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Evolutionary Algorithms > Lecture 5 > Flashcards

Lecture 5 Flashcards

1
Q

What is the definition of Pareto Dominance?

A

When the fitness of all the objectives of solution 1 are better (or equally as good) as those of solution 2. It is required that at least one objective the** fitness is better**

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2
Q

What is the definition of Pareto Optimal?

A

A solution is pareto optimal when a there is no other solution in the search space that dominates that solution.

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3
Q

What is the Pareto Set?

A

A set of all pareto optimal solutions.

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4
Q

What is the Pareto front?

A

A representation of the Pareto Set’s objective fitness values.

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5
Q

What is EMO?

A

Evolutionairy Multi-objective Optimalisation

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6
Q

How does EMO do selection?

A

By computing how many times a solution is dominated and then grouping those solutions in ranks.
Then you start (randomly) selecting individuals from the lowest (dominant) ranks upward.

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7
Q

What is elitism in MEA?

A

When we have more solutions in the most dominant rank than space in the next generation. Some of these solutions are consequently discarded

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8
Q

Does EMO have true Elitsm?

A

No, discarding dominant solutions can cause the elitist front to become worse.

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9
Q

What is the downside of elitist archive

A

The archive can potentially grow large, and therfore be slower.

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10
Q

What is an approximation set?

A

The resulting solutions from executing your EA is called an approximation set.

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11
Q

When using the Euclidean Distance as an performance indicator, what can be concluded from D _PF→S (S)

A

Measure of proximity as well as diversity

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12
Q

What are Performance indicators?

A

A function that produces a single value that represents how good a MOEA is.

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13
Q

When using the Euclidean Distance as an performance indicator, what can be concluded from D _S→PF (S)

A

Measure of proximity

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14
Q

What type of performance indicators are there?

A
  • Euclidean distance
  • Front Spread (diversity)
  • Front Occupation (proximity)
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15
Q

How can you determine the value of Front Spread from a graph

A

A complicated formula, that basically comes down to having the better diversity.

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16
Q

How can you determine the value of Front Occupation from a graph?

A

Number of solutions in approximation set

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17
Q

How can you decide on the better approximation set?

A

Undecidable, even when one seems favorable.** Unless **all four of the performance indicators are preferencing the same Aprroximation set.

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18
Q

In EMO, how can we bias the fitness evaluation?

A

By using exploitatoin and exploration

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19
Q

In EMO, what part of the EA process is bias when using exploitation?

A

Selection and replacement

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20
Q

In EMO, what part of the EA process is bias when using exploration?

A

variation

21
Q

In EMO, how can you apply Exploitation of proximity?

A
  • Selection pressure towards the Pareto front
  • Select non-dominated solutions (e.g. ranking, counting)
22
Q

In EMO, how can you apply Exploitation of diversitiy?

A
  • Selection pressure towards diversity allong the non-dominated front
23
Q

In EMO, how can you apply Exploration of proximity?

A

◮ Variation capable of producing new non-dominated solutions
◮ Must combine (good) features of good solutions to construct
better solutions
◮ Doesn’t differ much from single-objective variation operator design issues

24
Q

In EMO, how can you apply Exploration of diversity?

A

◮ If not able to produce diverse set of solutions, no diversity to
preserve in the first place
◮ Ideal: new non-dominated solutions spread across a wide range

25
Q

In EMO exploitation, which is a more important comparison key: proximity or diversity?

A

Proximity, we wouldn’t really care for awnsers that are very far apart

26
Q

In EMO exploration, which is a more important comparison key: proximity or diversity?

A

Both are equally important

27
Q

Why do we often (want to) apply clustering to EMO?

A

Because often within these clusters there is other logic happening that makes that specific cluster good, such that we dont apply the same reasoning in the entire search space.

28
Q

What do we expect when we alow for a large number of clusters in our EMO?

A

We lose diversity in the approximation set.

29
Q

In EMO, what is parameterized balancing?

A

It is when we apply a **selection operator ** that can pressure both diversity and proximity by using a single parameter.

30
Q

What are the selection steps for parameterized balancing?

A
  1. Compute domination count for all solutions (times dominated)
  2. Select the ⌊δτn⌋ solutions (δ ∈ [1, 1/τ ]) with the lowest count
  3. If there are more solutions with a count of 0, include them
  4. Select final ⌊τ n⌋ solutions using nearest neighbor heuristic

Example:
n = 22, δ = 5/3 , τ = 3/10
⌊δτ n⌋ = 11
⌊τ n⌋ = 6

31
Q

What is Multi objective Optimalisation with Scalarization techniques?

A

It is a(nother) way to optimize multi objective problems where we try to find solutions that are “closest” the the Utopian point.

32
Q

What is the Utopian point and how is it obtained.

A

The utopian point is used in distances based scalarization optimalisation. It is constructed out of the best possible value for each individual objective

33
Q

What would happen if the Utopian point did exist in the parameter space?

A

Then it would not be a multi-objective problem any more: because all objectives have been minimalised.

34
Q

In distance based scalarization, what is the manhatten distance? (and its symbol)

A

The manhattan distance is the sum of the one dimensional distances between the utopian point and the solution. It can be seen as a** straight line** in 2D. Its notation is L1.

35
Q

In distance based scalarization, what is the Euclidean distance? (and its symbol)

A

The Euclidean distance is the **root of the squared distances **between the utopian point and the solution. It can be seen as a circle in 2D. Its notation is L2.

36
Q

In distance based scalarization, what is the Tchebycheff distance? (and its symbol)

A

The tchebycheff distance is the largest single objective distance between the utopian point and the solution. It can be seen as a square in 2D. Its notation is L-infinite.

37
Q

How do weights affect distance based scalarizations?

A

It will deform the shape in which is measured from the Utopian point, as some objectives become more important. e.i. an circle will become more elipsoid.

38
Q

What is the biggest draw back for manhattan and euclidean based scalarizatins

A

It is not able to find concave pareto fronts.

39
Q

What is weakly dominant

A

When the Pareto front contains all the solutions in the populations.

(there are no dominated solutions)

40
Q

What is weighted augmented Tchebycheff scalarization and what does it solve?

A

It is still (visually) a square scalarization, however the furthest edge is now distorted such that ** it is pushed inwards.** It solves the weakly dominant possibility for normal Tchebycheff: because if there exist no medium solution, it will find the** locally optimal solutions for each objective.**

41
Q

Explain how Evolutionary Local Search works

A

It will apply single object optimalisations on each objective of the multi objective solution. We can evaluate if the “local” optimalisation is a improvement for the mutli objective solution by seeing if the L-norm has improved

42
Q

What is the downside of Evolutionary Local Search?

A

It still needs to repeat optimalisation for different weights in order to find multiple (biased) solutions.

43
Q

When is the Hypervolume pareto compliant?

A

Iff for a given solution set the HV is maximal, it means that that approximation set is a subset of the Pareto set.

44
Q

How can the hypervolume be used directly for optimalisation?

A

It can view solution sets as genotypes and then have the single objective to obtain the highest HV-value. Note: still an extra push is needed to improve dominant solutions/genotypes.

45
Q

What problem does Uncrowded Hypervolume solve?

A

“standard” HV will ignore dominated solutions in the set. UHV aims to drag these dominated solutions with the pareto set in order to improve the fitness of the set as a whole and converge faster.

46
Q

Why do we need to devide the euclidean distance by the set size in UHV?

A

It is essentially weighing down the impact of the ud on the UHV score. such that improvements of the pareto set are not prevented by the increase in eucledian distance.

47
Q

What is a better weighted aggregated pareto; convex or concave

A

convex

48
Q

What is a solution for the expending elitist archive?

A

discretize objective space: Store at most one solution per discretization box

Evolutionary Algorithms (9 decks)

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