organization, but is streamlined via a series of lecture notes that are intimately related, centered around coherent themes and concepts. It serves as a textbook mainly for a senior-level undergraduate course, yet is also suitable for a first-year graduate course. Readers benefit from having a good background in linear algebra, some exposure to probability, and basic familiarity with Python.

This book deals with critical infrastructure safety analysis based on reliability modelling of multistate ageing system. It shows how changes of the operation process as well as climate-weather changes in the operating area of the critical infrastructure do influence the safety parameters of its assets. Building upon previous authors' research, the book formulates an integrated modeling approach where the multistate critical infrastructure safety model is combined with semi-Markov models for its operation process and for the climate-weather change process. This approach is shown to be successful in determining basic critical infrastructure safety, risk and resilience indicators, regardless of the number of assets and the number of their safety states. Besides the theory, the book reports on a successful application to the safety analysis of a real critical infrastructure, such as a port oil terminal. All in all, this book proposes a comprehensive and timely review of cutting-edge mathematical methods for safety identification, prediction and evaluation of critical infrastructures. It demonstrates that these methods can be applied in practice for analyzing safety of critical infrastructure under time-varying operation and climate-weather change processes.

The results presented here (including the assessment of a new tool - inhibitory trees) offer valuable tools for researchers in the areas of data mining, knowledge discovery, and machine learning, especially those whose work involves decision tables with many-valued decisions. The authors consider various examples of problems and corresponding decision tables with many-valued decisions, discuss the difference between decision and inhibitory trees and rules, and develop tools for their analysis and design. Applications include the study of totally optimal (optimal in relation to a number of criteria simultaneously) decision and inhibitory trees and rules; the comparison of greedy heuristics for tree and rule construction as single-criterion and bi-criteria optimization algorithms; and the development of a restricted multi-pruning approach used in classification and knowledge representation.

Martin Grotschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grotschel s doctoral descendant tree 1983 2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants.

This book starts with a personal tribute to Martin Grotschel by the editors (Part I), a contribution by his very special predecessor Manfred Padberg on Facets and Rank of Integer Polyhedra (Part II), and the doctoral descendant tree 1983 2012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant.

The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixed-integer convex optimization, super classes of perfect graphs, efficient algorithms for subtree-telecenters, junctions in acyclic graphs and preemptive restricted strip covering, as well as efficient approximation of non-preemptive restricted strip covering.

Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions and more general mixed-integer nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, mean-risk optimization and gas network optimization.

Computational studies include a semidefinite branch and cut approach for the max k-cut problem, mixed-integer nonlinear optimal control, and mixed-integer linear optimization for scheduling and routing of fly-in safari planes.

The two closing articles are devoted to computational advances in general mixed integer linear optimization, the first by scientists working in industry, the second by scientists working in academia.

These articles reflect the scientific facets of Martin Grotschel who has set standards in theory, computation and applications.

The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood ratio (LR), Wald (W), and Rao score (S) tests. Due to the large literature about the LR, W and S tests, the gradient test is not frequently used to test hypothesis. The book covers topics on the local power of the gradient test, the Bartlett-corrected gradient statistic, the gradient statistic under model misspecification, and the robust gradient-type bounded-influence test.

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Nonlinear Optimization of Vehicle Safety Structures: Modeling of Structures Subjected to Large Deformations provides a cutting-edge overview of the latest optimization methods for vehicle structural design. The book focuses on large deformation structural optimization algorithms and applications, covering the basic principles of modern day topology optimization and comparing the benefits and flaws of different algorithms in use. The complications of non-linear optimization are highlighted, along with the shortcomings of recently proposed algorithms. Using industry relevant case studies, users will how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given. The authors draw on research work with the likes of MIRA, Jaguar Land Rover and Tata Motors European Technology Centre as part of multi-million pound European funded research projects, emphasizing the industry applications of recent advances. The book is intended for crash engineers, restraints system engineers and vehicle dynamics engineers, as well as other mechanical, automotive and aerospace engineers, researchers and students with a structural focus.

This book contains selected papers presented at ICGEC 2021, the 14th International Conference on Genetic and Evolutionary Computing, held from October 21-23, 2021 in Jilin City, China. The conference was technically co-sponsored by Springer, Northeast Electric Power University Fujian University of Technology, Shandong University of Science and Technology, and Western Norway University of Applied Sciences. It is intended as an international forum for the researchers and professionals in all areas of genetic and evolutionary computing. And the readers may learn the up-to-date techniques of the mentioned topics, including swarm intelligence, artificial intelligence, information hiding and data mining techniques, which can help them to bring new ideas or apply the designed approaches from the collected papers to their professional jobs.

A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.

This book covers using R for doing optimization, a key area of operations research, which has been applied to virtually every industry. The focus is on linear and mixed integer optimization. It uses an algebraic modeling approach for creating formulations that pairs naturally with an algebraic implementation in R. With the rapid rise of interest in data analytics, a data analytics platform is key. Working technology and business professionals need an awareness of the tools and language of data analysis. R reduces the barrier to entry for people to start using data analytics tools. Philosophically, the book emphasizes creating formulations before going into implementation. Algebraic representation allows for clear understanding and generalization of large applications, and writing formulations is necessary to explain and convey the modeling decisions made. Appendix A introduces R. Mathematics is used at the level of subscripts and summations Refreshers are provided in Appendix B. This book: * Provides and explains code so examples are relatively clear and self-contained. * Emphasizes creating algebraic formulations before implementing. * Focuses on application rather than algorithmic details. * Embodies the philosophy of reproducible research. * Uses open-source tools to ensure access to powerful optimization tools. * Promotes open-source: all materials are available on the author's github repository. * Demonstrates common debugging practices with a troubleshooting emphasis specific to optimization modeling using R. * Provides code readers can adapt to their own applications . This book can be used for graduate and undergraduate courses for students without a background in optimization and with varying mathematical backgrounds.

This book presents new techniques and methods for distributed control and optimization of networked microgrids. Distributed consensus issues under network-based and event-triggered mechanisms are first addressed in a multi-agent system framework, which can explicitly characterize the relationship between communication resources and the control performance. Then, considering the effects of network uncertainties, multi-agent system-based distributed schemes are tailored to solve the fundamental issues of networked microgrids such as distributed frequency regulation, voltage regulation, active power sharing/load sharing, and energy management. The monograph will contribute to stimulating extensive interest of researchers in electrical and control fields.

This book reports on the latest advances in adaptive critic control with robust stabilization for uncertain nonlinear systems. Covering the core theory, novel methods, and a number of typical industrial applications related to the robust adaptive critic control field, it develops a comprehensive framework of robust adaptive strategies, including theoretical analysis, algorithm design, simulation verification, and experimental results. As such, it is of interest to university researchers, graduate students, and engineers in the fields of automation, computer science, and electrical engineering wishing to learn about the fundamental principles, methods, algorithms, and applications in the field of robust adaptive critic control. In addition, it promotes the development of robust adaptive critic control approaches, and the construction of higher-level intelligent systems.

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As an ideal companion to the author's previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.

This book provides different approaches used to analyze, draw attention, and provide an understanding of the advancements in the optimization field across the globe. It brings all of the latest methodologies, tools, and techniques related to optimization and industrial engineering into a single volume to build insights towards the latest advancements in various domains. Applications of Advanced Optimization Techniques in Industrial Engineering includes the basic concept of optimization, techniques, and applications related to industrial engineering. Concepts are introduced in a sequential way along with explanations, illustrations, and solved examples. The book goes on to explore applications of operations research and covers empirical properties of a variety of engineering disciplines. It presents network scheduling, production planning, industrial and manufacturing system issues, and their implications in the real world. The book caters to academicians, researchers, professionals in inventory analytics, business analytics, investment managers, finance firms, storage-related managers, and engineers working in engineering industries and data management fields.

Optimization plays an invaluable role in the exciting and rapidly developing field of computer vision, yet this importance is often overlooked in the literature.

This practical and authoritative text/reference presents a broad introduction to the optimization methods used specifically in computer vision. In order to facilitate understanding, the presentation of the methods is supplemented by simple flow charts, followed by pseudocode implementations that reveal deeper insights into their mode of operation. These discussions are further supported by examples taken from important applications in computer vision.

Topics and features: provides a comprehensive overview of computer vision-related optimization; covers a range of techniques from classical iterative multidimensional optimization to cutting-edge topics of graph cuts and GPU-suited total variation-based optimization; describes in detail the optimization methods employed in computer vision applications; illuminates key concepts with clearly written and step-by-step explanations; presents detailed information on implementation, including pseudocode for most methods.

This easy-to-follow and applications-focused book is an essential resource for researchers and practitioners seeking guidance on implementing specific methods in computer vision.

Very little has been published on optimization of pharmaceutical portfolios. Moreover, most of published literature is coming from the commercial side, where probability of technical success (PoS) is treated as fixed, and not as a consequence of development strategy or design. In this book there is a strong focus on impact of study design on PoS and ultimately on the value of portfolio. Design options that are discussed in different chapters are dose-selection strategies, adaptive design and enrichment. Some development strategies that are discussed are indication sequencing, optimal number of programs and optimal decision criteria. This book includes chapters written by authors with very broad backgrounds including financial, clinical, statistical, decision sciences, commercial and regulatory. Many authors have long held executive positions and have been involved with decision making at a product or at a portfolio level. As such, it is expected that this book will attract a very broad audience, including decision makers in pharmaceutical R&D, commercial and financial departments. The intended audience also includes portfolio planners and managers, statisticians, decision scientists and clinicians. Early chapters describe approaches to portfolio optimization from big Pharma and Venture Capital standpoints. They have stronger focus on finances and processes. Later chapters present selected statistical and decision analysis methods for optimizing drug development programs and portfolios. Some methodological chapters are technical; however, with a few exceptions they require a relatively basic knowledge of statistics by a reader.

This book is about optimization techniques and is subdivided into two parts. In the first part a wide overview on optimization theory is presented. Optimization is presented as being composed of five topics, namely: design of experiment, response surface modeling, deterministic optimization, stochastic optimization, and robust engineering design. Each chapter, after presenting the main techniques for each part, draws application oriented conclusions including didactic examples. In the second part some applications are presented to guide the reader through the process of setting up a few optimization exercises, analyzing critically the choices which are made step by step, and showing how the different topics that constitute the optimization theory can be used jointly in an optimization process. The applications which are presented are mainly in the field of thermodynamics and fluid dynamics due to the author's background.

This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.

The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.

This book describes the modelling and optimisation of vibration reduction systems in an integrated fashion using nonlinear equations of motion. It proposes an effective optimisation method for determining the basic characteristics of the non-linear visco-elastic elements used in passive vibration reduction systems. In the case of semi-active and active vibration isolators, a design process of the advanced control systems is proposed that makes possible to optimise the controller settings relatively to the selected vibro-isolation criteria. The approach developed here is subsequently tested by means of experimental investigations conducted on various sample vibration reduction systems: passive, semi-active and active. The book presents a biomechanical modelling approach that allows users to select the properties of vibro-isolation systems for different types of oscillation and different optimisation criteria - and can significantly reduce the harmful vibrations that can affect the human body in the process. Further, the book equips readers to evaluate the viscoelastic characteristics of passive systems and design control systems for semi-active and active systems. Modelling and Control Design of Vibration Reduction Systems offers a valuable guide for researchers and practitioners alike. It also provides students and academics with systematic information on the procedures to be followed in the design process for semi-active or active vibration reduction systems.

This book presents simple design paradigms related to lightweight design, that are derived from an in-depth and theoretically sound analysis based on Pareto theory. It uses numerous examples, including torsion and inflated tubes, to fully explain the theories discussed. Lightweight Construction Principles begins by defining terms in relation to engineering design and optimal design of complex mechanical systems. It then discusses the analytical derivation of the Pareto-optimal set, before applying analytical formulae to optimal design of bent beams. The book moves through numerous case studies of different beam and tube construction including beams subject to bending, thin walled tubes under torsion and truss structures. This book will be of interest to researchers and graduate students in the field of structural optimisation and multi-objective optimization, as well as to practitioners such as design engineers.

The detailed survey on constraint handling techniques specifically penalty function approach is presented in the book; presents the Cohort Intelligence (CI) algorithm incorporated with a novel self-adaptive penalty function (SAPF) approach which helped in avoiding preliminary trials of selecting penalty parameter. The approach is referred to as CI-SAPF; CI-SAPF is further hybridized with Colliding Bodies Optimization (CBO) algorithm to promote a parameter less metaheuristic algorithm; presents solutions to several problems from discrete truss structure domain, mixed variable design engineering domain, and linear & nonlinear domain validating the CI-SAPF and CI-SAPF-CBO; behavior of SAPF approach on pseudo objective function, constraint violations, penalty function and penalty parameter have been analyzed and discussed in very detail; presents the in-depth analysis and comparison of the CI-SAPF, CI-SAPF-CBO and CBO algorithms with other contemporary techniques; provides the solution to real-world manufacturing problems of optimizing multi pass milling and turning processes using CI-SPF, CI-SAPF and CI-SAPF-CBO approaches.

Offers fundamental theories and practical and more sophisticated applications of Evolutionary Computation in varied industries Provides insight into various platforms, paradigms, techniques, and tools used in Evolutionary Computation for diverse fields Presents an understanding related to optimization, performance tuning, virtualization, deployment models, and their applications Covers a variety of applications for social and essential models and is based on real life examples Useful for decision making based on optimized data through Evolutionary Computation in multi-dimensions