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Xin-She Yang - Nature-Inspired Optimization Algorithms

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Nature-Inspired Optimization Algorithms: summary, description and annotation

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Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The books 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

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Nature-Inspired Optimization Algorithms First Edition Xin-She Yang School of - photo 1
Nature-Inspired Optimization Algorithms

First Edition

Xin-She Yang

School of Science and Technology Middlesex University London, London

Table of Contents Introduction to Algorithms Abstract Algorithms are important - photo 2

Table of Contents
Introduction to Algorithms
Abstract

Algorithms are important tools for solving problems computationally. All computation involves algorithms, and the efficiency of an algorithm largely determines its usefulness. This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation. A brief history of recent nature-inspired algorithms for optimization is outlined in this chapter.

Keywords

Algorithm

Optimization

Nature-inspired

Metaheuristic

Self-organization

Optimization is paramount in many applications, such as engineering, business activities, and industrial designs. Obviously, the aims of optimization can be anythingto minimize the energy consumption and costs, to maximize the profit, output, performance, and efficiency. It is no exaggeration to say that optimization is needed everywhere, from engineering design to business planning and from Internet routing to holiday planning. Because resources, time, and money are always limited in real-world applications, we have to find solutions to optimally use these valuable resources under various constraints. Mathematical optimization or programming is the study of such planning and design problems using mathematical tools. Since most real-world applications are often highly nonlinear, they require sophisticated optimization tools to tackle. Nowadays, computer simulations become an indispensable tool for solving such optimization problems with various efficient search algorithms.

Behind any computer simulation and computational methods, there are always some algorithms at work. The basic components and the ways they interact determine how an algorithm works and the efficiency and performance of the algorithm.

This chapter introduces algorithms and analyzes the essence of the algorithm. Then we discuss the general formulation of an optimization problem and describe modern approaches in terms of swarm intelligence and bio-inspired computation. A brief history of nature-inspired algorithms is reviewed.

1.1 What is an Algorithm?

In essence, an algorithm is a step-by-step procedure of providing calculations or instructions. Many algorithms are iterative. The actual steps and procedures depend on the algorithm used and the context of interest. However, in this book, we mainly concern ourselves with the algorithms for optimization, and thus we place more emphasis on iterative procedures for constructing algorithms.

For example, a simple algorithm of finding the square root of any positive number or can be written as 11 starting from a guess solution - photo 3 or can be written as 11 starting from a guess solution say - photo 4, can be written as

11 starting from a guess solution say Here - photo 5 (1.1)

starting from a guess solution Picture 6, say, Picture 7. Here, Picture 8 is the iteration counter or index, also called the pseudo-time or generation counter .

This iterative equation comes from the rearrangement of in the following form 12 For example for with - photo 9 in the following form:

12 For example for with we have - photo 10 (1.2)

For example, for with we have 13 14 - photo 11 with we have 13 14 1 - photo 12, we have

13 14 15 We can see that - photo 13 (1.3)

14 15 We can see that after just five iterations or generations is - photo 14 (1.4)

15 We can see that after just five iterations or generations is very - photo 15 (1.5)

We can see that after just five iterations or generations is very close to the true value of - photo 16 after just five iterations (or generations) is very close to the true value of which shows that this iteration method is very efficient The reason that this - photo 17 which shows that this iteration method is very efficient.

The reason that this iterative process works is that the series converges to the true value due to the fact that 16 as - photo 18 converges to the true value due to the fact that 16 as However a good choice of the initial value - photo 19 due to the fact that

16 as However a good choice of the initial value will speed up the - photo 20 (1.6)

as Picture 21. However, a good choice of the initial value Picture 22 will speed up the convergence. A wrong choice of Picture 23 could make the iteration fail; for example, we cannot use Picture 24 as the initial guess, and we cannot use Picture 25 either since Picture 26 (in this case, the iterations will approach another root: Picture 27).

So a sensible choice should be an educated guess. At the initial step, if Picture 28 is the lower bound and Picture 29 is upper bound. If Picture 30, then Picture 31

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