Error Using Optimization with Integer Variables and Non-linear Constraints

Question

Evelyn Lima 2024-4-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2112686-error-using-optimization-with-integer-variables-and-non-linear-constraints

编辑： Torsten 2024-4-29

Hi guys! I would be very grateful if you could help me!

I'm trying to minimize the norm of a vector using optimization algorithms in MATLAB, but I'm getting an error that says "Problems with integer variables and nonlinear equality constraints are not supported."

Could someone help me understand how I can solve this and minimize the norm of the vector?

Here's the implemented code:

wpass = 0.0318*pi;   
wstop = 0.15*pi;     
pb_ripple = 0.03;                  
sb_ripple = 0.03;    
n = 25;
l = 7;
k = 2^l;                               
N = 15*n;                              
w = linspace(0,pi,N);                  
A = [ones(N,1) 2*cos(kron(w',1:n))];
Ap  = A((0 <= w) & (w <= wpass),:);
As  = A((wstop <= w) & (w <= pi),:);
H_dac=sinc(w);
H_dac_p=H_dac(1,(0 <= w) & (w <= wpass));
H_dac_s=H_dac(1,(wstop <= w) & (w <= pi));
h = optimvar('h',(n+1), 'Type','integer','LowerBound',-inf,'UpperBound',inf);
norm_h=optimvar('norm_h','Type','integer');
prob = optimproblem('ObjectiveSense','minimize');
prob.Constraints.cons1 = norm_h==norm(cat(1,h(end:-1:2),h),1);
prob.Objective = norm_h;
prob.Constraints.cons2 = Ap*h <= k*(1 + pb_ripple);
prob.Constraints.cons3 = Ap*h >= k*(1 - pb_ripple);
prob.Constraints.cons4 = As*h <=  k*(sb_ripple); 
prob.Constraints.cons5 = As*h >= -k*(sb_ripple);
sol = solve(prob);

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2024-4-28

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2112686-error-using-optimization-with-integer-variables-and-non-linear-constraints#answer_1449211

编辑：Torsten 2024-4-28

在 MATLAB Online 中打开

Replace

norm_h=optimvar('norm_h','Type','integer');
prob = optimproblem('ObjectiveSense','minimize');
prob.Constraints.cons1 = norm_h==norm(cat(1,h(end:-1:2),h),1);
prob.Objective = norm_h;

by

%norm_h=optimvar('norm_h','Type','integer');
prob = optimproblem('ObjectiveSense','minimize');
%prob.Constraints.cons1 = norm_h==norm(cat(1,h(end:-1:2),h),1);
prob.Objective = norm(cat(1,h(end:-1:2),h),1);

Since h is integer valued, its 1-norm will also be integer-valued automatically.

The ga solver does not accept integer variables together with nonlinear equality constraints.

I think you can formulate the problem such that "intlinprog" can be used to solve it. This has several advantages over "ga" (which will most probably be chosen by MATLAB as solver for your problem).

2 个评论
显示无隐藏无

Evelyn Lima 2024-4-29

在 MATLAB Online 中打开

Dear Torsten,

Thank you for your reply, but it's still not working.

I'm trying to change the problem a little (using sqrt and .^), like this:

h = optimvar('h',n+1,'Type','integer');
Obj = sqrt(sum(cat(1,h(end:-1:1),h).^2)); 
prob = optimproblem("Objective",Obj);
x0.h = randi([0 0],n+1,1);
[sol,fval] = solve(prob,x0)

in this format, it works.

But once I add the constraints,

h = optimvar('h',n+1,'Type','integer');
Obj = sqrt(sum(cat(1,h(end:-1:1),h).^2));
prob = optimproblem("Objective",Obj);
prob.Constraints.cons2 = Ap*h <= k*(1 + pb_ripple);
prob.Constraints.cons3 = Ap*h >= k*(1 - pb_ripple);
prob.Constraints.cons4 = As*h <=  k*(sb_ripple); 
prob.Constraints.cons5 = As*h >= -k*(sb_ripple);
x0.h = randi([0 0],n+1,1);
[sol,fval] = solve(prob,x0)

I get a new error :

"Error using optim.problemdef.OptimizationProblem/solve

Incorrect size(model.obj)"

Torsten 2024-4-29

编辑：Torsten 2024-4-29

在 MATLAB Online 中打开

Which MATLAB version do you use ?

pb_ripple = sb_ripple = 0.03 gives the message that the linear bounds are infeasible.

For pb_ripple = sb_ripple = 0.3, your problem is solved by "ga".

If you use the 1-norm or infinity-norm instead of the 2-norm in your objective function, you can formulate the problem such that MATLAB is able to use "intinprog" instead of "ga" for its solution. This would be much faster and more reliable.

wpass = 0.0318*pi;   
wstop = 0.15*pi;     
pb_ripple = 0.3;                  
sb_ripple = 0.3;    
n = 5;
l = 7;
k = 2^l;                               
N = 15*n;                              
w = linspace(0,pi,N);                  
A = [ones(N,1) 2*cos(kron(w',1:n))];
Ap  = A((0 <= w) & (w <= wpass),:);
As  = A((wstop <= w) & (w <= pi),:);
H_dac=sinc(w);
H_dac_p=H_dac(1,(0 <= w) & (w <= wpass));
H_dac_s=H_dac(1,(wstop <= w) & (w <= pi));
h = optimvar('h',n+1,'Type','integer');
Obj = sqrt(sum(cat(1,h(end:-1:1),h).^2));
prob = optimproblem("Objective",Obj);
prob.Constraints.cons2 = Ap*h <= k*(1 + pb_ripple);
prob.Constraints.cons3 = Ap*h >= k*(1 - pb_ripple);
prob.Constraints.cons4 = As*h <=  k*(sb_ripple); 
prob.Constraints.cons5 = As*h >= -k*(sb_ripple);
x0.h = randi([0 0],n+1,1);
[sol,fval] = solve(prob,x0)
Solving problem using ga.
ga stopped because the average change in the penalty function value is less than options.FunctionTolerance and 
the constraint violation is less than options.ConstraintTolerance.
sol = struct with fields:
    h: [6x1 double]
fval = 28.7402
sol.h
ans = 6x1
     5
     9
     9
     9
     9
     8
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

请先登录，再进行评论。

Error Using Optimization with Integer Variables and Non-linear Constraints

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

2 个评论
显示无隐藏无

另请参阅

类别

标签

Community Treasure Hunt

Error Using Optimization with Integer Variables and Non-linear Constraints

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

2 个评论 显示 无隐藏 无

另请参阅

类别

标签

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

2 个评论
显示无隐藏无