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From Thorsten Schaefer <em...@thorstenschaefer.de>
Subject Re: [math] Speeding up optimization problem?
Date Thu, 02 May 2013 18:09:47 GMT
```Thanks Thomas for the information so far. It took me some time to create an example w/o dependencies,
but here is one smaller problem which is self-contained:
http://pastebin.com/7QVMMBpA

Solving it on my laptop takes around 400ms, but as said, there are several hundred similar
problems to solve and that in many iterations as the input (resources and payoffs) change.
Note that I first solve the problem regularly using simplex, and then round the values to
booleans to get a heuristic - even though it might not be conform exactly to the restrictions
its a good enough heuristic for me; if there are faster heuristics for such a problem structure
I'd be happy to hear them, but as far as I know Integer programming is considered harder in
general.
One observation I also made is: if I calculate the problem and then do it again with the same
input value, giving the optimal solution as an initial guess, the runtime doesn't change at
all. I suspect that the initial guess does not have any impacts on the simplex solver, but
it might make sense to warn the user about it.

Cheers,

Thorsten

On Apr 30, 2013, at 2:43 AM, Thomas Neidhart <thomas.neidhart@gmail.com> wrote:

> On 04/28/2013 11:14 PM, Thorsten Schaefer wrote:
>> Hello,
>>
>> I just started using common math and have a performance issue with the optimization
algorithm, hoping to be able to speed it up in some way, even if this reduces the accuracy
of the results.
>>
>> My problem is as follows:
>> There are n resources and m actions that can be performed for each resource. Each
combination of action/resource has a specific payoff, which I want to maximize. I linearized
the data into rows of size (n*m). An index i has the semantics of resource=n/i and action=n%i.
Each entry in a row must be non-negative, so I added a the respective constraint to the Optimization
data. Furthermore, the sum of all actions for any resource needs to be 1, which are n additional
constraints I have. Also, any type of action needs to be performed with a relative frequency
of x% (additional constraint). And finally there are constraints for the limited number of
resources.
>> I used the SimplexSolver and can find a working solution within about half a second
(the size of the problem n*m is somewhere about 2500). The problem is, that I need to perform
the calculation very frequently and its currently too slow. I wonder if there is a way to
restrict the number of iterations for example or tell the solver to return a solution even
if there might be way better after a certain number of iterations? I tried the MaxIter constraint,
which leads only to a TooManyIterations exception without being able to retrieve the result
found so far. I also tried to initialize the solver with different epsilon values, but either
it took the same amount of iterations (and time) or it finished with a NoFeasableSolutionException.
>> So my question is if there is a way to get non-optimal solutions, but those quicker?
>> If it would speed up the solution finding process, I could live with a solution where
we restrict the possible results to booleans, i.e., an action for any resource is either performed
never or always.
>
> Hi Thorsten,
>
> at the moment there is no way to get the best solution so far, if the
> maximum number of iterations has been reached.
>
> We could add a feature like this (as already several other people have
> requested it).
>
> Could you also attach your example somewhere, so I can take a look at it
> and maybe provide some more optimization tips?
>
> Thanks,
>
> Thomas
>
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```
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