Optimization, optimconstr: Unable to perform assignment because the left and right sides have a different number of elements.

This is a program about optimization. I use con=optimiconstr() and for loop to read the constraints. But Matlab shows something wrong with my code as follows. I don't know why it is wrong. Could you give me some tips?

clear;
data=[9.4888 8.7928 11.5960 11.5643 5.6756 9.8497 9.1756 13.1385 15.4663 15.5464;
    5.6817 10.3868 3.9294 4.4325 9.9658 17.6632 6.1517 11.8569 8.8721 15.5858];
d=zeros(10);
for i=1:9
    for j=2:10
        if j>i
            d(i,j)=norm(data(:,i)-data(:,j));
        end
    end
end
x=optimvar('x',10,1,LowerBound=0,UpperBound=1,Type='integer');
y=optimvar('y',10,10,LowerBound=0,UpperBound=1,Type='integer');
prob=optimproblem("ObjectiveSense","min");
prob.Objective=sum(x);
% Above are initiation, and constraints are as follows.
con=optimconstr(32,1);
con(32)=sum(y,1)>=1;% Matlab says here "Unable to perform assignment because

Unable to perform assignment because the left and right sides have a different number of elements.

%  the left and right sides have a different number of elements."
con(31)=sum(y,2)<=5;% Matlab says here the same mistake too as above.
for i=1:10
    for j=1:10
        con(i)=d(i,j)*y(i,j)<=10*x(i);
        con(i+10)=x(i)>=y(i,j);
    end
    con(i+20)=x(i)==y(i,i);
end
prob.Constraints=con;
[s,fval]=solve(prob);
show(prob);
s.x
s.y
fval

However, if I write the constraints in another way in which I don't use con=optimconstr(), then the program can run:

clear;
data=[9.4888 8.7928 11.5960 11.5643 5.6756 9.8497 9.1756 13.1385 15.4663 15.5464;
    5.6817 10.3868 3.9294 4.4325 9.9658 17.6632 6.1517 11.8569 8.8721 15.5858];
d=zeros(10);
for i=1:9
    for j=2:10
        if j>i
            d(i,j)=norm(data(:,i)-data(:,j));
        end
    end
end
x=optimvar('x',10,1,LowerBound=0,UpperBound=1,Type='integer');
y=optimvar('y',10,10,LowerBound=0,UpperBound=1,Type='integer');
prob=optimproblem("ObjectiveSense","min");
prob.Objective=sum(x);
% Above are initiation (same as the first program), and constraints are as follows.
con1=[1<=sum(y)';sum(y,2)<=5];% I don't use con=optimconstr(), I just create an ordinary vector.
con2=[];
for i=1:10
    con2=[con2;x(i)==y(i,i)];
    for j=1:10
        con1=[con1;d(i,j)*y(i,j)<=10*x(i);y(i,j)<=x(i)];
    end
end
prob.Constraints.con1=con1;
prob.Constraints.con2=con2;
[s,fval]=solve(prob);
s.x
s.y
fval

Answer 1

[Aditya]

Hi,

I understand that you are facing error when performing assignment to an OptimizationConstraint array.

The array con has preallocated memory for 32 OptimizationConstraint elements. When you perform the assignment operation:

con(32)=sum(y,1)>=1;

It is expected that sum(y,1) is a single OptimizationConstraint.

However, y is a 10x10 matrix. sum(y,1) is the sum along the 1st dimension, which is sum of each column, resulting in a 1x10 vector. The inequality constraint: sum(y,1)>=1 results in the following 10 inequality constraints:

sum(y,1)>=1 is same as [
    sum(y(:,1))  >= 1,
    sum(y(:,2))  >= 1,
    sum(y(:,3))  >= 1,
    sum(y(:,4))  >= 1,
    sum(y(:,5))  >= 1,
    sum(y(:,6))  >= 1,
    sum(y(:,7))  >= 1,
    sum(y(:,8))  >= 1,
    sum(y(:,9))  >= 1,
    sum(y(:,10)) >= 1
]

In summary, left side was expecting 1 OptimizationConstraint and right side had 10 OptimizationInequality constraints. Hence, the error "Unable to perform assignment because the left and right sides have a different number of elements."

You get the same error due to the same reason in this assignment

con(31)=sum(y,2)<=5;