Lecture 3

Question 1

why do we do encoding and decoding in EA?

Answer 1

we need to map the problem-specific representation (phenotype space) to bitstrings (genotype space) and back
=> the variation operators act on genotypes, the phenotypes are evaluated

Question 2

how do you solve a problem defined over real values?

Answer 2

• subdivide a solution into n segments of equal length
• decode

Question 3

what is exploration in EA?

Answer 3

discovering promising areas in the search space, gaining information on the problem (crossover)

Question 4

what is exploitation in EA?

Answer 4

optimizing a promising area, using information (mutation)

Question 5

how does a genetic algorithm work?

Answer 5

• initialize the population
• evaluate the population
  WHILE criteria not met:
• select parents to mate
• crossover with probability p_c => children
• mutation on children with probability p_m
• evaluate the children
• children form the new population

Question 6

what is a schema?

Answer 6

a partial instantiation of a string
H /in {0, 1, }
eg. 10000**10

Question 7

what is the order of a schema?

Answer 7

the number of instantiated elements in it:
o(H) = |{i|h_i /in {0,1}}|

Question 8

what is the defining length of a schema?

Answer 8

the length of the substring starting at the first and ending at the last instantiated element of the schema minus one
d(H) = max{i|h_i /in {0,1}} - min{i|h_i /in {0,1}}

Question 9

what is the probability that crossover does not occur within the defining length?

Answer 9

1 - (p_c * d(H) / (l - 1))

Question 10

what is the probability that the schema is not mutated?

Answer 10

(1 - p_m)^o(H)

Question 11

what is m(H,t)?

Answer 11

the expected number of instantiations of schema H in generation t

Question 12

what is the expected number of instantiations of H selected for crossover?

Answer 12

m(H,t) * f(H)/f_mean

Question 13

what were seen as explanations for the power of GAs?

Answer 13

implicit parallelism: a lot of different schemas are effectively processed in parallel by a GA

Building Blocks Hypothesis: GAs are able to detect short, low order and highly fit schemata and combine these into highly fit individuals

Question 14

what is the expected number of instances of a schema H in generation t+1?

Answer 14

m(H,t+1) = the expected number of instances of H selected for crossover * the probability that H is not destroyed by crossover * the probability that H is not destroyed by mutation