I was trying to find the optimised design variables using GA in MATLAB. When I run the program it was running and running. Can anyone please check the loops used in the codes?

Please help me to find out the optimised design variables using GA. When I run it, it was running and running. Not showing any error also. Please help me by checking the loops used.

[Walter Roberson]

type optimizationtry.m

clc
clear 
% Define lower and upper bounds for the design variables
 lb = [100; 100; 20; 30; 10; 150; 10; 30; 10; 10; 10; 3.14; 3.14;  1.57; 1.57; 0; 0; 0; 100; 100;];
 ub = [200; 200; 40; 60; 40; 260; 40; 60; 40; 50; 50; 3.45; 3.45; 3.14; 3.76; 6.28; 6.28; 6.28; 200; 200];
 
 % Define the length of the design vector
 n = length(lb);
 x = lb+ (ub - lb).* rand(1, n);
 [A, b] = l_constraints(x);
 
 
 % Define options for the genetic algorithm
 options = optimoptions('ga', 'MaxGenerations', 5, 'PopulationSize', 10);
 % Perform optimization
 [X_opt, fval] = ga(@(x) objectiveFunction(x), 20, A, b, [], [], lb, ub, @(x) nonlcon(x), options);

function[d_values] = d_calc(x)
[~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, d0, dT] = x_values(x);
d_values = linspace(d0, dT, 21);
end

%Linear constraints
function [A, b] = l_constraints(x)

        [d_values] = d_calc(x);
        
        for i = 1:length(d_values)
            d = d_values(i);      
            A1 = [1    0    -1     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0    0;
                -1     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0    0;
                -1     0    -1     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    0 0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    0 0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;];

            A2 = [0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     1    -1     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0    -1    -1     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0    -1    -1     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0    -1     1     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    0 0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    0 0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0];
            
            A3 =[0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0    -1    -1    -1     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     1    -1    -1     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0    -1     1     1     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0    -1    -1     1     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0  0   0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0;
                 0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0   0  0     0];


            A = A1 + A2 + A3;
            
            [l5, ~] = calc_l59(x);
    
            b1 = [d;-d;-d; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0];
            b2 = [0; 0; 0; l5+53.6; -l5+53.6; -l5-53.6; l5+53.6; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0]; %l6 = 53.6;
            b3 = [0; 0; 0; 0; 0; 0; 0; 0; -24; 24; 24; 24; 24; 0; 0; 0; 0; 0; 0; 0]; %l12 = 24;
            b = b1+b2+b3;
        end
end

function f = objectiveFunction(x)
         H_MCP = [0.0017 0.0860 0.1646 0.2377 0.3061 0.3699 0.4297 0.4855 0.5380 0.5879 0.6359 0.6819 0.7257 0.7679 0.8088 0.8487 0.8878 0.9261 0.9634 1.0003 1.0861];
         H_PIP = [0 0.1036 0.2022 0.2962 0.3860 0.4733 0.5594 0.6445 0.7288 0.8121 0.8943 0.9752 1.0545 1.1315 1.2062 1.2789 1.3497 1.4189 1.4867 1.5533 1.6190];
         H_DIP = [0 0.0157 0.0384 0.0679 0.1043 0.1464 0.1938 0.2459 0.3016 0.3598 0.4191 0.4789 0.5383 0.5966 0.6536 0.7085 0.7608 0.8108 0.8579 0.9018 0.9445];

      

         % Calculate the weights r_MCP, r_PIP, and r_DIP
         r_MCP = max(H_MCP) - min(H_MCP);
         r_PIP = max(H_PIP) - min(H_PIP);
         r_DIP = max(H_DIP) - min(H_DIP);

         % Calculate the denominator
         denominator = r_MCP + r_PIP + r_DIP;
        
         %Calculate E
         [~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, E_MCP, E_PIP, E_DIP] = calc_EFG(x);
        
         % Calculate the objective function
         f = (r_MCP/denominator)*sum((H_MCP-E_MCP).^2)+(r_PIP/denominator)*sum((H_PIP-E_PIP).^2)+(r_DIP/denominator)*sum((H_DIP - E_DIP).^2);
end
% Define nonlinear constraints
function [c, ceq] = nonlcon(x)
[~, ~, ~, ~, l7, ~, l10, l11, ~, l14, ~, ~, ~, ~, ~, ~, ~, ~, ~] = x_values(x);

[E3, F3, G3, E6, F6, G6, E10, F10, G10, E13, F13, G13, E_MCP, E_PIP, E_DIP] = calc_EFG(x);

c1 = (E3^2 + F3^2 - G3^2);
c2 = (E6^2 + F6^2 - G6^2);
c3 = (E10^2 + F10^2 - G10^2);
c4 = (E13^2 + F13^2 - G13^2);
c5 = (abs(53.6 - l7) + 3) - (53.6 + l7 - 3);
c6 = (abs(l10 - l11) + 3) - (l10 + l11 - 3);
c7 = (abs(24 - l14) + 3) - (24 + l14 - 3);
c8 = [E_MCP - 0, 1.57 - E_MCP];
c9 = [E_PIP - 0, 1.74 - E_PIP];
c10 = [E_DIP - 0, 1.39 - E_DIP];


c = [c1; c2; c3; c4; c5; c6; c7(:); c8; c9; c10];
ceq=[];
end

function [l5, l9] = calc_l59(x)
         [l1, l2, ~, ~, ~, l8, ~, ~, ~, ~, ~, alpha1, alpha2, alpha3, ~, ~, ~, ~, ~] = x_values(x);
         l5 = sqrt((l2*cos(alpha2)-l1*cos(alpha1))^2 + (l2*sin(alpha2)-l1*sin(alpha1))^2);
         l9 = sqrt((l2*cos(alpha2)-l8*cos(alpha3))^2 + (l2*sin(alpha2)-l8*sin(alpha3))^2);
end

function [E3, F3, G3, E6, F6, G6, E10, F10, G10, E13, F13, G13, E_MCP, E_PIP, E_DIP] = calc_EFG(~)
    num_iterations = 50;
    lb = [10; 10; 10; 10; 10; 10; 10; 10; 10; 10; 10; 3.14; 3.14;  1.57; 1.57; 0; 0; 0; 100; 100;];
    ub = [200; 200; 40; 60; 40; 260; 50; 60; 50; 50; 50; 3.45; 3.45; 3.14; 3.76; 6.28; 6.28; 6.28; 280; 280];
    
    while true
        try
            for i = 1:num_iterations
                x_design = lb + (ub - lb) .* rand(size(lb)); % Generate random design variables within bounds
                [l1, l2, l3, l4, l7, l8, l10, l11, l13, l14, l15, alpha1, alpha2, alpha3, ~, alpha5, alpha6, alpha7, d0, dT] = x_values(x_design);
                [l5, l9] = calc_l59(x_design);

                d_values = linspace(d0, dT, 21);  % Compute d_values for each iteration

                for j = 1:length(d_values)
                    d = d_values(j);

                    E3 = 2*l1*l3*cos(alpha1);
                    F3 = 2*l1*l3*sin(alpha1);
                    G3 = l1^2 + l3^2 - d^2;

                    if (E3^2 + F3^2 - G3^2) >= 0 && (E3 - G3) ~= 0
                        phi3 = 2*atan((F3 + sqrt(E3^2 + F3^2 - G3^2)) / (E3 - G3));
                        phi4 = phi3 + alpha3 + pi;
                        phi5 = atan((l2*sin(alpha2)-l1*sin(alpha1)) / (l2*cos(alpha2)-l1*cos(alpha1))); %phi1 = alpha1, phi2 = alphai2
                    else
                        error('Unable to find valid phi3, phi4, or phi5');
                    end

                    % Print values for debugging
                    fprintf('For d = %.2f:\n', d);
                    fprintf('For e3 = %.2f:\n', E3);
                    fprintf('For f3 = %.2f:\n', F3);
                    fprintf('For g3 = %.2f:\n', G3);
                    fprintf('For phi3 = %.2f:\n', phi3);
                    fprintf('For phi5 = %.2f:\n', phi5);

                    E6 = 2*56.13*(l4*cos(phi4) + l5*cos(phi5)); %l6=53.16
                    F6 = 2*56.13*(l4*sin(phi4) + l5*sin(phi5));
                    G6 = (l4*sin(phi4) + l5*sin(phi5))^2 + (l4*cos(phi4) + l5*cos(phi5))^2 + 56.13^2 - l7^2;
                    fprintf('For e6 = %.2f:\n', E6);
                    fprintf('For f6 = %.2f:\n', F6);
                    fprintf('For g6 = %.2f:\n', G6);

                    if ((E6^2+F6^2-G6^2) >=0 && E6-G6 ~=0)
                        phi6 = 2*atan(F6 - sqrt(E6^2 + F6^2 + G6^2) / (E6 - G6));

                        
                        phi9 = atan((l2*sin(alpha2)-l8*sin(alpha3))^2 / (l2*cos(alpha2)-l8*cos(alpha3)));
                        fprintf('For phi6 = %.2f:\n', phi6);
                        fprintf('For phi9 = %.2f:\n', phi9);
                        fprintf('For thetamcp = %.2f:\n', E_MCP);


                        E10 = 2*l10*(56.13*cos(phi6) + l9*cos(phi9));
                        F10 = 2*l10*(56.13*sin(phi6) + l9*sin(phi9));
                        G10 = (56.13*sin(phi6) + l9*sin(phi9))^2 + (56.13*cos(phi6) + l9*cos(phi9))^2 + l10^2 - l11^2;
                        
                        fprintf('For e10 = %.2f:\n', E10);
                        fprintf('For f10 = %.2f:\n', F10);
                        fprintf('For g10 = %.2f:\n', G10);


                        if ((E10^2+F10^2-G10^2)>=0 && E10-G10 ~=0)
                            phi10 = 2 * atan((F10 + sqrt(E10^2 + F10^2 - G10^2)) / (E10 - G10));
                            phi12 = phi10 + alpha6;               
                            phi15 = phi6 + alpha5;

                            E13 = 2*l13*(24*cos(phi12) + l15*cos(phi15)); %l12 = 24
                            F13 = 2*l13*(24*sin(phi12) + l15*sin(phi15));
                            G13 = (24*sin(phi12(1)) + l15*sin(phi15(1)))^2 + (24*cos(phi12(1)) + l15*cos(phi15(1)))^2 + l13^2 - l14^2;


                            if  (E13^2 + F13^2 - G13^2) >= 0 && (E13 - G13) ~= 0

                                phi13 = 2 * atan((F13 + sqrt(E13^2 + F13^2 - G13^2)) / (E13 - G13));
                                phi16 = phi13 + alpha7;



                                
                                E_MCP = phi_6 - pi;
                                E_PIP = phi_12 - phi_6;


                                E_DIP = phi16 - phi12;
                            else
                                error('Unable to find valid E13, F13, or G13');
                            end
                        else
                            error('Unable to find valid E10, F10, or G10');
                        end
                    else
                        error('Unable to find valid E6, F6, or G6');
                    end
                end
            end
            % If the code reaches this point without errors, break out of the while loop
            break;
        catch exception
            % Display the error message
            disp(exception.message);
            % Restart the calculations from the beginning
            continue;
        end
    end
end

function [l1, l2, l3, l4, l7, l8, l10, l11, l13, l14, l15, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6, alpha7, d0, dT] = x_values(x)
    l1 = x(1);
    l2 = x(2);
    l3 = x(3);
    l4 = x(4);
    l7 = x(5);
    l8 = x(6);
    l10 = x(7);
    l11 = x(8);
    l13 = x(9);
    l14 = x(10);
    l15 = x(11);
    alpha1 = x(12);
    alpha2 = x(13);
    alpha3 = x(14);
    alpha4 = x(15);
    alpha5 = x(16);
    alpha6 = x(17);
    alpha7 = x(18);
    d0 = x(19);
    dT = x(20);
end

[Nikunja]

Thank you so much for answering. Did you find any error?

[Nikunja]

Hello sir, when you ran the code, did you got the result? Please let me know sir.

Answer 1

[Walter Roberson]

Your objective function calls

         [~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, ~, E_MCP, E_PIP, E_DIP] = calc_EFG(x);

Your nonlinear constraint calls

         [E3, F3, G3, E6, F6, G6, E10, F10, G10, E13, F13, G13, E_MCP, E_PIP, E_DIP] = calc_EFG(x);

Your calc_EFG is defined as

function [E3, F3, G3, E6, F6, G6, E10, F10, G10, E13, F13, G13, E_MCP, E_PIP, E_DIP] = calc_EFG(~)

which completely ignores its input.

You should not be ignoring the input: you should be calculating given the input.

[Nikunja]

Can you please help me to fix it? So that I can find the optimum of those 20 variables. Please help me out.

[Walter Roberson]

calc_EFG should not have lb and ub . It should accept a vector x and should use that x as the [l1, l2, l3, l4, l7, l8, l10, l11, l13, l14, l15, alpha1, alpha2, alpha3, ~, alpha5, alpha6, alpha7, d0, dT]

I do not see the point of having d_values = linspace(d0, dT, 21) as you appear to be overwriting all of the variables for every d value.

[Nikunja]

In that calc_EFG, d values will change in every iteration in the range of d0 and dT. And I need in every iteration Design variables value also changed in between lb and ub.

[Nikunja]

In the objective function, I am minimising the error between H_mcp, H_pip, H_dip and E_mcp, E_pip,E_dip. H values are desired values and it is given in the codes. Matlab should calculate the E_mcp,E_pip,E_dip values from the calc_EFG. As I am giving 21 desired values(H_mcp,H_pip,H_dip) so matlab should calculate 21 values for E_mcp, E_pip,E_dip. That's why I was d_values=linespace(do,dt,21)

[Walter Roberson]

Well, good luck with that. I will not be able to assist you any further.

[Nikunja]

Formulas are all correct. I think I am not able to create the loop. Please help me to create the loop .

[Nikunja]

Please help me sir.

[Walter Roberson]

Sorry, your design makes no sense at all to me. Perhaps it will make sense to someone else.

[Nikunja]

This is an exoskeleton problem, where I am trying to find out optimum link lengths and angles.

[Nikunja]

Please sir Help me to fix the loop only

[Walter Roberson]

Sorry, I am completely unable to understand your design. You will need to find someone else.