Problem: Grasshopper Optimization Algorithm Implementation

The problem is to implement the Grasshopper Optimization Algorithm (GOA) in MATLAB, including defining benchmark functions, initializing agent positions, calculating distances and social interaction terms, and optimizing to find the global optimum of given objective functions.


Input/Output: The problem takes inputs including x (vector/matrix) for Ufun/F1-F17, a/k/m (scalars) for Ufun, F (string) for Get_Functions_details, N/dim (integers) for initialization/GOA, up/down (scalar/vector) for initialization, a/b (2-element vectors) for distance, r (scalar) for S_func, Max_iter (integer) and lb/ub (scalar/vector)/fobj (function handle) for GOA, and pre-defined matrices for F18-F23. It generates outputs: Ufun returns o (vector/matrix); F1-F23 return scalar o; Get_Functions_details returns lb/ub (scalar/vector), dim (integer), fobj; initialization returns X (matrix); distance returns d (scalar); S_func returns o (scalar); GOA returns TargetFitness (scalar), TargetPosition (vector), Convergence_curve (vector), Trajectories/fitness_history (matrices), position_history (3D matrix). Each function processes inputs via specified algorithms to produce outputs.

Required dependencies:

Sub-steps:
step_number: 1
step_description_prompt: Please use Matlab code to generate a function named Ufun that calculates element-wise values based on a piecewise function with input parameters x, a, k, m. The function is defined as: function o = Ufun(x, a, k, m). The algorithm flow is: 1. Calculate the contribution for x > a: perform element-wise exponentiation of (x - a) to the power m, multiply element-wise by k, then multiply element-wise by the logical array where x > a (elements where x ≤ a become 0). 2. Calculate the contribution for x < -a: perform element-wise exponentiation of (-x - a) to the power m, multiply element-wise by k, then multiply element-wise by the logical array where x < -a (elements where x ≥ -a become 0). 3. Sum the two contribution arrays element-wise to obtain the output o.
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 use Matlab code to generate a function named F1 that takes input x and returns the sum of the squares of the elements in x. The function definition is `function o = F1(x)`. The algorithm flow is: compute the sum of the squares of each element in x using `sum(x.^2)` and assign it to o.

Please use Matlab code to generate a function named F2 that takes input x and returns the sum of the absolute values of the elements in x plus the product of the absolute values of the elements in x. The function definition is `function o = F2(x)`. The algorithm flow is: compute the sum of absolute values of x using `sum(abs(x))` and the product of absolute values of x using `prod(abs(x))`, then add these two results and assign to o.

Please use Matlab code to generate a function named F3 that takes input x and returns the sum of the squares of the sums of the first i elements of x for i from 1 to the number of columns in x. The function definition is `function o = F3(x)`. The algorithm flow is: first get the number of columns of x as `dim = size(x, 2)`, initialize o to 0, then loop i from 1 to dim, in each iteration add the square of the sum of the first i elements of x (`sum(x(1:i))^2`) to o.

Please use Matlab code to generate a function named F4 that takes input x and returns the maximum value of the absolute values of the elements in x. The function definition is `function o = F4(x)`. The algorithm flow is: compute the maximum of the absolute values of x using `max(abs(x))` and assign to o.

Please use Matlab code to generate a function named F5 that takes input x and returns the sum of 100 times the square of (x's (i+1)-th element minus the square of x's i-th element) plus the square of (x's i-th element minus 1) for i from 1 to the number of columns in x minus 1. The function definition is `function o = F5(x)`. The algorithm flow is: first get the number of columns of x as `dim = size(x, 2)`, then compute the sum of `100*(x(2:dim) - (x(1:dim-1).^2)).^2 + (x(1:dim-1) - 1).^2` and assign to o.

Please use Matlab code to generate a function named F6 that takes input x and returns the sum of the squares of the absolute values of (each element of x plus 0.5). The function definition is `function o = F6(x)`. The algorithm flow is: compute the sum of the squares of `abs(x + 0.5)` using `sum(abs((x + 0.5)).^2)` and assign to o.

Please use Matlab code to generate a function named F7 that takes input x and returns the sum of the product of the index (from 1 to the number of columns in x) and the fourth power of each element of x, plus a random number between 0 and 1. The function definition is `function o = F7(x)`. The algorithm flow is: first get the number of columns of x as `dim = size(x, 2)`, then compute the sum of `[1:dim].*(x.^4)` using `sum([1:dim].*(x.^4))`, add a random number generated by `rand()`, and assign the result to o.

Please use Matlab code to generate a function named F8 that takes input x and returns the sum of -x elements multiplied by the sine of the square root of the absolute value of x elements. The function definition is `function o = F8(x)`. The algorithm flow is: compute the sum of `-x.*sin(sqrt(abs(x)))` using `sum(-x.*sin(sqrt(abs(x))))` and assign 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 functions named F9, F10, F11, F12, F13, F14, F15, F16, F17. Each function computes a specific mathematical function for a given input vector x.

Function definition for F9: function o = F9(x)
Algorithm for F9: Compute dim as the number of columns of x. Compute o as sum(x.^2 - 10*cos(2*pi.*x)) + 10*dim.

Function definition for F10: function o = F10(x)
Algorithm for F10: Compute dim as the number of columns of x. Compute o as -20*exp(-0.2*sqrt(sum(x.^2)/dim)) - exp(sum(cos(2*pi.*x))/dim) + 20 + exp(1).

Function definition for F11: function o = F11(x)
Algorithm for F11: Compute dim as the number of columns of x. Compute o as sum(x.^2)/4000 - prod(cos(x./sqrt([1:dim]))) + 1.

Function definition for F12: function o = F12(x)
Algorithm for F12: Compute dim as the number of columns of x. Compute the first part 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). Then add sum(Ufun(x,10,100,4)) to get o.

Function definition for F13: function o = F13(x)
Algorithm for F13: Compute dim as the number of columns of x. Compute the first part as 0.1*((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)). Then add sum(Ufun(x,5,100,4)) to get o.

Function definition for F14: function o = F14(x)
Algorithm for F14: Define aS as a 2x25 matrix: [-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; -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]. For j from 1 to 25, compute bS(j) as sum((x' - aS(:,j)).^6). Compute o as (1/500 + sum(1./([1:25] + bS))).^(-1).

Function definition for F15: function o = F15(x)
Algorithm for F15: Define aK as [0.1957 0.1947 0.1735 0.16 0.0844 0.0627 0.0456 0.0342 0.0323 0.0235 0.0246]. Define bK as 1./[0.25 0.5 1 2 4 6 8 10 12 14 16]. Compute o as sum((aK - ((x(1).*(bK.^2 + x(2).*bK))./(bK.^2 + x(3).*bK + x(4)))).^2).

Function definition for F16: function o = F16(x)
Algorithm for F16: 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).

Function definition for F17: function o = F17(x)
Algorithm for F17: 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.

Note: The function Ufun called in F12 and F13 is assumed to be pre-defined and does not need to be reimplemented.
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 calculate the values of the corresponding benchmark functions for the input vector x. Define function o = F18(x) that computes the value using the formula (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))). Define function o = F19(x) with pre-defined matrices 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]. Initialize o to 0, then loop i from 1 to 4 and update o as o = o - cH(i)*exp(-sum(aH(i,:).*((x - pH(i,:)).^2))). Define function o = F20(x) with pre-defined matrices 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]. Initialize o to 0, then loop i from 1 to 4 and update o as o = o - cH(i)*exp(-sum(aH(i,:).*((x - pH(i,:)).^2))). Define function o = F21(x) with pre-defined matrices 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]. Initialize o to 0, then loop i from 1 to 5 and update o as o = o - ((x - aSH(i,:))*(x - aSH(i,:))' + cSH(i))^(-1). Define function o = F22(x) with the same aSH and cSH as F21. Initialize o to 0, then loop i from 1 to 7 and update o as o = o - ((x - aSH(i,:))*(x - aSH(i,:))' + cSH(i))^(-1). Define function o = F23(x) with the same aSH and cSH as F21. Initialize o to 0, then loop i from 1 to 10 and update o as o = o - ((x - aSH(i,:))*(x - aSH(i,:))' + cSH(i))^(-1). Ensure all matrix values, indices, arithmetic operations (multiplication, exponentiation, summation), loop ranges and variable names are exactly as specified. All functions accept a vector x as input and return a scalar o as output.
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 string F (representing an objective function name) and returns four output parameters: lb (lower bound of the search space), ub (upper bound of the search space), dim (dimension of the problem), and fobj (a function handle to the corresponding objective function). The function maps each input F to its specific configuration.

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 fobj as a function handle to the function (e.g., @F1 for case 'F1'), and set lb, ub, dim to the specific values as follows. Note that the functions F1 to F23 called by fobj are assumed to be already defined and do not need to be redefined here.

The switch-case structure should include the following cases:
- Case 'F1': fobj = @F1; lb = -100; ub = 100; dim = 5;
- Case 'F2': fobj = @F2; lb = -10; ub = 10; dim = 5;
- Case 'F3': fobj = @F3; lb = -100; ub = 100; dim = 5;
- Case 'F4': fobj = @F4; lb = -100; ub = 100; dim = 5;
- Case 'F5': fobj = @F5; lb = -30; ub = 30; dim = 5;
- Case 'F6': fobj = @F6; lb = -100; ub = 100; dim = 5;
- Case 'F7': fobj = @F7; lb = -1.28; ub = 1.28; dim = 5;
- Case 'F8': fobj = @F8; lb = -500; ub = 500; dim = 5;
- Case 'F9': fobj = @F9; lb = -5.12; ub = 5.12; dim = 5;
- Case 'F10': fobj = @F10; lb = -32; ub = 32; dim = 5;
- Case 'F11': fobj = @F11; lb = -600; ub = 600; dim = 5;
- Case 'F12': fobj = @F12; lb = -50; ub = 50; dim = 5;
- Case 'F13': fobj = @F13; lb = -50; ub = 50; dim = 5;
- 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;

End the switch-case structure and the function.
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 = 793.91148438;
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 randomly initializes the position of agents in the search space.

Function Definition: [X] = initialization(N, dim, up, down), where:
- Input N: Number of agents (a positive integer).
- Input dim: Dimensionality of the search space (a positive integer).
- Input up: Upper bound of the search space; can be a scalar (same upper bound for all dimensions) or a dim-dimensional vector (different upper bound for each dimension).
- Input down: Lower bound of the search space; must have the same dimension as up (scalar or dim-dimensional vector).
- Output X: An N-by-dim matrix where each row represents the position of an agent in the search space.

Algorithm Flow:
1. Check the number of rows of the upper bound `up` using `size(up, 1)`.
2. If `up` is a scalar (i.e., `size(up, 1) == 1`):
   a. Generate an N-by-dim matrix of random numbers in the range [0, 1] using `rand(N, dim)`.
   b. Compute the initialized positions by scaling each element of the random matrix by the range `(up - down)` and shifting by `down` to map values to the interval [down, up]. Specifically, execute `X = rand(N, dim) .* (up - down) + down`.
3. If `up` is a vector (i.e., `size(up, 1) > 1`):
   a. Iterate over each dimension `i` from 1 to `dim`:
      i. Extract the upper bound for the i-th dimension: `high = up(i)`.
      ii. Extract the lower bound for the i-th dimension: `low = down(i)`.
      iii. Generate a 1-by-N vector of random numbers in the range [0, 1] using `rand(1, N)`.
      iv. Scale and shift the random vector to the interval [low, high] by computing `rand(1, N) .* (high - low) + low`.
      v. Assign the resulting vector to the i-th column of `X` (i.e., `X(:, i)`). MATLAB automatically transposes the 1-by-N random vector to an N-by-1 column vector to match the size of `X(:, i)`.
4. Return the initialized agent positions matrix `X`.
function_header: function [X]=initialization(N,dim,up,down)

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 distance that calculates the Euclidean distance between two 2-dimensional points. The function is defined as function d = distance(a,b) where a and b are 2-element vectors representing the coordinates of two points. Calculate the squared differences between the corresponding elements of a and b, sum them, and then take the square root of the sum. Specifically, compute (a(1)-b(1)) squared plus (a(2)-b(2)) squared, then apply the sqrt function to get the result d.
function_header: function d = distance(a,b)

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

a1 = [1.5, 2.5];
b1 = [4.5, 5.5];
val = distance(a1, b1);
correct = 4.242641;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

a2 = [1, 9];
b2 = [4, -7];
val = distance(a2, b2);
correct = 16.278821;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

a3 = [-10, 2];
b3 = [7, 9];
val = distance(a3, b3);
correct = 18.384776;
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 S_func that implements the calculation of a combination of exponential terms based on the input r. The function is defined as: function o = S_func(r). First, set the constant f to 0.5 and the constant l to 1.5. Then compute the output o using the formula o = f*exp(-r/l) - exp(-r). Functions called in the code are assumed to be pre-defined and do not need to be redefined.
function_header: function o=S_func(r)

end
test_cases: clear; clc;
rng(42);
r1 = 2.61;
val = S_func(r1);
correct = 0.01422566;
tol = abs((val-correct)/correct);
if tol>1e-4
    error('Wrong!')
end
r2 = 2.12;
val = S_func(r2);
correct = 0.00163379;
tol = abs((val-correct)/correct);
if tol>1e-4
    error('Wrong!')
end
r3 = 5.82;
val = S_func(r3);
correct = 0.00735781;
tol = abs((val-correct)/correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 9
step_description_prompt: Please write a MATLAB function named GOA that implements the Grasshopper Optimization Algorithm (GOA) to find the global optimum of a given objective function. The function estimates the global optimum by simulating the social behavior of grasshoppers, including initialization, fitness evaluation, position update, boundary handling, and convergence tracking.

The function definition must be: function [TargetFitness, TargetPosition, Convergence_curve, Trajectories, fitness_history, position_history] = GOA(N, Max_iter, lb, ub, dim, fobj)

The algorithm must strictly follow these steps:

1. **Initialization Check**: 
   - If size(ub,1) == 1, expand ub and lb to dim-dimensional vectors using ub = ones(dim,1)*ub and lb = ones(dim,1)*lb.
   - If mod(dim,2) ~= 0, increment dim by 1, append 100 to ub (ub = [ub; 100]), append -100 to lb (lb = [lb; -100]), and set flag = 1.

2. **Grasshopper Population Initialization**:
   - Generate initial grasshopper positions with GrassHopperPositions = initialization(N, dim, ub, lb) (initialization is pre-defined).
   - Initialize GrassHopperFitness = zeros(1,N), fitness_history = zeros(N, Max_iter), position_history = zeros(N, Max_iter, dim), Convergence_curve = zeros(1, Max_iter), Trajectories = zeros(N, Max_iter).

3. **Initial Fitness Evaluation**:
   - For each grasshopper i (1 to N):
     - If flag == 1, compute GrassHopperFitness(1,i) = fobj(GrassHopperPositions(i,1:end-1)).
     - Else, compute GrassHopperFitness(1,i) = fobj(GrassHopperPositions(i,:)).
     - Store initial fitness: fitness_history(i,1) = GrassHopperFitness(1,i).
     - Store initial position: position_history(i,1,:) = GrassHopperPositions(i,:).
     - Store first dimension position: Trajectories(:,1) = GrassHopperPositions(:,1).

4. **Sort Grasshoppers by Fitness**:
   - Sort GrassHopperFitness in ascending order to get sorted_fitness and sorted_indexes using [sorted_fitness, sorted_indexes] = sort(GrassHopperFitness).
   - Sort GrassHopperPositions using sorted_indexes to get Sorted_grasshopper (Sorted_grasshopper(newindex,:) = GrassHopperPositions(sorted_indexes(newindex),:) for newindex 1 to N).
   - Set TargetPosition = Sorted_grasshopper(1,:) and TargetFitness = sorted_fitness(1).

5. **Main Optimization Loop**:
   - Initialize l = 2. While l <= Max_iter:
     - Compute coefficient c = 1 - l * ((1 - 0.00004)/Max_iter).
     - For each grasshopper i (1 to N):
       - Transpose GrassHopperPositions to temp = GrassHopperPositions'.
       - Initialize S_i_total as a dim×1 vector. For k from 1 to dim step 2:
         - Compute S_i = zeros(2,1). For each j from 1 to N (j ~= i):
           - Compute Dist = distance(temp(k:k+1,j), temp(k:k+1,i)) (distance is pre-defined).
           - Compute r_ij_vec = (temp(k:k+1,j) - temp(k:k+1,i)) / (Dist + eps).
           - Compute xj_xi = 2 + mod(Dist, 2).
           - Compute s_ij = ((ub(k:k+1) - lb(k:k+1)) * c / 2) * S_func(xj_xi) .* r_ij_vec (S_func is pre-defined).
           - Accumulate s_ij into S_i.
         - Assign S_i to S_i_total(k:k+1, :).
       - Update position: X_new = c * S_i_total' + TargetPosition. Set GrassHopperPositions_temp(i,:) = X_new'.
     - Assign GrassHopperPositions = GrassHopperPositions_temp.
     - **Boundary Handling**: For each grasshopper i (1 to N):
       - Compute Tp = GrassHopperPositions(i,:) > ub' and Tm = GrassHopperPositions(i,:) < lb'.
       - Clamp positions: GrassHopperPositions(i,:) = GrassHopperPositions(i,:) .* (~(Tp + Tm)) + ub' .* Tp + lb' .* Tm.
     - **Fitness Update & Target Check**:
       - For each grasshopper i (1 to N):
         - If flag == 1, compute GrassHopperFitness(1,i) = fobj(GrassHopperPositions(i,1:end-1)).
         - Else, compute GrassHopperFitness(1,i) = fobj(GrassHopperPositions(i,:)).
         - Store fitness: fitness_history(i,l) = GrassHopperFitness(1,i).
         - Store position: position_history(i,l,:) = GrassHopperPositions(i,:).
         - Store first dimension position: Trajectories(:,l) = GrassHopperPositions(:,1).
         - Update Target: If GrassHopperFitness(1,i) < TargetFitness, set TargetPosition = GrassHopperPositions(i,:) and TargetFitness = GrassHopperFitness(1,i).
     - **Track Convergence**: Set Convergence_curve(l) = TargetFitness.
     - **Display Progress**: Use disp(['In iteration #', num2str(l), ' , target''s objective = ', num2str(TargetFitness)]).
     - Increment l by 1.

6. **Final Processing**:
   - If flag == 1, remove the last dimension from TargetPosition: TargetPosition = TargetPosition(1:dim-1).

Note: The functions initialization, distance, and S_func are assumed to be pre-defined and do not need to be reimplemented in this function. The function must strictly follow the above steps to ensure the output (TargetFitness, TargetPosition, Convergence_curve, Trajectories, fitness_history, position_history) is identical to the original code.
function_header: function [TargetFitness,TargetPosition,Convergence_curve,Trajectories,fitness_history, position_history]=GOA(N, Max_iter, 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]=GOA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
val = Best_score + sum(Best_pos) + sum(cg_curve);
correct = 53.27739920;
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]=GOA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
val = Best_score + sum(Best_pos) + sum(cg_curve);
correct = 47.27328612;
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]=GOA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
val = Best_score + sum(Best_pos) + sum(cg_curve);
correct = -7.19651612;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 10
step_description_prompt: Please use MATLAB code to create a function named func_plot that generates a 3D surface plot of the corresponding function based on the input function name. The function definition is function func_plot(func_name). First, call Get_Functions_details(func_name) to obtain lb, ub, dim, and fobj (note: Get_Functions_details is assumed to be pre-defined and does not need to be redefined). Then, set the ranges of x and y according to the value of func_name using the following cases:
- For 'F1', 'F2', 'F3', 'F4', 'F6', 'F14': x = -100:2:100; y = x;
- For 'F5': x = -200:2:200; y = x;
- For 'F7': x = -1:0.03:1; y = x;
- For 'F8', 'F11': x = -500:10:500; y = x;
- For 'F9', 'F15', 'F17', 'F19', 'F20', 'F21', 'F22', 'F23': x = -5:0.1:5; y = x;
- For 'F10': x = -20:0.5:20; y = x;
- For 'F12': x = -10:0.1:10; y = x;
- For 'F13': x = -5:0.08:5; y = x;
- For 'F16': x = -1:0.01:1; y = x;
- For 'F18': x = -5:0.06:5; y = x;

Calculate L as the length of x. Initialize an empty array f. Use nested for loops (i from 1 to L, j from 1 to L) to compute function values:
- 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]);

Finally, plot the 3D surface using 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: 11
step_description_prompt: Please write a MATLAB code with the function name GOA_demo which implements a demo of the Grasshopper Optimization Algorithm (GOA) to optimize the benchmark function F1 using 100 search agents over 500 iterations, visualizes the parameter space, search history, trajectory of the first grasshopper, average fitness of all grasshoppers, and convergence curve, then displays the best solution and its corresponding objective value. The function follows these steps:

1. Clear the workspace and command window using `clear all` and `clc`.
2. Set the random seed to 42 using `rng(42)`.
3. Define the number of search agents as 100 with `SearchAgents_no = 100`, the benchmark function name as 'F1' with `Function_name = 'F1'`, and the maximum number of iterations as 500 with `Max_iteration = 500`.
4. Load the details of the benchmark function using `[lb, ub, dim, fobj] = Get_Functions_details(Function_name)`, where `Get_Functions_details` is a pre-defined function that returns the lower bound (lb), upper bound (ub), dimension (dim), and objective function (fobj) of the specified benchmark function.
5. Run the GOA algorithm using `[Target_score, Target_pos, GOA_cg_curve, Trajectories, fitness_history, position_history] = GOA(SearchAgents_no, Max_iteration, lb, ub, dim, fobj)`, where `GOA` is a pre-defined function that implements the Grasshopper Optimization Algorithm and returns the best objective value (Target_score), best solution (Target_pos), convergence curve (GOA_cg_curve), trajectories of all grasshoppers (Trajectories), fitness history of all grasshoppers (fitness_history), and position history of all grasshoppers (position_history).
6. Create a figure with position `[454 445 894 297]` using `figure('Position', [454 445 894 297])`.
7. Create a 1x5 subplot layout to visualize different aspects of the optimization:
   a. Subplot 1 (1,5,1): Plot the parameter space of the benchmark function using `func_plot(Function_name)` (a pre-defined function for plotting benchmark functions). Set the title to 'Parameter space', x-label to 'x_1', y-label to 'x_2', z-label to `[Function_name,'( x_1 , x_2 )']`, enable the box around the plot using `box on`, and set tight axis limits using `axis tight`.
   b. Subplot 2 (1,5,2): Plot the search history of all grasshoppers (only x1 and x2 dimensions) by looping through each element in `position_history` with `for k1 = 1:size(position_history,1)` and `for k2 = 1:size(position_history,2)`, then using `plot(position_history(k1,k2,1), position_history(k1,k2,2), '.', 'markersize', 1, 'MarkerEdgeColor', 'k', 'markerfacecolor', 'k')` to plot black dots. Mark the best position `Target_pos` using `plot(Target_pos(1), Target_pos(2), '.', 'markersize', 10, 'MarkerEdgeColor', 'r', 'markerfacecolor', 'r')` as a red dot. Set the title to 'Search history (x1 and x2 only)', x-label to 'x1', y-label to 'x2', enable the box, and set tight axis limits.
   c. Subplot 3 (1,5,3): Plot the trajectory of the first grasshopper using `plot(Trajectories(1,:))`. Set the title to 'Trajectory of 1st grasshopper', x-label to 'Iteration#', enable the box, and set tight axis limits.
   d. Subplot 4 (1,5,4): Plot the average fitness of all grasshoppers over iterations using `plot(mean(fitness_history))`. Set the title to 'Average fitness of all grasshoppers', x-label to 'Iteration#', enable the box, and set tight axis limits.
   e. Subplot 5 (1,5,5): Plot the convergence curve of the best score obtained so far using `semilogy(GOA_cg_curve, 'Color','r')` with a red line. Set the title to 'Convergence curve', x-label to 'Iteration#', y-label to 'Best score obtained so far', enable the box, and set tight axis limits.
8. Adjust the figure position to `[39 479 1727 267]` using `set(gcf, 'position', [39 479 1727 267])`.
9. Display the best solution using `display(['The best solution obtained by GOA is : ', num2str(Target_pos)])` and the best optimal value of the objective function using `display(['The best optimal value of the objective function found by GOA is : ', num2str(Target_score)])`.

Note that the functions `Get_Functions_details`, `GOA`, and `func_plot` are assumed to be pre-defined and do not need to be reimplemented in the code.
test_cases: rng(42)
correct_score = 0.000002290097;
correct_pos = 0.000251225244;
val_score = sum(abs(Target_score(:)))*100;
val_pos = sum(abs(Target_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: