Which algorithm for this type of problem?
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Hi!
I would like to solve a problem, where I have run many optimization problems by using a loop. That problem has already been solved by another person, however the results that I get in each step of the loop are very different from the result of the other person who solved this problem. That is why, I would like to make sure that Matlab uses the best algorithm available for this type of problem.
The problem:
A =
174726 187180 -1
196094 171660 -1
87100 110042 -1
182625 157808 -1
188196 233574 -1
b =
91832600
165805408
51750400
113998496
158685200
f =
-110429 -120153 1
problem: min f^T*x
st Ax<=b, x>=0
--------------------
My code:
options=optimset('display','off');
[x,fval,exitflag,output]=linprog(f,A,b,[],[],zeros(1,3),[],[],options);
As previously mentioned, I have to run this code a number of times by using a loop. In each step only the two first elements of f change - otherwise the problem is exactly the same.
So, by not changing the algorithm Matlab uses "interior point" by default. I have tried to change something (largescale on/off, simplex, actice-set). But sometimes even though I change it in optimset it does not give me any error, and I can see in the output that the algorithm is stille the same. My question is, which algorithm is best for this type of problem and how do I tell Matlab to use it?
Thank you very much for your time and consideration!
Alex
1 个评论
Matt J
2013-9-29
Why do you think it matter which one you use? Your tests show that all the different alternatives are giving you the correct result.
采纳的回答
If you add upper bounds to your problem, you can compute the vertices of the feasible region using LCON2VERT (Available Here). Then you can simply evaluate f.'*V(i,:) for all the different vertices V(i,:) and all different f and find the minimum.
>> A,b
A =
174726 187180 -1
196094 171660 -1
87100 110042 -1
182625 157808 -1
188196 233574 -1
-1 0 0
0 -1 0
0 0 -1
1 0 0
0 1 0
0 0 1
b =
91832600
165805408
51750400
113998496
158685200
0
0
0
10000000
10000000
10000000
>> V=lcon2vert(A,b);
>> [~,i]=min(V*f(:)); x=V(i,:)
x =
143.2383 356.9032 0
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