New Optimization Algorithms in Physics


Book Description

Many physicists are not aware of the fact that they can solve their problems by applying optimization algorithms. Since the number of such algorithms is steadily increasing, many new algorithms have not been presented comprehensively until now. This presentation of recently developed algorithms applied in physics, including demonstrations of how they work and related results, aims to encourage their application, and as such the algorithms selected cover concepts and methods from statistical physics to optimization problems emerging in theoretical computer science.




Optimization Algorithms in Physics


Book Description

The past few years have witnessed a substantial growth in the number of applications for optimization algorithms in solving problems in the field of physics. Examples include determining the structure of molecules, estimating the parameters of interacting galaxies, the ground states of electronic quantum systems, the behavior of disordered magnetic materials, and phase transitions in combinatorial optimization problems. This book serves as an introduction to the field, while also presenting a complete overview of modern algorithms. The authors begin with the relevant foundations from computer science, graph theory and statistical physics, before moving on to thoroughly explain algorithms - backed by illustrative examples. They include pertinent mathematical transformations, which in turn are used to make the physical problems tractable with methods from combinatorial optimization. Throughout, a number of interesting results are shown for all physical examples. The final chapter provides numerous practical hints on software development, testing programs, and evaluating the results of computer experiments.




A New Meta-heuristic Optimization Algorithm Based on the String Theory Paradigm from Physics


Book Description

This book focuses on the fields of nature-inspired algorithms, optimization problems and fuzzy logic. In this book, a new metaheuristic based on String Theory from Physics is proposed. It is important to mention that we have proposed the new algorithm to generate new potential solutions in optimization problems in order to find new ways that could improve the results in solving these problems. We are presenting the results for the proposed method in different cases of study. The first case, is optimization of traditional benchmark mathematical functions. The second case, is the optimization of benchmark functions of the CEC 2015 Competition and we are also presenting results of the CEC 2017 Competition on Constrained Real-Parameter Optimization that are problems that contain the presence of constraints that alter the shape of the search space making them more difficult to solve. Finally, in the third case, we are presenting the optimization of a fuzzy inference system, specifically for finding the optimal design of a fuzzy controller for an autonomous mobile robot. It is important to mention that in all study cases we are presenting statistical tests in or-der to validate the performance of proposed method. In summary, we believe that this book will be of great interest to a wide audience, ranging from engineering and science graduate students, to researchers and professors in computational intelligence, metaheuristics, optimization, robotics and control.




Optimization Algorithms


Book Description

This book presents examples of modern optimization algorithms. The focus is on a clear understanding of underlying studied problems, understanding described algorithms by a broad range of scientists and providing (computational) examples that a reader can easily repeat.




Experimental Methods for the Analysis of Optimization Algorithms


Book Description

In operations research and computer science it is common practice to evaluate the performance of optimization algorithms on the basis of computational results, and the experimental approach should follow accepted principles that guarantee the reliability and reproducibility of results. However, computational experiments differ from those in other sciences, and the last decade has seen considerable methodological research devoted to understanding the particular features of such experiments and assessing the related statistical methods. This book consists of methodological contributions on different scenarios of experimental analysis. The first part overviews the main issues in the experimental analysis of algorithms, and discusses the experimental cycle of algorithm development; the second part treats the characterization by means of statistical distributions of algorithm performance in terms of solution quality, runtime and other measures; and the third part collects advanced methods from experimental design for configuring and tuning algorithms on a specific class of instances with the goal of using the least amount of experimentation. The contributor list includes leading scientists in algorithm design, statistical design, optimization and heuristics, and most chapters provide theoretical background and are enriched with case studies. This book is written for researchers and practitioners in operations research and computer science who wish to improve the experimental assessment of optimization algorithms and, consequently, their design.




Optimization Algorithms on Matrix Manifolds


Book Description

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.




Stochastic Optimization


Book Description

This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.




Recent Trends In Chaotic, Nonlinear And Complex Dynamics


Book Description

In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.




New Optimization Algorithms and their Applications


Book Description

New Optimization Algorithms and Applications: Atom-Based, Ecosystem-Based and Economics-Based presents the development of three new optimization algorithms - an Atom Search Optimization (ASO) algorithm, an Artificial Ecosystem-Based Optimization algorithm (AEO), a Supply Demand Based Optimization (SDO), and their applications within engineering. These algorithms are based on benchmark functions and typical engineering cases. The book describes the algorithms in detail and demonstrates how to use them in engineering. The title verifies the performance of the algorithms presented, simulation results are given, and MATLAB® codes are provided for the methods described. Over seven chapters, the book introduces ASO, AEO and SDO, and presents benchmark functions, engineering problems, and coding. This volume offers technicians and researchers engaged in computer and intelligent algorithm work and engineering with one source of information on novel optimization algorithms. Presents three novel optimization algorithms for engineering Gives various applications and design examples for each algorithm Provides simulation results to verify algorithm performance Includes MATLAB® codes for optimization methods Describes the mathematical models needed




Nature-Inspired Optimization Algorithms


Book Description

Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective optimization. This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications. Researchers and engineers as well as experienced experts will also find it a handy reference. Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literature Provides a theoretical understanding as well as practical implementation hints Provides a step-by-step introduction to each algorithm