Lecture 8

Question 1

What does FOS stand for?

Answer 1

Family of Subsets

Question 2

What is the definition of a FOS?

Answer 2

FOS ℱ is a subset of powerset of 𝑆, i.e.,
ℱ ⊆ ℘(𝑺) where ℱ = {𝑭0, 𝑭1, … }

Where the powerset is the set of all possible subsets, including the full and null set. And 𝑺 is the set of indices of the solution variables

Question 3

What is the linkage set?

Answer 3

A FOS in which every variable of the genotype is in at least one FOS subset.

Question 4

What is the univariate FOS?

Answer 4

Every variable is in its own individual FOS subset; independent from other other variable

Question 5

What is the MP FOS?

Answer 5

The Marginal Product FOS is a FOS where every variable is in only one FOS subset.

Such that every FOS subset is independent from each other.

Question 6

What is a LT FOS?

Answer 6

• The linkage tree (LT) FOS is a hierarchical structure
• The group of all variables is in there
• For any subset 𝑭𝑖 with more than one variable, there
  .are subsets 𝑭𝑗 and 𝑭𝑘 such that:
  𝑭𝑗 ∩ 𝑭𝑘 = ∅,
  𝑭𝑗 < 𝑭𝑖 ,
  𝑭𝑘 < 𝑭𝑖 ,
  𝑎𝑛𝑑 𝑭𝑗 ∪ 𝑭𝑘 = 𝑭𝑖

Question 7

How does FOS do variation?

Answer 7

Recombination of two solutions via crossover.

Question 8

For which type of FOS does crossover not make sense and why?

Answer 8

LT FOS; The hierarchical structure of LT makes it so that the crossovers that happened in the lower tree levels are overwritten by the larger subsets. This makes the crossover very complex to understand and therefor not useful in practise. Also large probability the tree is no longer valid because we dont evaluate during crossover.

Question 9

How can we implement FOS subsets for EDA?

Answer 9

We have a probability table for each subset in the FOS.

Question 10

Why is the size of the probability table of the FOS subsets for EDA equal to 2 ^|𝑭𝑖|− 1 ?

Answer 10

The probability of each combination of FOS subsets must be represented (hence binary part). The last probability can be calculated using 1 - sum, so it does not need to be stored.

Question 11

How is the probability table for FOS-based EDA determined?

Answer 11

Maximum Likelihood (ML) aka frequency counting.

Question 12

Consider univariate FOS in GA and EDA.
Is there any difference?

Answer 12

Variables treated completely independently only in EDA. Whereas for GA it depends which solutions are the parents of the offspring. This introduces weak dependencies between the variables and the variation operator.

Question 13

What does ECGA stand for?

Answer 13

Extended Compact Genetic Algorithm

Question 14

What kind of EA is ECGA an example of?

Answer 14

MP FOS learning

Question 15

How does ECGA work?

Answer 15

• Each MP structure is scored.
• Choose probability distribution with the best score
• We then use greedy search, because prob. model is not our goal so using greedy is plausible
• Then use standard MPM:
• Start joining univariate variables until no improvement is found

Question 16

What is MDL?

Answer 16

Minimum Discription Length:
A measure of complexity.

Question 17

What are the two subcomponents of MDL?

Answer 17

1. Compressed population complexity: how good is the prob. distribution est.
2. Model complexity: number of bits required to store all parameters of the model

Question 18

Do we want to maximize or minimize MDL?

Answer 18

Minimize

Question 19

Explain why LT FOS is both dependent and independent

Answer 19

The Linking Tree acts as a path through dependence space, from univariate to joint.

Question 20

What does OMEA stand for?

Answer 20

Optimal Mixing EA

Question 21

What is the main characteristic of OMEA?

Answer 21

It uses intermediate function evaluations inside variation operator

Question 22

What is ROM?

Answer 22

Recombinative OM: GA-like where you select a single solution to perform OM with

Question 23

What is GOM

Answer 23

Gene-pool OM: EDA-like where you select a new solution for each substructure in OM.

Question 24

Does OMEA ensure elitism?

Answer 24

Yes, because it only improves solution

Question 25

Explain the psuedo code for ROMEA

Answer 25

You randomly select two parents, p0 and p1.
Then you make two copies who act as the offspring: o0 and o1.
For each FOS, you crossover o1 and o2 (for that FOS) and see if the fitness of o0 improved.
If o0 improved, keep the change otherwise revert.
At the end, only return o0.

Question 26

Explain the psuedo code for GOMEA

Answer 26

You first create a single offspring from a single parent (copy).
Then you iterate over the amount of FOS/linkage sets.
For every FOS you randomly pick a new parent and crossover for that specific FOS.
If there was an improvement on the offspring, keep the change.

Question 27

Why do OMEAs require much smaller populations?

Answer 27

In order to sample every possible genotype you must sample 𝑛 ≥ 2^ℓ.
However for OMEA, we only need to have sampled every block/FOS once, which is 𝑛 ≥ 2^𝑘.

Where k is block length.

Question 28

Give an example of why choosing a population size of 2 will not be able to find the best solution. (OneMAx)

Answer 28

Due to the crossover operator and the selection process, it could happen that f.i. the 1 one a specific variable gets lost.
This is called a Unrecoverable problem !!! This is solved using GOMEA

Question 29

What are the four parallel models for Evo Computation (EC)

Answer 29

1. ‘Embarrassingly’ parallel
2. Parallel evaluation of the population
3. Parallel evaluation of single solution
4. Parallel Island model

Question 30

Describe ‘embarrassingly’ parallel

Answer 30

Perform N runs in paralles, which will result in N outcomes.
Then you can do one final evaluation of the N outcomes to reduce it to one coutcome.

Question 31

Describe Parallel evaluation of the population.

Answer 31

Generally the fitness function requires the most computation power, hence it makes sence to speed this up using parallelism.

Question 32

What is required fo parallel evaluation of single solution?

Answer 32

Requires knowledge about optimization problem (e.g. GBO setting)

Question 33

Explain the general Parallel Island Model.

Answer 33

Where there are multiple EAs working simulteneously, that migrate parts of the population to other EAs at a certain point.

Question 34

When is Parallel Island Model Homogeneous?

Answer 34

Each of N islands is the
same EA with identical parameters.

Question 35

When is Parallel Island Model Heterogeneous?

Answer 35

Each of N islands my be a different EA with different parameters.

Question 36

How does the migration size (q) influence our diversity and convergence rate?

Answer 36

• High q: Islands converge to same solution; large communication cost.
• Low q: Slower convergence; more diversity.

Question 37

Where does VIG stand for

Answer 37

Variable Interaction Graph