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2023 | Book

Derivative-free DIRECT-type Global Optimization

Applications and Software


About this book

After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables.

Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels.

Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.

Table of Contents

Chapter 1. The Role of the DIRECT Algorithm in Derivative-Free Global Optimization
This chapter serves as an introduction to the global optimization problems explored within this book, offering a succinct overview of existing derivative-free techniques for global optimization. Specifically, we will position the DIRECT algorithm within other derivative-free global solution techniques, while also exploring its popularity and the diverse range of applications. By doing so, the readers will gain valuable insights into the significance and role of DIRECT in the context of solving complex global optimization challenges.
Linas Stripinis, Remigijus Paulavičius
Chapter 2. Development of DIRECT-Type Algorithms
The deterministic derivative-free DIRECT-type algorithms have gained significant recognition in the optimization community due to their simplicity and efficiency. This chapter provides a comprehensive review of the advancements made in the development of novel approaches and extensions of the DIRECT algorithm. Although the original DIRECT algorithm and its modifications were primarily designed for solving box-constrained global optimization problems, this chapter emphasizes the extensions that tackle general constraints, including hidden constraints and multi-objective cases. Additionally, the chapter sheds light on the existing research gaps in DIRECT-type algorithms that require further attention from the optimization community. By doing so, this chapter offers a thorough assessment of the progress made in DIRECT-type algorithms and highlights their significance in the context of derivative-free global optimization.
Linas Stripinis, Remigijus Paulavičius
Chapter 3. Applications and Software
This chapter discusses the software development aspects of DIRECT-type algorithms. It explores the implementation of both sequential and parallel versions of these algorithms. Various software tools, including the DIRECTGO toolbox and the GENDIRECT algorithmic framework, are discussed in detail. Furthermore, this chapter provides an overview of the DIRECTGOLib library, which includes a collection of global optimization tests and practical problems in the real world. We conduct a thorough examination of test benchmark cases and practical real-world optimization problems and offer a detailed implementation analysis. A significant portion of this chapter is devoted to a numerical benchmark study. As part of this study, various DIRECT-type algorithms are compared with state-of-the-art approaches, including stochastic ones, using different classes of problems, such as box-constrained test problems, problems with various constraints, and real-world practical problems.
Linas Stripinis, Remigijus Paulavičius
Derivative-free DIRECT-type Global Optimization
Linas Stripinis
Remigijus Paulavičius
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Print ISBN