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 = {10101, 11101} 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

Partially Mapped Crossover

Genetic Algorithm cycle Initial Population Evaluation Selection Elitist strategy Next Generation Crossover Mutation Selected Population Parents Offspring Rank selection Fitness proportional Tournament Make sure that best individual survives

Note: In the plot, fitnesses are plotted as (1-R2) and The problem can be thought as a minimization.

Source: A. Yasri and D. 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.

Search space in feature selection A data set with 10 features