Introduction: Optimization and Metaheuristics Algorithms

Abstract

Present chapter embodies an introductory overview of optimization and metaheuristic algorithms. An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of Applied Mathematics. More generally, optimization consists of finding best available values of some objective function given a defined domain including a variety of different types of objective functions and different types of domains. One of the most significant trends in the field of optimization is the continually increasing emphasis on the interdisciplinary nature. Optimization has been a basic tool in all areas of Applied Mathematics, Engineering, Economics, Medical Science and other field of Sciences. The latest developments over the last few decades tend to use metaheuristic algorithms. In fact, a vast majority of modern optimization techniques includes metaheuristic algorithms. Metaheuristic algorithms such as Particle Swarm Optimization, Ant Colony Optimization, Artificial Bee Colony, Genetic Algorithm, Simulated Annealing, Cuckoo Search, Differential Evaluation, Biography Based Optimization and Harmony Search etc. are becoming very powerful in solving hard optimization problems and they have been applied in almost all major areas of science and engineering as well as industrial applications. In this chapter a general overview from the era of Fermat and Lagrange who introduced calculus based formulae to identify optima is given. Also, foundation of optimization provides a brief introduction to the underlying nature of optimization and the common approaches to optimization problems, random number generation, the Monte Carlo method, and the Markov chain Monte Carlo method. This chapter introduces all the major metaheuristic algorithms and a wide range of applications that use metaheuristic algorithms to solve challenging optimization problems while also introducing various modifications used for multi-objective optimization. Throughout this chapter, the author presents worked out examples and real world applications that illustrate the modern relevance of the topic. In addition, references to the current literature enable readers to investigate individual algorithms and methods in greater detail.