NFL theorem is unusable on structured classes of problems

Weinberg, Benjamin; Talbi, El‐Ghazali

doi:10.1109/cec.2004.1330860

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…The search problem is to have all of these values match those of the target values, e.g. those in Equation 10. After the complete genome is examined, the total number of places where the perceptron output and the target differs is recorded.…”

Section: Analysis Of Endogenous Information In Evmentioning

confidence: 99%

“…However, the normalized histogram for ev in Figure 2A is far from Gaussian (see below for a demonstration). If the bias is large, it can push 10 This number includes the five bases that are not searched. all of the elements in S to be positive.…”

Section: Performance Analysis Of the Ev Perceptronmentioning

confidence: 99%

“…We have two empirical estimates of the upper bound on the endogenous information of the ev problem. In both cases we conservatively assume there is only one perceptron that generates an output matching a desired 16 bit target, like that of Equation 10.…”

Section: Performance Analysis Of the Ev Perceptronmentioning

confidence: 99%

“…Algorithms that conduct even moderately sized searches require external assistance to be successful. When such an algorithm produces apparently impressive results, conservation of information [1][2][3], including the No Free Lunch Theorem [4][5][6][7][8][9][10][11], dictates we are faced with one of two possibilities. The first is that the search problem under consideration is not as difficult as it first appears.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Vivisection of the ev Computer Organism: Identifying Sources of Active Information

Montanez¹,

Ewert²,

Dembski³

et al. 2010

BIO-Complexity

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ev is an evolutionary search algorithm proposed to simulate biological evolution. As such, researchers have claimed that it demonstrates that a blind, unguided search is able to generate new information. However, analysis shows that any non-trivial computer search needs to exploit one or more sources of knowledge to make the search successful. Search algorithms mine active information from these resources, with some search algorithms performing better than others. We illustrate these principles in the analysis of ev. The sources of knowledge in ev include a Hamming oracle and a perceptron structure that predisposes the search towards its target. The original ev uses these resources in an evolutionary algorithm. Although the evolutionary algorithm finds the target, we demonstrate a simple stochastic hill climbing algorithm uses the resources more efficiently. Cite as: Montañez G, Ewert W, Dembski WA, Marks II RJ (2010) A vivisection of the ev computer organism: Identifying sources of active information. BIO-Complexity 2010(3):1-6.

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Section: Analysis Of Endogenous Information In Evmentioning

confidence: 99%

Section: Performance Analysis Of the Ev Perceptronmentioning

confidence: 99%

Section: Performance Analysis Of the Ev Perceptronmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Vivisection of the ev Computer Organism: Identifying Sources of Active Information

Montanez¹,

Ewert²,

Dembski³

et al. 2010

BIO-Complexity

View full text Add to dashboard Cite

show abstract

“…Most criticisms of COI are aimed at the uniformity assumption imposed by Bernoulli's PrOIR [17], [32], [64] where the meaning of "absence of any prior knowledge" is often misconstrued. Indeed, once imposed, the uniformity assumption is robust on mappings of the search space.…”

Section: Conservation Of Informationmentioning

confidence: 99%

Bernoulli's principle of insufficient reason and conservation of information in computer search

Dembski

Marks

2009

2009 IEEE International Conference on Systems, Man and Cybernetics

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Abstract-Conservation of information (COI) popularized by the no free lunch theorem is a great leveler of search algorithms, showing that on average no search outperforms any other. Yet in practice some searches appear to outperform others. In consequence, some have questioned the significance of COI to the performance of search algorithms. An underlying foundation of COI is Bernoulli's Principle of Insufficient Reason 1 (PrOIR) which imposes of a uniform distribution on a search space in the absence of all prior knowledge about the search target or the search space structure. The assumption is conserved under mapping. If the probability of finding a target in a search space is p, then the problem of finding the target in any subset of the search space is p. More generally, all some-to-many mappings of a uniform search space result in a new search space where the chance of doing better than p is 50-50. Consequently the chance of doing worse is 50-50. This result can be viewed as a confirming property of COI. To properly assess the significance of the COI for search, one must completely identify the precise sources of information that affect search performance. This discussion leads to resolution of the seeming conflict between COI and the observation that some search algorithms perform well on a large class of problems.Index Terms-active information, Bernoulli's principle of insufficient reason, Bernoulli's principle of non-sufficient reason, Bertrand's paradox, conservation of generalization performance, conservation of information, endogenous information, equal distribution of ignorance, evolutionary search, no free lunch theorem, principle of indifference, uniform distribution

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A Generalized Hybrid Approach for the Synthesis of Uniform Amplitude Pencil Beam Ring-Arrays

Bucci

Pinchera

2012

IEEE Trans. Antennas Propagat.

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A generalized hybrid algorithm for the synthesis of uniform amplitude ring-arrays is introduced. The method exploits the analytical properties of the field radiated by a circular array in order to get advantages from the use of convex programming techniques. The method, aimed to the synthesis of circularly symmetric patterns, is very flexible and allows the use of different kind of feeds as well as stepped excitations. The synthesis procedure is demonstrated in the case of high-directivity pencil beam patterns

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NFL theorem is unusable on structured classes of problems

Cited by 7 publications

References 13 publications

A Vivisection of the ev Computer Organism: Identifying Sources of Active Information

A Vivisection of the ev Computer Organism: Identifying Sources of Active Information

Bernoulli's principle of insufficient reason and conservation of information in computer search

A Generalized Hybrid Approach for the Synthesis of Uniform Amplitude Pencil Beam Ring-Arrays

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