This discussion needs to be taken off (this) list, as it appears to
have nothing to do with R.

-- Bert

On Thu, Aug 2, 2012 at 2:27 AM, khris <khris...@gmail.com> wrote:
>
> On Aug 2, 2012, at 12:39 PM, Petr Savicky [via R] wrote:
>
>> On Wed, Aug 01, 2012 at 04:55:30AM -0700, khris wrote:
>> > Hi Petr,
>> >
>> > It been sometime since I wrote. But here are the latest developments.
>> >
>> > When I give the binary linear opt problem to lpSolve optimizer than for 
>> > small instance it gives correct answer but when size of nodes increase 
>> > let's say 16 then there are about 2000 binary variables and lpSolve just 
>> > does not come back with any answer even after running for a full day. I 
>> > plan to solve for node size upto atleast 100, so I guess I need to do 
>> > something fundamentally different.
>> >
>> > Now I understand that lpSolve is using Branch and Bound Algorithm which to 
>> > me looks highly inefficient, for in the wrost case it will try to solve 
>> > 2^n LP relaxation problem. Maybe that's why I do not get answer even when 
>> > n=16. So what do I do to make lpSolve solve problem efficiently.
>>
>> Integer linear programming is an NP-complete problem and in general requires 
>> an
>> exponential time. It is not surprising that lpSolve failed to solve a problem
>> with 2000 variables. It can solve some problems with a few hundreds of 
>> variables,
>> but not every such problem.
>>
>
> OK. I guess then my approach to solve the Graph matching problem using binary 
> opt pr. seems destined to fail. I know you told about Kohenan maps but I am 
> not exited about it since it some sort of neural network which involves 
> training. So that approach may not be suitable.
> I wrote about another approach, reducing the "Graph matching with upper bound 
> on degree of vertex" to "Graph isomorphism where degree of vertex has upper 
> bound" since "Graph isomorphism where degree of vertex has upper bound" has 
> tractable solution. This approach seems promising.
>
> I also came across solving Graph matching using Simulated Annealing 
> (http://randomwalker.info/luther/kaggle-deanonymization/Graph_Matching_via_Simulate.html)
>  which also seems promising.
>
> How do you feel about these?
>
>
>> > In the lpSolve document there does not seem to be any option where one can 
>> > specify which variable should the optimizer use to use LP relaxation 
>> > first? Is there way to control in some way Branch and Bound algorithm used 
>> > by lpSolve apart from the going in side the code and tweaking it.
>>
>> I do not know, whether this may be controlled.
>>
>> Do you have a specific reason to use lpSolve for your problem?
>
> I thought lpSolve is the best optimizer freely available in R so I was using 
> it. Do you recommend another one? But if my model consist of 100,00 binaray 
> variable then I assume even commercial optimizer also won't scale?
>
> Appreciate your comments.
>
> Thanks in adv
> Khris.
>
>
>
>
>>
>> Petr.
>>
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-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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