Lecture 5 Flashcards
What is the definition of Pareto Dominance?
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**
What is the definition of Pareto Optimal?
A solution is pareto optimal when a there is no other solution in the search space that dominates that solution.
What is the Pareto Set?
A set of all pareto optimal solutions.
What is the Pareto front?
A representation of the Pareto Set’s objective fitness values.
What is EMO?
Evolutionairy Multi-objective Optimalisation
How does EMO do selection?
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.
What is elitism in MEA?
When we have more solutions in the most dominant rank than space in the next generation. Some of these solutions are consequently discarded
Does EMO have true Elitsm?
No, discarding dominant solutions can cause the elitist front to become worse.
What is the downside of elitist archive
The archive can potentially grow large, and therfore be slower.
What is an approximation set?
The resulting solutions from executing your EA is called an approximation set.
When using the Euclidean Distance as an performance indicator, what can be concluded from D _PF→S (S)
Measure of proximity as well as diversity
What are Performance indicators?
A function that produces a single value that represents how good a MOEA is.
When using the Euclidean Distance as an performance indicator, what can be concluded from D _S→PF (S)
Measure of proximity
What type of performance indicators are there?
- Euclidean distance
- Front Spread (diversity)
- Front Occupation (proximity)
How can you determine the value of Front Spread from a graph
A complicated formula, that basically comes down to having the better diversity.
How can you determine the value of Front Occupation from a graph?
Number of solutions in approximation set
How can you decide on the better approximation set?
Undecidable, even when one seems favorable.** Unless **all four of the performance indicators are preferencing the same Aprroximation set.
In EMO, how can we bias the fitness evaluation?
By using exploitatoin and exploration
In EMO, what part of the EA process is bias when using exploitation?
Selection and replacement
In EMO, what part of the EA process is bias when using exploration?
variation
In EMO, how can you apply Exploitation of proximity?
- Selection pressure towards the Pareto front
- Select non-dominated solutions (e.g. ranking, counting)
In EMO, how can you apply Exploitation of diversitiy?
- Selection pressure towards diversity allong the non-dominated front
In EMO, how can you apply Exploration of proximity?
◮ 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
In EMO, how can you apply Exploration of diversity?
◮ 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
In EMO exploitation, which is a more important comparison key: proximity or diversity?
Proximity, we wouldn’t really care for awnsers that are very far apart
In EMO exploration, which is a more important comparison key: proximity or diversity?
Both are equally important
Why do we often (want to) apply clustering to EMO?
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.
What do we expect when we alow for a large number of clusters in our EMO?
We lose diversity in the approximation set.
In EMO, what is parameterized balancing?
It is when we apply a **selection operator ** that can pressure both diversity and proximity by using a single parameter.
What are the selection steps for parameterized balancing?
- Compute domination count for all solutions (times dominated)
- Select the ⌊δτn⌋ solutions (δ ∈ [1, 1/τ ]) with the lowest count
- If there are more solutions with a count of 0, include them
- Select final ⌊τ n⌋ solutions using nearest neighbor heuristic
Example:
n = 22, δ = 5/3 , τ = 3/10
⌊δτ n⌋ = 11
⌊τ n⌋ = 6
What is Multi objective Optimalisation with Scalarization techniques?
It is a(nother) way to optimize multi objective problems where we try to find solutions that are “closest” the the Utopian point.
What is the Utopian point and how is it obtained.
The utopian point is used in distances based scalarization optimalisation. It is constructed out of the best possible value for each individual objective
What would happen if the Utopian point did exist in the parameter space?
Then it would not be a multi-objective problem any more: because all objectives have been minimalised.
In distance based scalarization, what is the manhatten distance? (and its symbol)
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.
In distance based scalarization, what is the Euclidean distance? (and its symbol)
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.
In distance based scalarization, what is the Tchebycheff distance? (and its symbol)
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.
How do weights affect distance based scalarizations?
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.
What is the biggest draw back for manhattan and euclidean based scalarizatins
It is not able to find concave pareto fronts.
What is weakly dominant
When the Pareto front contains all the solutions in the populations.
(there are no dominated solutions)
What is weighted augmented Tchebycheff scalarization and what does it solve?
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.**
Explain how Evolutionary Local Search works
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
What is the downside of Evolutionary Local Search?
It still needs to repeat optimalisation for different weights in order to find multiple (biased) solutions.
When is the Hypervolume pareto compliant?
Iff for a given solution set the HV is maximal, it means that that approximation set is a subset of the Pareto set.
How can the hypervolume be used directly for optimalisation?
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.
What problem does Uncrowded Hypervolume solve?
“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.
Why do we need to devide the euclidean distance by the set size in UHV?
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.
What is a better weighted aggregated pareto; convex or concave
convex
What is a solution for the expending elitist archive?
discretize objective space: Store at most one solution per discretization box
