Introduction to Nature-Inspired Optimization

George Lindfield, John Penny

• Publisher: Academic Press
• Year: 2017
• ISBN:
  9780128036662
• Topic: Mathématiques
• Subtopic: Mathématiques générales

Introduction to Nature-Inspired Optimization brings together many of the innovative mathematical methods for non-linear optimization that have their origins in the way various species behave in order to optimize their chances of survival. The book describes each method, examines their strengths and weaknesses, and where appropriate, provides the MATLAB code to give practical insight into the detailed structure of these methods and how they work.

Nature-inspired algorithms emulate processes that are found in the natural world, spurring interest for optimization. Lindfield/Penny provide concise coverage to all the major algorithms, including genetic algorithms, artificial bee colony algorithms, ant colony optimization and the cuckoo search algorithm, among others. This book provides a quick reference to practicing engineers, researchers and graduate students who work in the field of optimization.

• Applies concepts in nature and biology to develop new algorithms for nonlinear optimization
• Offers working MATLAB® programs for the major algorithms described, applying them to a range of problems
• Provides useful comparative studies of the algorithms, highlighting their strengths and weaknesses
• Discusses the current state-of-the-field and indicates possible areas of future development

Chapter 1

An Introduction to Optimization

Abstract

In this chapter we introduce the main classes of optimization problems and briefly describe some of the classical methods used to solve such problems. We discuss some of the limitations of classical methods and explain why methods of solution inspired by nature are attractive in solving global optimization problems.

Keywords

Linear programming; Non-linear optimization; Lévy distribution; Lagrange multiplier; Gradient search

1.1 Introduction

Optimization is the task of finding the best solutions to particular problems. These best solutions are found by adjusting the parameters of the problem to give either a maximum or a minimum value for the solution. For example, in a mathematical model of a manufacturing process we might wish to adjust the process parameters in order to maximize profit. In contrast, in the design of a steel structure required to carry a particular load, we might adjust the design parameters to minimize the weight of steel used, thereby minimizing the material cost. In both examples we are seeking to find an optimum solution. The function for which the optimum value is being sought is called the objective function, fitness function or cost function. The latter name arises because the purpose of optimization is often to reduce costs. Note that optimizing a function means finding the values of the function parameters to give the optimal or best value of the function.

In the following sections we discuss some of the classes of optimization problems and methods of solution.

1.2 Classes of Optimization Problems

Optimization problems can usefully be divided into two broad classes, linear and non-linear optimization. We begin by discussing linear optimization. As the name implies, both the objective function and the constraints are linear functions. Linear optimization problems are also referred to as linear programming problems. (Here programming does not refer to computer programming.) The general form of this problem is give by (1.1) thu...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• About the Authors
• Preface
• Acknowledgment
• Notation
• Chapter 1: An Introduction to Optimization
• Chapter 2: Evolutionary Algorithms
• Chapter 3: Particle Swarm Optimization Algorithms
• Chapter 4: The Cuckoo Search Algorithm
• Chapter 5: The Firefly Algorithm
• Chapter 6: Bacterial Foraging Inspired Algorithm
• Chapter 7: Artificial Bee and Ant Colony Optimization
• Chapter 8: Physics Inspired Optimization Algorithms
• Chapter 9: Integer, Constrained and Multi-Objective Optimization
• Chapter 10: Recent Developments and Comparative Studies
• Appendix A: Test Functions
• Appendix B: Program Listings
• Solutions to Problems
• References
• Index