Xin-She Yang - Nature-Inspired Algorithms and Applied Optimization

School of Science and Technology, Middlesex University, London, NW4 4BT, UK

Xin-She Yang

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Optimization is important in many disciplines from engineering designs to business scheduling. Most such optimization problems require sophisticated optimization tools to solve, and there are a diverse spectrum of algorithms used in the literature, from traditional gradient-based algorithms and simplex methods to evolutionary algorithms and nature-inspired metaheuristic algorithms []. Most of such nature-inspired algorithms are based on swarm intelligence, intending to mimic the diverse characteristics in natural systems.

Though the literature in this area is quite vast, however, most studies are about various applications of algorithms. There is little literature on theoretical analysis of these algorithms. In fact, there is a significant gap between theory and practice. Most nature-inspired metaheuristic algorithms have successful applications in practice, but their theoretical analysis lags far behind. Apart from a few limited results about the convergence and stability concerning particle genetic algorithms [] and others, no theoretical analysis has been carried out about many other algorithms. It is often the case that we know these algorithms can work well in practice, but we rarely understand why they work. As a result, the applications can be a heuristic process itself and there is little information on how to improve them. Such lack of understanding may hinder the development of effective algorithms and some researchers even cast doubt on certain metaheuristics. Therefore, there is a strong need to do more rigorous mathematical analysis of nature-inspired algorithms.

Therefore, this book chapter will first introduce the fundamentals of algorithms and optimization in Sect. concludes with some discussions and open problems.

Optimization problems tend to be nonlinear with complex objective landscapes. The algorithms used for solving optimization can be traditional algorithms such as gradient-based methods and quadratic programming, evolutionary algorithms, heuristic or metaheuristic algorithms and various hybrid techniques.