No abstract is provided for this article.
No abstract is provided for this article.
In nature-inspired metaheuristic algorithms, two key components are local intensification and global diversification, and their interaction can significantly affect the efficiency of a metaheuristic algorithm.However, there is no rule for how to balance these important components.In this paper, we provide a first attempt to give some theoretical basis for the optimal balance of exploitation and exploration for 2D multimodal objective functions.Then, we use it for choosing algorithm-dependent parameters.Finally, we use the recently developed eagle strategy and cuckoo search to solve two benchmarks so as to confirm if the optimal balance can be achieved in higher dimensions.For multimodal problems, computational effort should focus on the global explorative search, rather than intensive local search.We also briefly discuss the implications for further research.
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:
Most optimization problems rely heavily on simulations to evaluate design solutions according to a set of design criteria under stringent constraints. While an inverse problem may also rely on simulation-driven methods, it can sometimes be viewed more properly as a constrained optimization problem because the main aim of inversion is to find the best parameter estimates so as to minimize the differences between predicted results and observations. In this paper, we will take a unified approach to inversion and optimization. We use the latest cuckoo search to solve inverse problems and shape optimization in heat transfer applications. Simulation results show that cuckoo search is also very efficient for inversion.
No abstract is provided for this article.
No abstract is provided for this article.
No abstract is provided for this article.
Most optimization problems rely heavily on simulations to evaluate design solutions according to a set of design criteria under stringent constraints. While an inverse problem may also rely on simulation-driven methods, it can sometimes be viewed mor
