A Review of No Free Lunch Theorems, and Their Implications for Metaheuristic Optimisation

2017 ◽  
pp. 27-51 ◽  
Author(s):  
Thomas Joyce ◽  
J. Michael Herrmann
Keyword(s):  
Free Lunch ◽  
No Free Lunch Theorems ◽  
No Free Lunch

scholarly journals FREE LUNCH OR NO FREE LUNCH: THAT IS NOT JUST A QUESTION?

2012 ◽  
Vol 21 (03) ◽  
pp. 1240010 ◽  
Author(s):  
XIN-SHE YANG
Keyword(s):  
Convergence Analysis ◽  
Practical Importance ◽  
Metaheuristic Algorithms ◽  
Performance Evaluations ◽  
Algorithm Analysis ◽  
Free Lunch ◽  
Open Problems ◽  
No Free Lunch Theorems ◽  
And Performance ◽  
No Free Lunch

The increasing popularity of metaheuristic algorithms has attracted a great deal of attention in algorithm analysis and performance evaluations. No-free-lunch theorems are of both theoretical and practical importance, while many important studies on convergence analysis of various metaheuristic algorithms have proven to be fruitful. This paper discusses the recent results on no-free-lunch theorems and algorithm convergence, as well as their important implications for algorithm development in practice. Free lunches may exist for certain types of problem. In addition, we will highlight some open problems for further research.

Remarks on a recent paper on the "no free lunch" theorems

2001 ◽  
Vol 5 (3) ◽  
pp. 295-296 ◽  
Author(s):  
M. Koppen ◽  
D.H. Wolpert ◽  
W.G. Macready
Keyword(s):  
Free Lunch ◽  
No Free Lunch Theorems ◽  
No Free Lunch

scholarly journals Scientific Creativity: Discovery and Invention as Combinatorial

2021 ◽  
Vol 12 ◽  
Author(s):  
Dean Keith Simonton
Keyword(s):  
Scientific Explanation ◽  
Personality Characteristics ◽  
Free Lunch ◽  
Scientific Creativity ◽  
Developmental Experiences ◽  
The Arts ◽  
No Free Lunch Theorems ◽  
Current Article ◽  
Definition Of ◽  
No Free Lunch

Although scientific creativity has often been described as combinatorial, the description is usually insufficiently formulated to count as a precise scientific explanation. Therefore, the current article is devoted to elaborating a formalization defined by three combinatorial parameters: the initial probability p, the final utility u, and the scientist’s prior knowledge of that utility v. These parameters then lead logically to an 8-fold typology involving two forms of expertise, two irrational combinations, and four “blind” combinations. One of the latter provides the basis for the definition of personal creativity as c=(1−p)u(1−v), that is, the multiplicative product of originality, utility, and surprise. This three-criterion definition then has six critical implications. Those implications lead to a discussion of various combinatorial processes and procedures that include a treatment of the No Free Lunch Theorems regarding optimization algorithms as well as the creativity-maximizing phenomena of mind wandering and serendipity. The article closes with a discussion of how scientific creativity differs from artistic creativity. Besides the obvious contrasts in the ideas entering the combinatorial processes and procedures, scientific combinations, products, and communities strikingly differ from those typical of the arts. These differences also imply contrasts in developmental experiences and personality characteristics. In sum, the formal combinatorial analysis enhances our understanding of scientific creativity.

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