i work in a research team to solve a multi objective engineering problem and i concentrate on NSGA-II algorithm ,but now i stuck i need to understand how SBX crossover work with numerical example so i can implement it or even if there's a ready made code i can adapt according to our problem but first i need to see numerical example so i can go on,any resource available for that i only found a presentation on http://www.slideshare.net/ but only equations no example.
These days I also spent more time on SBX coz it is a better choice for crossover in number coding problem. I checked the original paper and the slides you pointed out. Although I have not known the complete process of SBX, I can tell you what I have learnt which maybe help you know SBX in a further step.
1:The idea is from binary coding with single point crossover. For instance, the parent chromosome p1 and p2, their children c1 and c2.
2:In binary coding, it has the property: (p1+p2)/2=(c1+c2)/2. We denote |(c1-c2)/(b1-b2)| as beta, and b is sometimes equaled to 1 according to the simulation.
3:When we use this idea with number coding, this property should be retained, for which, an solution for c1 and c2 in number coding:
c1 = (p1+p2)/2 +0.5*beta(p1-p2) and c2 = (p1+p2)/2-0.5*beta(p1-p2) and p1>p2 In further, the value of beta is our goal.
All above are what I learn from SBX. Sorry for it is not complete!