Swarm-Based Metaheuristic Algorithms and No-Free-Lunch Theorems

Convergence analysis is another challenging area.One of the main difficulties concerning the convergence analysis of metaheuristic algorithms is that no generic framework exists, though 1 www.intechopen.com 2 Will-be-set-by-IN-TECH substantial studies have been carried out using dynamic systems and Markov processes.However, convergence analysis still remains one of the active research areas with many encouraging results (Clerc and Kennedy, 2002; Trelea, 2003;Ólafsson, 2006;Gutjahr, 2002).In optimization, there is a so-called 'no-free-lunch (NFL) theorem' proposed by Wolpert and Mcready (1997), which states that any algorithm will on average perform equally well as a random search algorithm over all possible functions.In other words, two algorithms A and B will on average have equal performance;' that is, if algorithm A performs better than B for some problems, then algorithm B will outperform A for other problems.This means that there is no universally superior algorithm for all types of problems.However, this does not mean that some algorithms are not better than other algorithms for some specific types of problems.In fact, we do not need to measure performance on average for all functions.More often, we need to measure how an algorithm performs for a given class of problems.Furthermore, the assumptions of the NLF theorem are not valid for all cases.In fact, there are quite a few no-free-lunch (NFL) theorems (Wolpert and Mcready, 1997;Igel and Toussaint, 2003).While in well-posed cases of optimization where its functional space forms finite domains, NFL theorems do hold; however, free lunches are possible in continuous domains (Auger and Teytaud, 2010; Wolpert and Mcready 2005;Villalobos-Arias et al., 2005).In this chapter, we intend to provide a state-of-the-art review of the recent studies of no-free-lunch theory and also free lunch scenarios.This enables us to view the NLF and free lunch in a unified framework, or at least, in a convenient way.We will also briefly highlights some of the convergence studies.Based on these studies, we will summarize and propose a series of recommendations for further research.Theory and New Applications of Swarm Intelligence www.intechopen.comSwarm-Based Metaheuristic Algorithms and No-Free-Lunch Theorems How to referenceIn order to correctly reference this scholarly work, feel free to copy and paste the following: