Optimization Live Editor task Error "Your objective function must return a scalar value"

Hi，I'm trying to maximize a function with genetic algorithm or patternsearch using Optimization Live Editor task. But it confuses me that an Error "Your objective function must return a scalar value" always occurs, and I have alreay checked out the output of my objective function. Can somebody tell me how to fix this problem? Would appreciate any help!

I checked out the the output of my objective function as follows:

input = [0 0.5];
MaxSidelobe = FindBestPlacingGA(input);
TF = isscalar(MaxSidelobe);
disp(TF);

The objective function and other functions needed：

function MaxSidelobe= FindBestPlacingGA(input)
input(1) = deg2rad(input(1));
mic_pos = [0	0.24	0
-0.2078	-0.12	0
0.2078	-0.12	0];
mic_pos = [Array3N(input(1),input(2));mic_pos];
MaxSidelobe= FPSF_Function(mic_pos,500,0:1:80);
end

function mic_pos = Array3N(theta,rho)
theta3N = [theta+pi/2;theta+pi*7/6;theta+pi*11/6];
mic_pos = zeros(3,3);
mic_pos(:,3) = 0;
[mic_pos(:,1),mic_pos(:,2)] = pol2cart(theta3N,rho);
end

function MSL= FPSF_Function(mic_pos,f,El)

Num_mic = size(mic_pos,1);   
Az = -180:1: 180; 
c = 343;
k0 = [0 0 -1]; 
numAz = length(Az);
numEl = length(El);
K = zeros(3, numAz, numEl);

for i = 1:numAz
    for j = 1:numEl
        az_rad = deg2rad(Az(i));
        el_rad = deg2rad(El(j));
        x = cos(az_rad) * sin(el_rad);
        y = sin(az_rad) * sin(el_rad);
        z = cos(el_rad);
        K(:, i, j) = [x; y; z]; 
    end
end
W = zeros(numAz,numEl);
for p = 1:numAz
    for q = 1:numEl
        for n = 1:Num_mic
            W(p,q) = exp(-1i*dot(K(:,p,q)'-k0,mic_pos(n,:))*2*pi*f/c) + W(p,q);
        end
    end
end
W = W/Num_mic;
Y = 10*log10((abs(W)).^2);
local_max = imregionalmax(Y);
max_values = Y(local_max);
Mainlobe = max(max_values(:));
sidelobes = max_values(max_values~=Mainlobe);
MSL = Mainlobe - max(sidelobes(:));
end

Answer 1

[Cris LaPierre]

I believe the issue is related to your initial point. If your dimensions are 1x2, then your initial point should be 1x2 as well. Since it is just 0, when you run the optimization, the first input tried is [0,0]. Your objective function returns an empty array is this scenario, which results in the error about the output not being scalar.

MaxSidelobe= FindBestPlacingGA([0 0])

MaxSidelobe =

  0x1 empty double column vector

Use the dropdown menu to change the initial point from 0 to a variable containing your initial point. Just make sure that variable is defined before you run the optmiization task. I used a variable named input0.

One other difference I noticed. In my version of MATLAB, the patternsearch solver is not available, so I used fmincon. The solution is very different between these two solvers:

• patternsearch: [59.8330, 0.2899]
• fmincon: [0.6559, 0.5000]

function MaxSidelobe= FindBestPlacingGA(input)
input(1) = deg2rad(input(1));
mic_pos = [0	0.24	0
-0.2078	-0.12	0
0.2078	-0.12	0];
mic_pos = [Array3N(input(1),input(2));mic_pos];
MaxSidelobe= FPSF_Function(mic_pos,500,0:1:80);
end

function mic_pos = Array3N(theta,rho)
theta3N = [theta+pi/2;theta+pi*7/6;theta+pi*11/6];
mic_pos = zeros(3,3);
mic_pos(:,3) = 0;
[mic_pos(:,1),mic_pos(:,2)] = pol2cart(theta3N,rho);
end

function MSL= FPSF_Function(mic_pos,f,El)

Num_mic = size(mic_pos,1);   
Az = -180:1: 180; 
c = 343;
k0 = [0 0 -1]; 
numAz = length(Az);
numEl = length(El);
K = zeros(3, numAz, numEl);

for i = 1:numAz
    for j = 1:numEl
        az_rad = deg2rad(Az(i));
        el_rad = deg2rad(El(j));
        x = cos(az_rad) * sin(el_rad);
        y = sin(az_rad) * sin(el_rad);
        z = cos(el_rad);
        K(:, i, j) = [x; y; z]; 
    end
end
W = zeros(numAz,numEl);
for p = 1:numAz
    for q = 1:numEl
        for n = 1:Num_mic
            W(p,q) = exp(-1i*dot(K(:,p,q)'-k0,mic_pos(n,:))*2*pi*f/c) + W(p,q);
        end
    end
end
W = W/Num_mic;
Y = 10*log10((abs(W)).^2);
local_max = imregionalmax(Y);
max_values = Y(local_max);
Mainlobe = max(max_values(:));
sidelobes = max_values(max_values~=Mainlobe);
MSL = Mainlobe - max(sidelobes(:));
end

[隐]

I had a misunderstanding about the initial point. I thought that setting it to 0 would set both variables in the "input" to 0. Now it works after setting it as you said.

I also noticed that the solution could be very different between different solvers. I think it is related to the periodicity of the object function and initial point. More work needs to be done to find out the best solution.

I really appreciate your help!

;)

[Cris LaPierre]

Your thought is correct - setting Initial Point to 0 does set both values to 0, but your obejctive function does not return a value in that case.

[隐]

I see, then there's another bug in my objective function code to fix. Thank you again.