Second Order Behavior Of Pattern Search
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A Derivative-free Two Level Random Search Method for Unconstrained Optimization
The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.
Derivative-Free and Blackbox Optimization
This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix.
Metaheuristic Algorithms: New Methods, Evaluation, and Performance Analysis
This book encompasses three distinct yet interconnected objectives. Firstly, it aims to present and elucidate novel metaheuristic algorithms that feature innovative search mechanisms, setting them apart from conventional metaheuristic methods. Secondly, this book endeavors to systematically assess the performance of well-established algorithms across a spectrum of intricate and real-world problems. Finally, this book serves as a vital resource for the analysis and evaluation of metaheuristic algorithms. It provides a foundational framework for assessing their performance, particularly in terms of the balance between exploration and exploitation, as well as their capacity to obtain optimal solutions. Collectively, these objectives contribute to advancing our understanding of metaheuristic methods and their applicability in addressing diverse and demanding optimization tasks. The materials were compiled from a teaching perspective. For this reason, the book is primarily intended for undergraduate and postgraduate students of Science, Electrical Engineering, or Computational Mathematics. Additionally, engineering practitioners who are not familiar with metaheuristic computation concepts will appreciate that the techniques discussed are beyond simple theoretical tools because they have been adapted to solve significant problems that commonly arise in engineering areas.