SCHEMATA THEOREM (Holland)

SCHEMATA THEOREM (Holland). h(i) raw fitness for population sample i f(i) = normalized fitness f(i) = h(i)/Σh(i) A schema denotes a set of substrings that have identical values at certain loci: 1#101 = m(S,t) number of scheme exemplars in pop at generation t

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• selection
• fitness proportional
• variable selection
• feature selection
• schemata theorem holland
• average schemata grow exponentially

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SCHEMATA THEOREM (Holland)

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1. SCHEMATA THEOREM (Holland) • h(i) raw fitness for population sample i • f(i) = normalized fitness f(i) = h(i)/Σh(i) • A schema denotes a set of substrings that have identical • values at certain loci: 1#101 = • m(S,t) number of scheme exemplars in pop at generation t • Number of schema of individual S present in next generation is • proportional to chance of an individual being picked that has • the schema according to: • m(S,t+1) = m(S,t) n f(S)/Σf = m(S,t) f(S)/fave= m(S,t) fave(1+c) • m(S,t+1) = m(S,0) (1+c)t • Better than average schemata grow exponentially
2. Partially Mapped Crossover
3. Initial Population Evaluation Fitness proportional Crossover Parents Tournament Selection Selected Population Mutation Rank selection Parents Offspring Elitist strategy Evaluation Next Generation Make sure that best individual survives Genetic Algorithm cycle
4. Note: In the plot, fitnesses are plotted as (1-R2) and The problem can be thought as a minimization.
5. Source: A. Yasri andD. Hartsough, Toward an Optimal Procedure for Variable Selection and QSAR Model Building J. Chem. Inf. Comput. Sci. 2001 Vol. 41, No.5, pp. 1218-1227.
6. Search space in feature selection A data set with 10 features

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