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Linprog Error - Matrix Coefficients are too Large

Luka Celic さんによって質問されました 2018 年 12 月 21 日
最新アクティビティ Alan Weiss
さんによって コメントされました 2019 年 1 月 21 日
I'm trying to use linprog to calculate the smallest amount of time to accumulate gear damage targets in a mechanical durability test. I have 7 cases (maneuvers) which each generate a certain amount of damage (there are 5 damage equations). I would like to determine how many cycles of each case to perform to reach all 5 damage targets in the shortest amount of time possible.
lb=zeros(7,1);
lb(1)=4000;
lb(2)=70000;
lb(3)=70000;
lb(4)=90000;
lb(5)=40000;
lb(6)=340000;
lb(7)=390000;
ub=inf(7,1);
ub(1)=5000;
ub(2)=80000;
ub(3)=80000;
ub(4)=100000;
ub(5)=50000;
ub(6)=350000;
ub(7)=400000;
A=zeros(0,7);
b=zeros(0,0);
Aeq=zeros(5,7); % Equations
Aeq(1,[1,2,3,4,5,6,7])=[2.56e13,8.55e12,0,8.79e12,0,1.5e12,4.58e11];
Aeq(2,[1,2,3,4,5,6,7])=[0,0,5.9e12,0,1.41e13,9.25e11,2.04e11];
Aeq(3,[1,2,3,4,5,6,7])=[9.67e32,1.42e31,0,3.29e30,0,1e31,3.63e31];
Aeq(4,[1,2,3,4,5,6,7])=[0,0,5.17e31,0,2.86e32,2.75e30,4.09e30];
Aeq(5,[1,2,3,4,5,6,7])=[1.57e21,9.515e20,9.515e20,1.165e21,1.165e21,8.67e19,1.688e21];
beq=zeros(5,1); % Damage Targets
beq(1)=1.87e18;
beq(2)=1.07e18;
beq(3)=1.98e37;
beq(4)=1.24e37;
beq(5)=7.19e26;
f=zeros(7,1); % The time it takes for each cycle to be performed
f(1)=28.2;
f(2)=22.8;
f(3)=19.2;
f(4)=45.6;
f(5)=23.5;
f(6)=2.8;
f(7)=1;
[x fval] = linprog(f,A,b,Aeq,beq,lb,ub)
I get the following error:
Error using linprog (line 345)
LINPROG stopped because some objective or constraint matrix coefficients are too large in magnitude.
Error in Attempt2 (line 146)
[x fval] = linprog(f,A,b,Aeq,beq,lb,ub)
I'm not sure why it won't solve as I know there are solutions within the bounds I have specified. Is this just a case of the damage coefficients being too large?
Thank you!

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1 件の回答

Alan Weiss
回答者: Alan Weiss
2018 年 12 月 26 日
編集済み: Alan Weiss
2018 年 12 月 26 日

The default linprog algorithm is the same as a portion of the intlinprog algorithm, a dual-simplex method. For this algorithm, large coefficients are disallowed. I suggest that you scale some of your coefficients to be in a smaller range and then rescale the solution afterward. Or, switch to the 'interior-point' algorithm. Still, solvers struggle with poorly-scaled problems, so you will probably get more reliable answers if you scale your coefficients.
One more thing: pass A and b as [] instead of zero matrices.
Alan Weiss
MATLAB mathematical toolbox documentation

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Alan Weiss
2019 年 1 月 8 日
The problem as you gave it is infeasible. You can see this by calculating
Aeq*lb - beq
You get all positive entries. (I suggest that you scale things first to avoid numerical issues.) This means that, even with the entries of x as small as the lower bound allows, they are still larger than the linear constraints would want (all entries of Aeq are nonnegative, so the only way to get the entries of Aeq*x to be as small as beq is to have some be less than their lower bounds).
If you think that you have some point that works, well, all I can guess is that the very large scale causes numerical issues in Excel and leads to a spurious solution. But the problem, as given, is infeasible.
Alan Weiss
MATLAB mathematical toolbox documentation
Luka Celic 2019 年 1 月 11 日
I've scaled the numbers and changed the lower bounds to zero. Now the Aeq*lb - beq expression is negative.
lb=zeros(7,1);
lb(1)=0;
lb(2)=0;
lb(3)=0;
lb(4)=0;
lb(5)=0;
lb(6)=0;
lb(7)=0;
ub=inf(7,1);
ub(1)=5000;
ub(2)=80000;
ub(3)=80000;
ub(4)=100000;
ub(5)=50000;
ub(6)=350000;
ub(7)=400000;
>> Aeq*lb-beq
ans =
1.0e+12 *
-0.0000
-0.0000
-1.9800
-1.2400
-0.0000
However, I still get a "No feasible solution found" error. Is there something else I am doing wrong with this problem?
Thank you!
Luka
Alan Weiss
2019 年 1 月 21 日
Your problem is, doubtless, still infeasible. See Check Linear Constraints.
Alan Weiss
MATLAB mathematical toolbox documentation

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