How it works Simulated Binary Crossover?

[MaxiPigna]

Hello,

I read this paper where it is presented the Simulated Binary Crossover. Unfortunately, I can not understand how it works and actually what is the idea behind this operator.

I ask this because I implemented an NSGA2 algorithm using this crossover operator, but I want to understand if it is useful for my problem. 

I am facing a feature weighting problem where individual's cells contain a value between 0 and 1. 

Moreover, why in your nsga2 example eta is set to 20, when I read that it is suggested a value between 2 and 5? 

[François-Michel De Rainville]

It simulates the exchange of bits between two (binary coded) floating point numbers without having to use a binary representation.

We use these values to reproduce Deb's NSGA-2 results. They are taken from Deb's code directly.

Cheers

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[MaxiPigna]

Sorry, but I do not understand what are the advantages of using this kind of crossover operator. Can you tell me someone?

Furthermore, do you think for a multi-objective GA is better to use SBX or I can prefer a common crossover operator like Uniform crossover?

[François-Michel De Rainville]

It has some advantages for some problems yes. Unlike uniform, it will generate genes that are close to the original ones but not exactly similar which can boost diversity in your population. Read the paper this is all explained...

I suggest you to try both and compare the average best over several runs.

[MaxiPigna]

In your opinion, what is the best way to compare the performance of two crossover operators? Should I look how the average best fitnesses increases over the generations?

[François-Michel De Rainville]

Look at the average best after a fixed number of evaluations.

Regards,

François-Michel