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I am having a hard time trying to make sense of the phrase "Scalable optimization", be it dynamic or not. I read from a few papers discussing that some global optimization solvers like BARON, ANTIGONE, etc. do not scale well with the number of scenarios.

I quote from "Languages and Tools for Optimization of Large−Scale Systems":

Model scalability means the granularity of the model behaviour should be easy to change, without the need to re-build the model.

My very basic understanding and experience with optimization is that optimization would not work well if scaling of the problem is not done properly, and computational time increases with problem size or dimension (large scale system). As to model scalability, I thought a model is built for a specific subject/process and its granularity/level of detail cannot be changed unless we rebuild it?

Can someone shed some light on this?

mathsnovice
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  • What does it mean to 'build' a model? – LinAlg Mar 25 '21 at 22:17
  • Is this a trick question? or should I have used the word construct or develop or create? For example, if I were to set up a model for a distillation column, I have the option of going easy with a shortcut method, or a detailed stage-wise calculation, or use a more complex thermodynamics model or a simpler one. – mathsnovice Mar 26 '21 at 00:14
  • Not a trick question. I just try to understand your question. The comment about BARON makes sense to me: how does the solution time scale with the instance size? For example, a model to solve TSP does not scale well. You cannot solve that by 'rebuilding the model'. The quote about granularity I don't get at all. Do they mean 'build a different model' instead of rebuilding the same model? – LinAlg Mar 26 '21 at 00:20
  • The quote about granularity is what I am hoping to get some expert's insight. Using the distillation column example, I will not be able to manipulate the level of detail of a (shortcut) model unless I build a completely different one using the complex method. I understand that for the TSP problem, if the size of TSP is big the solution time is definitely going to be huge. I also understand that scaling ensures some variables are not weighted more than others. So when someone talks about "optimisation methods that scale well with problem size", what is the idea behind it? – mathsnovice Mar 26 '21 at 00:38

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