Swarm Intelligence and Bio-Inspired Computation: 3. Lévy Flights and Global Optimization

Random walks play an important and central role in metaheuristic and stochastic optimization algorithms. The two key components of the search process in metaheuristic algorithms (MAs) are intensification and diversification. The overall efficiency of a metaheuristic optimization algorithm depends on a sound balance between these two components. In MAs, exploration is achieved by randomization in combination with a deterministic procedure. In this way, the newly generated solutions are distributed as diversely as possible in the problem search space. In most of the MAs, randomization is realized using a uniform or Gaussian distribution. However, this is not the only way to achieve randomization. In recent years, the use of Lévy distribution has emerged as an alternative to uniform or Gaussian distributions. In view of these details, this chapter focuses on using Lévy flights (LFs) in the context of global optimization. A survey of the most important MAs using LFs to achieve intensification and diversification for solving global optimization problems is presented. The different components and concepts of Lévy-flight-based MAs are discussed and their similarities and differences are analyzed.