[@karannchew2534]

Notes for my future revision.
Objective: Use Schema Theorem to prove the Genetic Algorithm will approach an optimal solution.
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Fitness
= how good the solution is
= How close the values of variables meet the optimisation objective.
Proportionate Selection = Probability is proportional to fitness score.
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*_REPRODUCTION_*
N = population size
O(H) = No. of fixed positions (bits) in schema H.
δ(H) = Defining Length of Schema H = Distance between the first and last position in a string.
m(H,t) = No. of strings (chromosomes) belonging to Schema H at t_th generation.
f(H) = Average fitness of a strings of a schema H at t_th generation = Schema overall fitness
Σf = Total fitness (of population at t_th generation)
No. of string in the next generation
= m(H,t+1)
= m(H,t) x N x f(H) / Σf
= m(H,t) x f(H) / f_bar,
where
f_bar = Average fitness of the population
= Σf / N
= Total fitness of population of this generation / Population size
= Average fitness of a string of the population
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*_CROSSOVER (Single Point)_*
Probability of a schema is destroyed
= Probability a crossover happen within defining length
= p_c x δ(H)/(L-1)
where
p_c = Prob of a crossover
δ(H) = defining length of schema H
L = total length
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*_MUTATION (bit wise)_*
p_s
= Probability a schema survive a mutation
= (1-p_m) x (1-p_m)... for number of fixed position of schema
= (1-p_m)^O(H)
≈ 1 - O(H) x p_m as p_m