CODEWITHSUNDEEP
algorithmoptimizationmathematical-optimizationevolutionary-algorithm
Cord Kaldemeyer
Cord Kaldemeyer

Reputation: 6917

Impact of fitness function domain selection in multi-objective evolutionary optimization

I am using evolutionary algorithms e.g. the NSGA-II algorithm to solve unconstrained optimization problems with multiple objectives.

As my fitness functions sometimes have very different domains (e.g. f1(x) generates fitness values within [0..1] and f2(x) within [10000..10000000]) I am wondering if this has an effect on the search behaviour of the selected algorithm.

Does the selection of the fitness function domain (e.g. scaling all domains to a common domain from [lb..ub]) impact the solution quality and the speed of finding good solutions? Or is there no general answer to this question?

Unfortunately, I could not find anything on this topic. Any hints are welcome!

Upvotes: 2

Views: 191

Answers (2)

Julian
Julian

Reputation: 506

I have just come across your question and I have to disagree with the previous answer. If you read the paper carefully you will see that the crowding distance is supposed to be calculated in the normalized objective space. Exactly for the reason that one objective shall not dominating another.

My PhD advisor is Kalyanmoy Deb who has proposed NSGA-II and I have implemented the algorithm by myself (available in our evolutionary multi-objective optimization framework pymoo). So I can state with certainty that normalization is supposed to be incorporated into the algorithm. If you are curious about a vectorized crowding distance implementation feel free to have a look at pymoo/algorithms/nsga2.py in pymoo on GitHub.

Upvotes: 0

Dario Izzo
Dario Izzo

Reputation: 320

Your question is related to the selection strategy implemented in the algorithm. In the case of the original NSGA II, selection is made using a mixture of pareto rank and crowding distance. While the pareto rank (i.e. the non dominated front id of a point) is not changing scaling the numerical values by some constant, the crowding distance does.

So the answer is yes, if your second objective is in [10000 .. 10000000] its contribution to the crowding distance might be eating up the one of the other objective.

In algorithms such as NSGA II units count!

Upvotes: 4

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