Problem: MATLAB Function Implementation and SCA Optimization

The problem involves implementing MATLAB functions (Ufun, F1-F23, Get_Functions_details, initialization) and the SCA optimization algorithm with test cases.


Input/Output: The problem takes function definitions (Ufun, F1-F23, Get_Functions_details, initialization, SCA) with specified algorithms and test cases as input. It generates correct MATLAB code for each function that passes the test cases, and outputs SCA optimization results (best fitness, position, convergence curve) when executed with given parameters.

Required dependencies:

Sub-steps:
step_number: 1
step_description_prompt: Please write a MATLAB function named Ufun that calculates a piecewise function based on the input arguments x, a, k, and m. The function definition should be: function o = Ufun(x, a, k, m). The algorithm flow is as follows: 1. For each element in x, compute the term k.*((x - a).^m) and multiply it by a logical array where each element is 1 if the corresponding element in x is greater than a, and 0 otherwise. 2. For each element in x, compute the term k.*((-x - a).^m) and multiply it by a logical array where each element is 1 if the corresponding element in x is less than -a, and 0 otherwise. 3. Add the two resulting arrays from steps 1 and 2 element-wise to get the final output o (since each element in x can satisfy at most one of the two conditions (x > a or x < -a), the sum effectively combines the two piecewise components while setting values between -a and a to 0). The function uses element-wise operations (.* and .^) to ensure correct handling of array inputs for x.
function_header: function o=Ufun(x,a,k,m)

end
test_cases: clear; clc;
rng(42);
correct = 32.0000;
x = [-3, -1, 0, 1, 3];
a = 1;
k = 2;
m = 3;
result = Ufun(x, a, k, m);
val = sum(result);
if val~=correct
    error('Wrong')
end
correct = 500.0000;
x = [-4, -6, 2, 3, 5];
a = 2;
k = 5;
m = 3;
result = Ufun(x, a, k, m);
val = sum(result);
if val~=correct
    error('Wrong')
end
correct = 1302.00000;
x = [-1, -2, 5, 6, 4];
a = 1;
k = 6;
m = 3;
result = Ufun(x, a, k, m);
val = sum(result);
if val~=correct
    error('Wrong')
end
disp('Completely right!')

step_number: 2
step_description_prompt: Please write a MATLAB function named F1 that computes the sum of the squares of each element in the input vector x.
Function Definition: function o = F1(x)
Algorithm Flow: Compute the sum of the element-wise square of x and assign it to o.

Please write a MATLAB function named F2 that computes the sum of the absolute values of each element in the input vector x plus the product of the absolute values of each element in x.
Function Definition: function o = F2(x)
Algorithm Flow: Compute the sum of the absolute values of x, compute the product of the absolute values of x, then add these two results and assign to o.

Please write a MATLAB function named F3 that computes the sum of the squares of the cumulative sums of the first i elements of the input vector x for i from 1 to the number of columns of x.
Function Definition: function o = F3(x)
Algorithm Flow: 1. Get the number of columns of x and assign it to dim. 2. Initialize o to 0. 3. For each i from 1 to dim, compute the sum of the first i elements of x, square this sum, and add it to o.

Please write a MATLAB function named F4 that computes the maximum value of the absolute values of each element in the input vector x.
Function Definition: function o = F4(x)
Algorithm Flow: Compute the maximum of the absolute values of x and assign it to o.

Please write a MATLAB function named F5 that computes the sum of 100 times the square of (the i-th element minus the square of the (i-1)-th element) plus the square of (the (i-1)-th element minus 1) for i from 2 to the number of columns of the input vector x.
Function Definition: function o = F5(x)
Algorithm Flow: 1. Get the number of columns of x and assign it to dim. 2. Compute the sum of 100 multiplied by the square of (elements from the 2nd to dim-th column of x minus the square of elements from the 1st to (dim-1)-th column of x) plus the square of (elements from the 1st to (dim-1)-th column of x minus 1), then assign the result to o.

Please write a MATLAB function named F6 that computes the sum of the squares of the absolute values of (each element in the input vector x plus 0.5).
Function Definition: function o = F6(x)
Algorithm Flow: Compute the sum of the square of the absolute value of (x plus 0.5) for each element and assign it to o.

Please write a MATLAB function named F7 that computes the sum of the product of each index (from 1 to the number of columns of x) and the fourth power of the corresponding element in the input vector x, then adds a uniformly distributed random number between 0 and 1.
Function Definition: function o = F7(x)
Algorithm Flow: 1. Get the number of columns of x and assign it to dim. 2. Compute the sum of (indices from 1 to dim) multiplied by the fourth power of the corresponding elements in x, then add the result of the rand() function (which generates a random number between 0 and 1) and assign to o.

Please write a MATLAB function named F8 that computes the sum of the product of -x (element-wise) and the sine of the square root of the absolute value of x (element-wise) for each element in the input vector x.
Function Definition: function o = F8(x)
Algorithm Flow: Compute the sum of (-x) multiplied by the sine of the square root of the absolute value of x (element-wise) and assign it to o.
test_cases: clear; clc;
rng(42);
correct = 6659.399639;
x = [1.2, -0.5, 2.3, -1.8, 0.7];
val = F1(x) + F2(x) + F3(x) + F4(x) + F5(x) + F6(x) + F7(x) + F8(x);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong')
end
correct = 116785.710695;
x = [1.6, -0.3, 5.6, -1.7, 0.9];
val = F1(x) + F2(x) + F3(x) + F4(x) + F5(x) + F6(x) + F7(x) + F8(x);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong')
end
correct = 24863.690416;
x = [2.5, -1.6, 2.6, -3.2, 1.3];
val = F1(x) + F2(x) + F3(x) + F4(x) + F5(x) + F6(x) + F7(x) + F8(x);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong')
end
disp('Completely right!')

step_number: 3
step_description_prompt: Please use MATLAB code to generate a function named F9 that implements the function which calculates the sum of each element of x squared minus 10 times the cosine of 2π times each element of x, then adds 10 times the number of columns in x. The function takes a vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F9(x)
Algorithm flow:
1. Compute dim as the number of columns of x using size(x, 2).
2. Compute o as sum(x.^2 - 10*cos(2*pi.*x)) + 10*dim.

Please use MATLAB code to generate a function named F10 that implements the function which calculates -20 times the exponential of -0.2 times the square root of the mean of squared elements of x, minus the exponential of the mean of the cosine of 2π times each element of x, then adds 20 plus the base of the natural logarithm (exp(1)). The function takes a vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F10(x)
Algorithm flow:
1. Compute dim as the number of columns of x using size(x, 2).
2. Compute o as -20*exp(-.2*sqrt(sum(x.^2)/dim)) - exp(sum(cos(2*pi.*x))/dim) + 20 + exp(1).

Please use MATLAB code to generate a function named F11 that implements the function which calculates the sum of squared elements of x divided by 4000, minus the product of the cosine of each element of x divided by the square root of its 1-based index, then adds 1. The function takes a vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F11(x)
Algorithm flow:
1. Compute dim as the number of columns of x using size(x, 2).
2. Compute o as sum(x.^2)/4000 - prod(cos(x./sqrt([1:dim]))) + 1.

Please use MATLAB code to generate a function named F12 that implements the function which calculates (π divided by the number of columns of x) multiplied by the sum of: 10 times the square of the sine of π times (1 plus (the first element of x plus 1 divided by 4)), plus the sum over elements 1 to n-1 of ((element i plus 1 divided by 4) squared multiplied by (1 plus 10 times the square of the sine of π times (1 plus (element i+1 plus 1 divided by 4)) )), plus (the last element of x plus 1 divided by 4) squared; then adds the sum of the Ufun function applied to x with parameters 10, 100, 4. The function takes a vector x (row or column) as input and returns a scalar output o. Note: Ufun is assumed to be pre-defined.
Function definition: function o = F12(x)
Algorithm flow:
1. Compute dim as the number of columns of x using size(x, 2).
2. Compute term1 as (pi/dim) * (10*((sin(pi*(1 + (x(1)+1)/4)))^2) + sum((((x(1:dim-1)+1)./4).^2) .* (1 + 10.*((sin(pi.*(1 + (x(2:dim)+1)./4)))).^2)) + ((x(dim)+1)/4)^2 ).
3. Compute term2 as sum(Ufun(x, 10, 100, 4)).
4. Compute o as term1 + term2.

Please use MATLAB code to generate a function named F13 that implements the function which calculates 0.1 times the sum of: the square of the sine of 3π times the first element of x, plus the sum over elements 1 to n-1 of ((element i minus 1) squared multiplied by (1 plus the square of the sine of 3π times element i+1)), plus (the last element of x minus 1) squared multiplied by (1 plus the square of the sine of 2π times the last element of x); then adds the sum of the Ufun function applied to x with parameters 5, 100, 4. The function takes a vector x (row or column) as input and returns a scalar output o. Note: Ufun is assumed to be pre-defined.
Function definition: function o = F13(x)
Algorithm flow:
1. Compute dim as the number of columns of x using size(x, 2).
2. Compute term1 as .1*((sin(3*pi*x(1)))^2 + sum((x(1:dim-1)-1).^2 .* (1 + (sin(3.*pi.*x(2:dim))).^2)) + ((x(dim)-1)^2)*(1 + (sin(2*pi*x(dim)))^2)).
3. Compute term2 as sum(Ufun(x, 5, 100, 4)).
4. Compute o as term1 + term2.

Please use MATLAB code to generate a function named F14 that implements the function which uses a pre-defined 2×25 matrix aS, computes for each column j of aS the sum of the 6th power of the difference between x (transposed to a column vector) and column j of aS, stores these sums in a vector bS, then calculates (1/500 plus the sum of 1 divided by (j plus bS(j)) for j from 1 to 25) raised to the power of -1. The function takes a vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F14(x)
Algorithm flow:
1. Define matrix aS as a 2×25 matrix where the first row is [-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32] and the second row is [-32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32].
2. Initialize a 1×25 vector bS.
3. For j from 1 to 25: compute bS(j) as sum((x' - aS(:, j)).^6).
4. Compute o as (1/500 + sum(1./([1:25] + bS))).^(-1).

Please use MATLAB code to generate a function named F15 that implements the function which calculates the sum of squared differences between a pre-defined vector aK and the values (x₁*(bK² + x₂*bK))/(bK² + x₃*bK + x₄) for each element in bK, where bK is the reciprocal of a pre-defined vector. The function takes a 4-element vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F15(x)
Algorithm flow:
1. Define vector aK as [.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246].
2. Define vector bK as [.25 .5 1 2 4 6 8 10 12 14 16], then compute bK as 1./bK.
3. Compute o as sum((aK - ((x(1).*(bK.^2 + x(2).*bK))./(bK.^2 + x(3).*bK + x(4)))).^2).

Please use MATLAB code to generate a function named F16 that implements the function which calculates 4 times the square of the first element of x minus 2.1 times the fourth power of the first element of x plus one-third the sixth power of the first element of x, plus the product of the first and second elements of x, minus 4 times the square of the second element of x plus 4 times the fourth power of the second element of x. The function takes a 2-element vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F16(x)
Algorithm flow:
1. Compute o as 4*(x(1)^2) - 2.1*(x(1)^4) + (x(1)^6)/3 + x(1)*x(2) - 4*(x(2)^2) + 4*(x(2)^4).

Please use MATLAB code to generate a function named F17 that implements the function which calculates the square of (the second element of x minus (the square of the first element of x) times 5.1 divided by (4 times π squared) plus 5/π times the first element of x minus 6), plus 10 times (1 minus 1/(8π)) times the cosine of the first element of x, then adds 10. The function takes a 2-element vector x (row or column) as input and returns a scalar output o.
Function definition: function o = F17(x)
Algorithm flow:
1. Compute o as (x(2) - (x(1)^2)*5.1/(4*(pi^2)) + 5/pi*x(1) - 6)^2 + 10*(1 - 1/(8*pi))*cos(x(1)) + 10.
test_cases: clear; clc;
rng(42);
correct = 143.557619;
x5 = [0.5, 1.2, 0.3, 1.5, 0.8];
x2 = [0.5, 1.2];
x4 = [0.3, 0.7, 1.5, 2.1];
val = F9(x5) + F10(x5) + F11(x5) + F12(x5) + F13(x5) + F14(x2) + F15(x4) + F16(x2) + F17(x2);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
correct = 148.143694;
x5 = [0.6, 2.2, 2.2, 1.6, 0.9];
x2 = [0.1, 1.2];
x4 = [0.3, 0.2, 2.3, 1.1];
val = F9(x5) + F10(x5) + F11(x5) + F12(x5) + F13(x5) + F14(x2) + F15(x4) + F16(x2) + F17(x2);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
correct = 131.306685;
x5 = [0.8, 1.4, 0.3, 1.2, 0.8];
x2 = [0.2, 1.1];
x4 = [0.4, 0.3, 1.1, 2.1];
val = F9(x5) + F10(x5) + F11(x5) + F12(x5) + F13(x5) + F14(x2) + F15(x4) + F16(x2) + F17(x2);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 4
step_description_prompt: Please use MATLAB code to generate functions named F18, F19, F20, F21, F22, F23 that implement the following functionalities exactly.

function o = F18(x)
o=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*(x(2)^2)))*...
    (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2)));
end

function o = F19(x)
aH=[3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2];
pH=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828];
o=0;
for i=1:4
    o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end

function o = F20(x)
aH=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14];
cH=[1 1.2 3 3.2];
pH=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;...
.2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381];
o=0;
for i=1:4
    o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end

function o = F21(x)
aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];
cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0;
for i=1:5
    o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end

function o = F22(x)
aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];
cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0;
for i=1:7
    o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end

function o = F23(x)
aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];
cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0;
for i=1:10
    o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end
test_cases: clear; clc;
rng(42);
correct = 16649.063712;
x2 = [0.5, 1.2];  
x3 = [0.3, 0.7, 1.5]; 
x4 = [0.3, 0.7, 1.5, 2.1];
x6 = [0.2, 0.4, 0.6, 0.8, 1.0, 1.2]; 
val = F18(x2) + F19(x3) + F20(x6) + F21(x4) + F22(x4) + F23(x4);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

correct = 17899.312189;
x2 = [0.6, 1.3];  
x3 = [0.5, 1.7, 1.2]; 
x4 = [0.1, 1.5, 1.6, 2.1];
x6 = [0.5, 0.2, 1.6, 0.8, 1.1, 1.2]; 
val = F18(x2) + F19(x3) + F20(x6) + F21(x4) + F22(x4) + F23(x4);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

correct = 42552.178761;
x2 = [0.2, 1.3];  
x3 = [1.3, 0.7, 1.3]; 
x4 = [2.2, 0.6, 1.2, 0.5];
x6 = [0.2, 0.1, 0.7, 0.2, 1.0, 1.1]; 
val = F18(x2) + F19(x3) + F20(x6) + F21(x4) + F22(x4) + F23(x4);
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 5
step_description_prompt: Please write a MATLAB function named Get_Functions_details that takes an input parameter F (a string representing the function name) and returns four output parameters: lb (lower bound), ub (upper bound), dim (dimension of the function), and fobj (a function handle to the corresponding objective function). The function definition must be: function [lb,ub,dim,fobj] = Get_Functions_details(F). Use a switch-case structure to handle different values of F. For each case (from 'F1' to 'F23'), assign the corresponding values to lb, ub, dim, and fobj (fobj is a function handle to F1-F23, which are assumed to be pre-defined and do not need to be implemented here). The specific assignments are as follows:
- Case 'F1': fobj = @F1; lb = -100; ub = 100; dim = 10;
- Case 'F2': fobj = @F2; lb = -10; ub = 10; dim = 10;
- Case 'F3': fobj = @F3; lb = -100; ub = 100; dim = 10;
- Case 'F4': fobj = @F4; lb = -100; ub = 100; dim = 10;
- Case 'F5': fobj = @F5; lb = -30; ub = 30; dim = 10;
- Case 'F6': fobj = @F6; lb = -100; ub = 100; dim = 10;
- Case 'F7': fobj = @F7; lb = -1.28; ub = 1.28; dim = 10;
- Case 'F8': fobj = @F8; lb = -500; ub = 500; dim = 10;
- Case 'F9': fobj = @F9; lb = -5.12; ub = 5.12; dim = 10;
- Case 'F10': fobj = @F10; lb = -32; ub = 32; dim = 10;
- Case 'F11': fobj = @F11; lb = -600; ub = 600; dim = 10;
- Case 'F12': fobj = @F12; lb = -50; ub = 50; dim = 10;
- Case 'F13': fobj = @F13; lb = -50; ub = 50; dim = 10;
- Case 'F14': fobj = @F14; lb = -65.536; ub = 65.536; dim = 2;
- Case 'F15': fobj = @F15; lb = -5; ub = 5; dim = 4;
- Case 'F16': fobj = @F16; lb = -5; ub = 5; dim = 2;
- Case 'F17': fobj = @F17; lb = [-5, 0]; ub = [10, 15]; dim = 2;
- Case 'F18': fobj = @F18; lb = -2; ub = 2; dim = 2;
- Case 'F19': fobj = @F19; lb = 0; ub = 1; dim = 3;
- Case 'F20': fobj = @F20; lb = 0; ub = 1; dim = 6;
- Case 'F21': fobj = @F21; lb = 0; ub = 10; dim = 4;
- Case 'F22': fobj = @F22; lb = 0; ub = 10; dim = 4;
- Case 'F23': fobj = @F23; lb = 0; ub = 10; dim = 4;
function_header: function [lb,ub,dim,fobj] = Get_Functions_details(F)

end
test_cases: clear; clc;
rng(42);
test_funcs = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6', 'F7', 'F8', 'F9', 'F10', ...
              'F11', 'F12', 'F13', 'F14', 'F15', 'F16', 'F17', 'F18', 'F19', ...
              'F20', 'F21', 'F22', 'F23'};
total = 0;
correct = 864.188863;
for i = 1:length(test_funcs)
    [lb, ub, dim, fobj] = Get_Functions_details(test_funcs{i});
    if isscalar(lb) && isscalar(ub)
        x = (lb + ub) / 2 * ones(1, dim);
    else
        x = (lb + ub) / 2;
    end
    fval = fobj(x);
    total = total + sum(lb(:)) + sum(ub(:)) + dim + fval;
end
tol = abs(total-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 6
step_description_prompt: Please write a MATLAB function named initialization that initializes the position matrix of search agents. The function takes four inputs: SearchAgents_no (number of search agents), dim (dimensionality of the search space), ub (upper bound of the search space), lb (lower bound of the search space), and returns X (the initialized position matrix of search agents with size SearchAgents_no×dim). 

Function definition: function X=initialization(SearchAgents_no,dim,ub,lb)

Algorithm steps:
1. Compute Boundary_no as the number of columns of ub using size(ub,2).
2. If Boundary_no equals 1 (indicating all variables have the same upper and lower bounds, and ub/lb are single values), generate X by: X = rand(SearchAgents_no,dim).*(ub-lb) + lb.
3. If Boundary_no is greater than 1 (indicating each variable has different upper and lower bounds), loop through each dimension i from 1 to dim:
   a. Extract ub_i = ub(i) and lb_i = lb(i).
   b. Assign the i-th column of X as: X(:,i) = rand(SearchAgents_no,1).*(ub_i - lb_i) + lb_i.

Ensure the output X strictly matches the result of the original code.
function_header: function X=initialization(SearchAgents_no,dim,ub,lb)

end
test_cases: clear; clc;
rng(42);

correct = 85.422048;
X1 = initialization(5, 3, 10, -5);
X2 = initialization(4, 3, [5,10,15], [-2,0,3]);
X3 = initialization(3, 2, 0, 0);
val = sum(X1(:)) + sum(X2(:)) + sum(X3(:));
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

correct = 94.834255;
X1 = initialization(2, 5, 10, -7);
X2 = initialization(4, 3, [5,8,12], [-1,1,3]);
X3 = initialization(2, 2, 1, 4);
val = sum(X1(:)) + sum(X2(:)) + sum(X3(:));
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

correct = 59.955864;
X1 = initialization(6, 2, 8, -8);
X2 = initialization(4, 3, [2,10,12], [-2,2,6]);
X3 = initialization(3, 4, 0, 1);
val = sum(X1(:)) + sum(X2(:)) + sum(X3(:));
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 7
step_description_prompt: Please write a MATLAB function named SCA that implements the Sine Cosine Algorithm (SCA) for optimization. The function takes population size N, maximum number of iterations Max_iteration, lower bound lb, upper bound ub, dimension dim, and objective function fobj as inputs, and returns the best fitness value Destination_fitness, the best position Destination_position, and the convergence curve Convergence_curve.

function [Destination_fitness,Destination_position,Convergence_curve]=SCA(N,Max_iteration,lb,ub,dim,fobj)

First, display 'SCA is optimizing your problem'. Then initialize the population X using the initialization function with parameters N, dim, ub, lb. Initialize Destination_position as a 1-by-dim zero vector, Destination_fitness as infinity, Convergence_curve as a 1-by-Max_iteration zero vector, and Objective_values as a 1-by-size(X,1) zero vector.

Next, loop over each individual i from 1 to size(X,1): compute Objective_values(1,i) by applying fobj to X(i,:). If i is 1, set Destination_position to X(i,:) and Destination_fitness to Objective_values(1,i). Else if Objective_values(1,i) is less than Destination_fitness, update Destination_position to X(i,:) and Destination_fitness to Objective_values(1,i). Assign All_objective_values(1,i) to Objective_values(1,i).

Set t to 2, then enter a while loop while t <= Max_iteration: set a to 2, reassign Max_iteration to itself, compute r1 as a minus t multiplied by (a divided by Max_iteration). Loop over each individual i from 1 to size(X,1) and each dimension j from 1 to size(X,2): compute r2 as 2*pi*rand(), r3 as 2*rand(), r4 as rand(). If r4 is less than 0.5, update X(i,j) as X(i,j) plus (r1*sin(r2)*abs(r3*Destination_position(j)-X(i,j))); else, update X(i,j) as X(i,j) plus (r1*cos(r2)*abs(r3*Destination_position(j)-X(i,j))).

After updating all X elements, handle boundary constraints for each individual i: create Flag4ub as X(i,:) > ub, Flag4lb as X(i,:) < lb, then update X(i,:) using (X(i,:).*(~(Flag4ub+Flag4lb))) + ub.*Flag4ub + lb.*Flag4lb.

Then loop over each individual i from 1 to size(X,1): recompute Objective_values(1,i) using fobj on X(i,:). If Objective_values(1,i) is less than Destination_fitness, update Destination_position and Destination_fitness. Assign Convergence_curve(t) to Destination_fitness. If t modulo 50 equals 0, display the message ['At iteration ', num2str(t), ' the optimum is ', num2str(Destination_fitness)]. Increment t by 1.

End the loop and return the outputs. The initialization function called in the code is assumed to be pre-defined.
function_header: function [Destination_fitness,Destination_position,Convergence_curve]=SCA(N,Max_iteration,lb,ub,dim,fobj)

end
test_cases: clear; clc;
rng(42);

SearchAgents_no = 30;
Max_iteration = 5;
Function_name = 'F2';
[lb,ub,dim,fobj]=Get_Functions_details(Function_name);
[Best_score,Best_pos,cg_curve]=SCA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
val = Best_score + sum(Best_pos) + sum(cg_curve);
correct = 169.615351;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

SearchAgents_no = 20;
Max_iteration = 10;
Function_name = 'F11';
[lb,ub,dim,fobj]=Get_Functions_details(Function_name);
[Best_score,Best_pos,cg_curve]=SCA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
val = Best_score + sum(Best_pos) + sum(cg_curve);
correct = 751.206251;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

SearchAgents_no = 30;
Max_iteration = 6;
Function_name = 'F20';
[lb,ub,dim,fobj]=Get_Functions_details(Function_name);
[Best_score,Best_pos,cg_curve]=SCA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
val = Best_score + sum(Best_pos) + sum(cg_curve);
correct = -10.897764;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 8
step_description_prompt: Please write a MATLAB function named func_plot that takes a string func_name as input, retrieves function details (lb, ub, dim, fobj) via the pre-defined Get_Functions_details function, generates x and y vectors based on func_name, computes objective function values for all (x,y) pairs (handling different input dimensions for specific functions), and creates a 3D surface plot with surfc (no line style). Function definition: function func_plot(func_name). Steps: 1. Call [lb, ub, dim, fobj] = Get_Functions_details(func_name); (Get_Functions_details is pre-defined and no need to redefine.) 2. Use switch-case to set x and y vectors according to func_name: - Case 'F1', 'F2', 'F3', 'F4', 'F6', 'F14': x = -100:2:100; y = x; - Case 'F5': x = -200:2:200; y = x; - Case 'F7': x = -1:0.03:1; y = x; - Case 'F8', 'F11': x = -500:10:500; y = x; - Case 'F9', 'F15', 'F17', 'F19', 'F20', 'F21', 'F22', 'F23': x = -5:0.1:5; y = x; - Case 'F10': x = -20:0.5:20; y = x; - Case 'F12': x = -10:0.1:10; y = x; - Case 'F13': x = -5:0.08:5; y = x; - Case 'F16': x = -1:0.01:1; y = x; - Case 'F18': x = -5:0.06:5; y = x; 3. Compute L = length(x); initialize f as an empty array. 4. Use nested loops (i from 1 to L, j from 1 to L) to calculate f(i,j): - If func_name is not 'F15', 'F19', 'F20', 'F21', 'F22', 'F23': f(i,j) = fobj([x(i), y(j)]); - If func_name is 'F15': f(i,j) = fobj([x(i), y(j), 0, 0]); - If func_name is 'F19': f(i,j) = fobj([x(i), y(j), 0]); - If func_name is 'F20': f(i,j) = fobj([x(i), y(j), 0, 0, 0, 0]); - If func_name is 'F21', 'F22', or 'F23': f(i,j) = fobj([x(i), y(j), 0, 0]); 5. Plot with surfc(x, y, f, 'LineStyle', 'none').
ground_truth_code: function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

switch func_name 
    case 'F1' 
        x=-100:2:100; y=x; 
        
    case 'F2' 
        x=-100:2:100; y=x;
        
    case 'F3' 
        x=-100:2:100; y=x;
        
    case 'F4' 
        x=-100:2:100; y=x; 
    case 'F5' 
        x=-200:2:200; y=x;
    case 'F6' 
        x=-100:2:100; y=x;
    case 'F7' 
        x=-1:0.03:1;  y=x;
    case 'F8' 
        x=-500:10:500;y=x; 
    case 'F9' 
        x=-5:0.1:5;   y=x;  
    case 'F10' 
        x=-20:0.5:20; y=x;
    case 'F11' 
        x=-500:10:500; y=x;
    case 'F12' 
        x=-10:0.1:10; y=x;
    case 'F13' 
        x=-5:0.08:5; y=x;
    case 'F14' 
        x=-100:2:100; y=x;
    case 'F15' 
        x=-5:0.1:5; y=x;
    case 'F16' 
        x=-1:0.01:1; y=x;
    case 'F17' 
        x=-5:0.1:5; y=x;
    case 'F18' 
        x=-5:0.06:5; y=x;
    case 'F19' 
        x=-5:0.1:5; y=x;
    case 'F20' 
        x=-5:0.1:5; y=x;      
    case 'F21' 
        x=-5:0.1:5; y=x;
    case 'F22' 
        x=-5:0.1:5; y=x;    
    case 'F23' 
        x=-5:0.1:5; y=x;  
end    

    

L=length(x);
f=[];

for i=1:L
    for j=1:L
        if strcmp(func_name,'F15')==0 && strcmp(func_name,'F19')==0 && strcmp(func_name,'F20')==0 && strcmp(func_name,'F21')==0 && strcmp(func_name,'F22')==0 && strcmp(func_name,'F23')==0
            f(i,j)=fobj([x(i),y(j)]);
        end
        if strcmp(func_name,'F15')==1
            f(i,j)=fobj([x(i),y(j),0,0]);
        end
        if strcmp(func_name,'F19')==1
            f(i,j)=fobj([x(i),y(j),0]);
        end
        if strcmp(func_name,'F20')==1
            f(i,j)=fobj([x(i),y(j),0,0,0,0]);
        end       
        if strcmp(func_name,'F21')==1 || strcmp(func_name,'F22')==1 ||strcmp(func_name,'F23')==1
            f(i,j)=fobj([x(i),y(j),0,0]);
        end          
    end
end

surfc(x,y,f,'LineStyle','none');

end
function_header: function func_plot(func_name)

end

step_number: 9
step_description_prompt: Please use MATLAB code to create a script that uses the Sine Cosine Algorithm (SCA) to optimize the test function specified by 'Function_name', visualizes the test function and convergence curve, and displays the best solution and optimal objective value. The script must follow these steps exactly:

1. Clear the workspace and command window with `clear all` and `clc`.
2. Set the random seed to 42 using `rng(42)` for reproducibility.
3. Define the following parameters with comments:
   - `SearchAgents_no = 30; % Number of search agents`
   - `Function_name = 'F1';`
   - `Max_iteration = 1000; % Maximum numbef of iterations` (retain the typo "numbef" in the comment)
4. Obtain the test function details by calling `[lb, ub, dim, fobj] = Get_Functions_details(Function_name)`; assume `Get_Functions_details` is already defined and returns the lower bound (lb), upper bound (ub), dimension (dim), and objective function handle (fobj) of the specified test function.
5. Run the SCA optimization by calling `[Best_score, Best_pos, cg_curve] = SCA(SearchAgents_no, Max_iteration, lb, ub, dim, fobj)`; assume the `SCA` function is already defined and returns the best objective score (`Best_score`), best solution position (`Best_pos`), and convergence curve (`cg_curve`).
6. Create a figure with the position `[284 214 660 290]` using `figure('Position', [284 214 660 290])`.
7. Add the comment `%Draw search space` and then create the first subplot to visualize the test function:
   - Use `subplot(1,2,1)`.
   - Plot the test function with `func_plot(Function_name)` (assume `func_plot` is already defined).
   - Set the title to 'Test function', xlabel to 'x_1', ylabel to 'x_2', and zlabel to `[Function_name, '( x_1 , x_2 )']`.
   - Turn off the grid with `grid off`.
8. Add the comment `%Draw objective space` and then create the second subplot to visualize the convergence curve:
   - Use `subplot(1,2,2)`.
   - Plot the convergence curve with `semilogy(cg_curve, 'Color', 'b')`.
   - Set the title to 'Convergence curve', xlabel to 'Iteration', and ylabel to 'Best flame (score) obtained so far'.
   - Set the axis to tight with `axis tight`, turn off the grid with `grid off`, turn on the box with `box on`, and add a legend with 'SCA' using `legend('SCA')`.
9. Display the best solution using `display(['The best solution obtained by SCA is : ', num2str(Best_pos)])` and the best optimal objective value using `display(['The best optimal value of the objective funciton found by SCA is : ', num2str(Best_score)])` (retain the typo "funciton" in the message).
10. Ensure all parameter values, function calls, plot settings, comments, and display messages are identical to the above description. The functions `Get_Functions_details`, `SCA`, and `func_plot` are pre-defined and do not need to be reimplemented.
test_cases: rng(42)
correct_score = 1.056050e-26;
correct_pos = 1.027862e-13;
val_score = sum(Best_score(:));
val_pos = sum(Best_pos(:));
tol_score = abs((val_score-correct_score)/correct_score);
if tol_score > 1e-4
    error('Wrong')
end
tol_pos = abs((val_pos-correct_pos)/correct_pos);
if tol_pos > 1e-4
    error('Wrong')
end
disp('Completely right!')

General solution:

General tests: