Reinterpreting No Free Lunch

Rowe, Jon; Vose, Michael D.; Wright, Alden H.

doi:10.1162/evco.2009.17.1.117

Cited by 29 publications

(20 citation statements)

References 6 publications

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“…A different approach to NFL showed that the theorem also holds for arbitrary domains and co-domains [28]. In contrast, other studies [29,30] showed that the NFL theorem does not hold in continuous domains although its soft form of NFL holds in countably infinite domains.…”

Section: Discrete Vs Continuous Spacementioning

confidence: 92%

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

Mavrovouniotis

Yang

2017

Swarm and Evolutionary Computation

492

213

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Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given.

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Section: Discrete Vs Continuous Spacementioning

confidence: 92%

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

Mavrovouniotis

Yang

2017

Swarm and Evolutionary Computation

492

213

View full text Add to dashboard Cite

show abstract

“…From the no-free-lunch (NFL) theorems for optimization, that have already been widely discussed from various points of view (Wolpert and Macready 1997;Köppen et al 2001;Schumacher et al 2001;Droste et al 2002;Whitley and Rowe 2008;Rowe et al 2009;Duéñez-Guzmán and Vose 2013), it is well known that the performance of all heuristic optimizers averaged over all problems is equal. Although it is generally understood that only a very small fraction of "all problems" [for a detailed discussion of what "all problems" means, see Wolpert and Macready (1997) and Schumacher et al (2001)] is of interest to anyone Toussaint 2003, 2004), it is very unfortunate that the implications of the NFL are rarely considered and discussed when novel metaheuristics are proposed.…”

Section: Background: Recent Criticisms Of Optimization Metaheuristicsmentioning

confidence: 99%

Searching for structural bias in particle swarm optimization and differential evolution algorithms

Piotrowski

Napiorkowski

2016

Swarm Intell

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During the last two decades, a large number of metaheuristics have been proposed, leading to various studies that call for a deeper insight into the behaviour, efficiency and effectiveness of such methods. Among numerous concerns that are briefly reviewed in this paper, the presence of a structural bias (i.e. the tendency, not justified by the fitness landscape, to visit some regions of the search space more frequently than other regions) has recently been detected in simple versions of the genetic algorithm and particle swarm optimization. As of today, it remains unclear how frequently such a behaviour occurs in population-based swarm intelligence and evolutionary computation methods, and to what extent structural bias affects their performance. The present study focuses on the search for structural bias in various variants of particle swarm optimization and differential evolution algorithms, as well as in the traditional direct search methods proposed by Nelder-Mead and Rosenbrock half a century ago. We found that these historical direct search methods are structurally unbiased. However, most tested new metaheuristics are structurally biased, and at least some presence of structural bias can be observed in almost all their variants. The presence of structural bias seems to be stronger in particle swarm optimization algorithms than in differential evolution algorithms. The relationships between the strength of the structural bias and the dimensionality of the search space, the number of allowed function calls and the population size are complex and hard to generalize. For 14 algorithms tested on the CEC2011 realworld problems and the CEC2014 artificial benchmarks, no clear relationship between the strength of the structural bias and the performance of the algorithm was found. However, at least for artificial benchmarks, such old and structurally unbiased methods like Nelder-Mead algorithm performed relatively well. This is a warning that the presence of structural bias in novel metaheuristics may hamper their search abilities.

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“…We begin by summarizing the basic definitions of Black Box search algorithms, following notation used in [6].…”

Section: Black Box Algorithmsmentioning

confidence: 99%

Unbiased black box search algorithms

Rowe

Vose

2011

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

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We formalize the concept of an unbiased black box algorithm, which generalises the idea previously introduced by Lehre and Witt. Our formalization of bias relates to the symmetry group of the problem class under consideration, establishing a connection with previous work on No Free Lunch. Our definition is motivated and justified by a series of results, including the outcome that given a biased algorithm, there exists a corresponding unbiased algorithm with the same expected behaviour (over the problem class) and equal or better worst-case performance. For the case of evolutionary algorithms, it is already known how to construct unbiased mutation and crossover operators, and we summarise those results.

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Reinterpreting No Free Lunch

Cited by 29 publications

References 6 publications

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

Searching for structural bias in particle swarm optimization and differential evolution algorithms

Unbiased black box search algorithms

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