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ml-recall

#building-blocks

1 question from Genetic Algorithms

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Question 1: Short answer

hardAI-checkedGenetic Algorithms

Holland's schema theorem states

E⁡[m(H,t+1)]≥m(H,t) f(H)at (1−p),p=δ(H)l−1 pc+o(H) pm,\operatorname{E}[m(H, t+1)] \ge \frac{m(H, t)\, f(H)}{a_t}\,(1 - p), \qquad p = \frac{\delta(H)}{l - 1}\,p_c + o(H)\,p_m,

where m(H,t)m(H, t) is the number of strings in schema HH at generation tt, f(H)f(H) their average fitness, ata_t the average fitness of the population, ll the string length, and pcp_c, pmp_m the crossover and mutation probabilities. For HH = ***1*0*1*** (l=11l = 11), m(H,t)=20m(H, t) = 20, f(H)=6f(H) = 6, at=4a_t = 4, pc=0.5p_c = 0.5 and pm=0.01p_m = 0.01, what lower bound does the theorem give for E⁡[m(H,t+1)]\operatorname{E}[m(H, t+1)]?

a number, 1 decimal