Decision Making

Decision Making:1:Genetic Algorithms, Noise, and the Sizing of Population:David E. Goldberg, Kalyanmoy Deb, James H. Clark:December 1991:Department of General Engineering, University of Illinois at Urbana-Champaign

Decide What?BBsBB (fitness BBpopulationcopies)population sizepopulation size?Time vs. Quality

()population-sizing equationconservativepopulation sizeSGASGAcomplexity

GA works GA worksworksGA

GA workscondition by GoldbergKnow what the GA is processing: building blocksEnsure an adequate supply of building blocks either initially or temporally(what supply?)Ensure the growth of necessary building blocks(selection)Ensure the mixing of necessary building blocks(crossover)Solve problems that are building-blocks tractable or recode them so they areDecide well among competing building blocks population

Decision Making(1)String vs. Schemata(by Holland) -armed bandit problem(by Holland and De Jong)

Decision Making(2)Noise in the decision process(by Grefenstette & Fitzpatrick)mGAs( Goldberg, Deb, Korb):reduced the building-block noise face initially during selection and recombination within a simple GA What difference between De Jong and GoldbergInstead of worrying about the form of the optimal allocation of trials over all function evaluations as Holland and De Jong did originally, we simply require that the error in building-block decision makingGoldbergGApopulation sizingWhat is noise?In common use, the word noise means unwanted sound or noise pollution.() Noise can block, distort, or change the meaning of a message in both human and electronic communication.GABB

Population sizing equation

Collateral noise(1)

1.H1H2competing BB2.fH1fH2mean fitness3.f() H2fitnessnoise

convolution:fsample H2fitnesssample H1fitnessCollateral noise(2)The convolution of two normal distributions is itself normal: the mean of the convolution is calculated as the difference in the means of the two individual distributions and the variance of the convolution is simply the sum of the individual variancesSignal difference:The mean variance of the two building block: The probability of making an error on a single trial of each schema may be calculated by finding the probability such that :

The ordinate of a unit, one-sided, normal deviateCollateral noise(3)

251fCollateral noise(4)

n=n/k (n:population, k:competing schemata) constant c :

Other sources of NoiseSources: fitness function, selection processThe ith source of noise( ) with magnitude:relative noise coefficient:

The total additional relative noise coefficient:

population sizing:

Specializing the sizing equation(1)String of length l over alphabets of cardinality xThe best BB order: k