Problem: MATLAB Implementation of HGSO Algorithm

The problem involves implementing the HGSO algorithm in MATLAB with necessary helper functions and a main script for optimization and convergence plotting.


Input/Output: The problem takes a predefined fitness function, number of dimensions (dim), search space lower bound (Lb), upper bound (Ub), and optional number of iterations (var_niter), gases (var_n_gases), types (var_n_types). It returns the best solution vector (xf), its fitness value (fval), a 1D vector of best fitness per iteration (vec_Gbest_iter), and a semilogy plot of the convergence curve. The HGSO algorithm uses helper functions to minimize the fitness function.

Required dependencies:

Sub-steps:
step_number: 1
step_description_prompt: Please write a MATLAB function named fun_getDefaultOptions that returns default options including the number of gases, number of types, and number of iterations. The function definition should be: function [var_n_gases, var_n_types, var_niter] = fun_getDefaultOptions(). Inside the function, assign the following values directly: var_n_gases = 35; var_n_types = 5; var_niter = 1000. Any functions called in the provided code are assumed to be already defined and do not need to be redefined.
function_header: function [var_n_gases,var_n_types,var_niter] = fun_getDefaultOptions()

end
test_cases: clear; clc;
rng(42)
[var_n_gases, var_n_types, var_niter] = fun_getDefaultOptions();
if var_n_gases~=35
    error('Wrong!')
end
if var_n_types~=5
    error('Wrong!')
end
if var_niter~=1000
    error('Wrong!')
end
disp('Completely right!')

step_number: 2
step_description_prompt: Please write a MATLAB function named Create_Groups that creates groups of gas positions using the total number of gases, number of gas types, and a position matrix. Function definition: function [Group] = Create_Groups(var_n_gases, var_n_types, X). Algorithm workflow: First, calculate the number of gases per type as N = var_n_gases / var_n_types. Initialize the index variable i to 1. Then, loop j from 1 to var_n_types: assign Group{j}.Position as the submatrix of X from row i to row i+N (inclusive) for all columns; update i to j*N + 1. If i + N exceeds var_n_gases, set i to j*N. The output Group is a cell array where each element is a structure with a 'Position' field storing the corresponding group's positions.
function_header: function[Group]=Create_Groups(var_n_gases,var_n_types,X)

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

var_n_gases = 20;
var_n_types = 4;
dim = 3;
X = rand(var_n_gases, dim);
Group = Create_Groups(var_n_gases, var_n_types, X);
val = 0;
for i = 1:var_n_types
    val = val + sum(Group{i}.Position(:));
end
correct = 34.910486;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

var_n_gases = 10;
var_n_types = 5;
dim = 6;
X = rand(var_n_gases, dim);
Group = Create_Groups(var_n_gases, var_n_types, X);
val = 0;
for i = 1:var_n_types
    val = val + sum(Group{i}.Position(:));
end
correct = 44.712927;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

var_n_gases = 30;
var_n_types = 6;
dim = 8;
X = rand(var_n_gases, dim);
Group = Create_Groups(var_n_gases, var_n_types, X);
val = 0;
for i = 1:var_n_types
    val = val + sum(Group{i}.Position(:));
end
correct = 142.627207;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 3
step_description_prompt: Please write a MATLAB function named sumsqu that calculates the sum of each element in the input vector multiplied by the square of the element and its 1-based index. The function takes a vector xx as input and returns the computed sum as output y.
Function Definition: [y] = sumsqu(xx) where xx is a 1-dimensional input vector of any length, and y is the scalar output.
Algorithm Flow: 1. Compute the length of the input vector xx and assign it to variable d. 2. Initialize a variable sum to 0. 3. Iterate over each index ii from 1 to d (using 1-based indexing): a. Extract the ii-th element of xx and store it in variable xi. b. Update sum by adding ii multiplied by (xi squared) to the current sum. 4. Assign the final value of sum to the output variable y. 5. End the function.
function_header: function [y] = sumsqu(xx)

end
test_cases: clear; clc;
rng(42);
xx1 = [1.2, 2.3, 3.4];
xx2 = [0.5, 1.5, 2.5, 3.5, 4.5];
xx3 = [-1.0, 0.5, -2.0, 1.5];
val = sumsqu(xx1);
correct = 46.700000;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
val = sumsqu(xx2);
correct = 173.750000;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
val = sumsqu(xx3);
correct = 22.500000;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 4
step_description_prompt: Please write a MATLAB function named Evaluate that evaluates and updates the fitness and position of gases based on the given objective function, then returns the updated gas structure, the best fitness value, and the best position. The function is defined as: function [X, best_fit, best_pos] = Evaluate(objfunc, var_n_types, var_n_gases, X, Xnew, init_flag). 

Algorithm flow: 
1. If init_flag == 1: Loop j from 1 to var_n_gases/var_n_types, set X.fitness(j) = objfunc(X.Position(j, :)). 
2. If init_flag ~= 1: Loop j from 1 to var_n_gases/var_n_types, first compute temp_fit = objfunc(Xnew.Position(j, :)). If temp_fit < X.fitness(j), update X.fitness(j) to temp_fit and X.Position(j, :) to Xnew.Position(j, :). 
3. After processing all j, calculate [best_fit, index_best] = min(X.fitness(:)) to get the minimum fitness value and its index. Then set best_pos = X.Position(index_best, :). 

The objfunc called in the function is assumed to be pre-defined and does not need to be redefined in this function.
function_header: function [X,best_fit,best_pos] = Evaluate(objfunc,var_n_types,var_n_gases, X,Xnew,init_flag)

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

objfunc = @(x) sum(x.^2);
var_n_types = 2;
var_n_gases = 6;  
dim = 3;

X.Position = rand(var_n_gases/var_n_types, dim);
Xnew.Position = rand(var_n_gases/var_n_types, dim);
result = 0;
init_flag = 1;
[X1, best_fit1, best_pos1] = Evaluate(objfunc, var_n_types, var_n_gases, X, Xnew, init_flag);
result = result + best_fit1 + sum(best_pos1) + 10;
correct = 11.533328;
tol = abs(result-correct);
if tol>1e-4
    error('Wrong!')
end
init_flag = 0;
X2.Position = rand(var_n_gases/var_n_types, dim);
X2.fitness = inf(1, var_n_gases/var_n_types);
Xnew2.Position = rand(var_n_gases/var_n_types, dim);
[X2_updated, best_fit2, best_pos2] = Evaluate(objfunc, var_n_types, var_n_gases, X2, Xnew2, init_flag);
result = result + best_fit2 + sum(best_pos2) + 20;
correct = 33.113123;
tol = abs(result-correct);
if tol>1e-4
    error('Wrong!')
end
var_n_types3 = 3;
var_n_gases3 = 3;
dim3 = 1;
X3.Position = rand(var_n_gases3/var_n_types3, dim3);
Xnew3.Position = rand(var_n_gases3/var_n_types3, dim3);
init_flag3 = 1;
[X3_updated, best_fit3, best_pos3] = Evaluate(objfunc, var_n_types3, var_n_gases3, X3, Xnew3, init_flag3);
result = result + best_fit3 + sum(best_pos3) + 30;
correct = 63.510526;
tol = abs(result-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 5
step_description_prompt: Please use MATLAB code to create a function named update_variables that updates the K array and computes the matrix S based on iterative parameters, temperature scaling, and input matrices. The function definition is: function [S] = update_variables(var_iter, var_niter, K, P, C, var_n_types, var_n_gases). The algorithm flow is: 1. Calculate T using the formula T = exp(-var_iter / var_niter). 2. Set the constant T0 to 298.15. 3. Initialize the index variable i to 1. 4. Compute N as the quotient of var_n_gases divided by var_n_types (N = var_n_gases / var_n_types). 5. Iterate j from 1 to var_n_types: a. Update K(j) by multiplying its current value with exp(-C(j) * (1/T - 1/T0)). b. Assign the submatrix S(i:i+N, :) the product of the submatrix P(i:i+N, :) and K(j). c. Update i to j * N + 1. d. If i + N exceeds var_n_gases, set i to j * N. Ensure the function uses the exact variable names and operations as specified. The other functions called in the code are assumed to be predefined.
function_header: function [S]=update_variables(var_iter,var_niter,K,P,C,var_n_types,var_n_gases)

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

var_iter1 = 10;
var_niter1 = 100;
var_n_types1 = 2;
var_n_gases1 = 6;
dim1 = 3;
K1 = [0.3; 0.7];  
P1 = [1.0, 2.0, 3.0;   
      4.0, 5.0, 6.0;
      7.0, 8.0, 9.0;
      1.5, 2.5, 3.5;
      4.5, 5.5, 6.5;
      7.5, 8.5, 9.5];
C1 = [0.4; 0.6];
S1 = update_variables(var_iter1, var_niter1, K1, P1, C1, var_n_types1, var_n_gases1);
val = sum(S1(:));
correct = 30.617510;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 6
step_description_prompt: Please write a MATLAB function named update_positions that updates the positions of gases in each type group based on the current group states, best positions, and given parameters. The function takes the current group structure, best positions of each group, global best position vector, group scaling factors, total number of gases, number of gas types, global best fitness, alpha parameter, beta parameter, and number of variables as inputs, and returns the updated group structure with new positions.
function [Group] = update_positions(Group, best_pos, vec_Xbest, S, var_n_gases, var_n_types, var_Gbest, alpha, beta, var_nvars)
vec_flag = [1, -1];
for i = 1:var_n_types
    for j = 1:var_n_gases/var_n_types
        gama = beta * exp(-(var_Gbest + 0.05) / (Group{i}.fitness(j) + 0.05));
        flag_index = floor(2 * rand() + 1);
        var_flag = vec_flag(flag_index);
        for k = 1:var_nvars
            Group{i}.Position(j,k) = Group{i}.Position(j,k) + var_flag * rand() * gama * (best_pos{i}(k) - Group{i}.Position(j,k)) + rand() * alpha * var_flag * (S(i) * vec_Xbest(k) - Group{i}.Position(j,k));
        end
    end
end
end
The function follows these steps: 1) Define a direction flag vector vec_flag as [1, -1]. 2) Iterate over each gas type from 1 to var_n_types. 3) For each gas in the current type (from 1 to var_n_gases/var_n_types), compute gama using the formula beta*exp(-(var_Gbest+.05)/(Group{i}.fitness(j)+.05)). 4) Generate flag_index as floor(2*rand()+1) to select a direction flag var_flag from vec_flag. 5) Iterate over each variable from 1 to var_nvars and update the gas's position using the exact formula that combines the direction flag, random values, gama, best_pos of the group, scaled global best position (S(i)*vec_Xbest), and current position. All input structures and parameters are used directly, and any externally called functions are assumed to be predefined.
function_header: function [Group]=update_positions(Group,best_pos,vec_Xbest,S,var_n_gases,var_n_types,var_Gbest,alpha,beta,var_nvars)

end
test_cases: clear; clc;
rng(42);
var_n_types = 2;
var_n_gases = 4;
var_nvars = 2;
var_Gbest = 0.5;
alpha = 0.3;
beta = 0.4;
for i = 1:var_n_types
    group_size = var_n_gases/var_n_types;
    Group{i}.Position = rand(group_size, var_nvars);
    Group{i}.fitness = rand(group_size, 1);
end
best_pos = cell(1, var_n_types);
for i = 1:var_n_types
    best_pos{i} = rand(1, var_nvars);
end
vec_Xbest = rand(1, var_nvars);
S = rand(1, var_n_types);
Group_updated = update_positions(Group, best_pos, vec_Xbest, S, var_n_gases, var_n_types, var_Gbest, alpha, beta, var_nvars);
val = 0;
for i = 1:var_n_types
    val = val + sum(Group_updated{i}.Position(:));
end
correct = 5.479684;
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 fun_checkpoisions that checks and corrects the position values of gas particles in a Group structure: if the first position element is below the lower bound, set the entire position to the lower bound; if any position element is above the upper bound (and the first element is not below the lower bound), set the entire position to the upper bound.
Function definition: function Group = fun_checkpoisions(dim, Group, var_n_gases, var_n_types, var_down, var_up)
Algorithm flow:
1. Initialize a 1×dim lower bound vector Lb with all elements equal to var_down using Lb = var_down * ones(1, dim).
2. Initialize a 1×dim upper bound vector Ub with all elements equal to var_up using Ub = var_up * ones(1, dim).
3. Iterate over each type index j from 1 to var_n_types:
   a. For each gas particle index i in the current type from 1 to (var_n_gases / var_n_types):
      i. Compute a 1×dim logical vector isBelow1 where each element k (1 ≤ k ≤ dim) is true if Group{j}.Position(i, k) < Lb(k).
      ii. Compute a 1×dim logical vector isAboveMax where each element k (1 ≤ k ≤ dim) is true if Group{j}.Position(i, k) > Ub(k).
      iii. Check if the first element of isBelow1 is true (MATLAB implicitly uses only the first element of a vector in an if condition):
          - If true, set Group{j}.Position(i, :) = Lb (replace the entire row with Lb).
      iv. Else, check if there are any true elements in isAboveMax using find(isAboveMax == true) (which returns non-empty indices if any element is true):
          - If true, set Group{j}.Position(i, :) = Ub (replace the entire row with Ub).
function_header: function Group=fun_checkpoisions(dim,Group,var_n_gases,var_n_types,var_down,var_up)

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

dim = 2;
var_n_gases = 4;
var_n_types = 1;
var_down = -5;
var_up = 5;
Group{1}.Position = [6, 7; -6, 3; 2, 2; 4, -8];
Group_checked = fun_checkpoisions(dim, Group, var_n_gases, var_n_types, var_down, var_up);
val = sum(Group_checked{1}.Position(:));
correct = 7.000000;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

dim = 2;
var_n_gases = 4;
var_n_types = 1;
var_down = -5;
var_up = 5;
Group{1}.Position = [1.2, 2.5; -3.1, 4.2; 0.5, -2.8; 3.7, -1.3];
Group_checked = fun_checkpoisions(dim, Group, var_n_gases, var_n_types, var_down, var_up);
val = sum(Group_checked{1}.Position(:));
correct = 4.900000;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

dim = 3;
var_n_gases = 3;
var_n_types = 1;
var_down = -3;
var_up = 3;
Group{1}.Position = [
    1.5, 0.8, -2.1;
    -0.7, 2.4, 1.3;
    2.9, -1.2, 0.5
];
Group_checked = fun_checkpoisions(dim, Group, var_n_gases, var_n_types, var_down, var_up);
val = sum(Group_checked{1}.Position(:));
correct = 5.400000;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 8
step_description_prompt: Please use MATLAB code to generate a function named worst_agents that replaces the positions of the worst-performing agents in the population X with random values within the specified range [G_min, G_max] based on the calculated number of agents Nw to replace. Function definition: function [X] = worst_agents(X, M1, M2, dim, G_max, G_min, var_n_gases, var_n_types). Algorithm flow: 1. Sort the fitness values of agents in X (X.fitness) in descending order using the sort function to get the sorted fitness values X_sort and their original indices X_index. 2. Calculate M1N as M1 multiplied by var_n_gases divided by var_n_types. 3. Calculate M2N as M2 multiplied by var_n_gases divided by var_n_types. 4. Compute Nw as the rounded value of a random number uniformly distributed between M1N and M2N, calculated as round((M2N - M1N) .* rand(1,1) + M1N). 5. For each k from 1 to Nw, set the position of the k-th worst-performing agent (determined by X_index(k)) in X.Position to a random vector of length dim where each element lies within [G_min, G_max]; this random vector is generated as G_min + rand(1, dim) .* (G_max - G_min). Note: The functions called in the code (such as sort) are assumed to be already defined and do not need to be redefined.
function_header: function [X]=worst_agents(X,M1,M2,dim,G_max,G_min,var_n_gases,var_n_types)

end
test_cases: clear; clc;
rng(42);
result = 0;
M1 = 0.1;
M2 = 0.3;
dim1 = 3;
G_max1 = 10;
G_min1 = -10;
var_n_gases1 = 20;
var_n_types1 = 4;
group_size1 = var_n_gases1/var_n_types1;
X1.Position = rand(group_size1, dim1) * 20 - 10;
X1.fitness = rand(group_size1, 1) * 100; 
X1_updated = worst_agents(X1, M1, M2, dim1, G_max1, G_min1, var_n_gases1, var_n_types1);
result = result + sum(X1_updated.Position(:)) + sum(X1_updated.fitness(:));
correct = 139.274855;
tol = abs(result-correct);
if tol>1e-4
    error('Wrong!')
end

result = 0;
M1_2 = 0.8;
M2_2 = 1.0;
dim2 = 2;
G_max2 = 5;
G_min2 = -5;
var_n_gases2 = 10;
var_n_types2 = 2;
group_size2 = var_n_gases2/var_n_types2;
X2.Position = ones(group_size2, dim2) * 0.5;
X2.fitness = (group_size2:-1:1)';
X2_updated = worst_agents(X2, M1_2, M2_2, dim2, G_max2, G_min2, var_n_gases2, var_n_types2);
result = result + sum(X2_updated.Position(:)) + sum(X2_updated.fitness(:));
correct = 5.810697;
tol = abs(result-correct);
if tol>1e-4
    error('Wrong!')
end

result = 0;
M1_3 = 0.2;
M2_3 = 0.2;
dim3 = 4;
G_max3 = 1;
G_min3 = 0;
var_n_gases3 = 15;
var_n_types3 = 3;
group_size3 = var_n_gases3/var_n_types3;
X3.Position = rand(group_size3, dim3);
X3.fitness = rand(group_size3, 1) * 50;
X3_updated = worst_agents(X3, M1_3, M2_3, dim3, G_max3, G_min3, var_n_gases3, var_n_types3);
result = result + sum(X3_updated.Position(:)) + sum(X3_updated.fitness(:));
correct = 145.184771;
tol = abs(result-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 9
step_description_prompt: Please use MATLAB code to generate a function named HGSO that implements the Henry Gas Solubility Optimization algorithm for minimizing an objective function. The function optimizes the given objective function within specified bounds and returns the best solution vector, the corresponding best objective value, and the best objective value at each iteration.

Function Definition:
function [vec_Xbest, var_Gbest, vec_Gbest_iter] = HGSO(objfunc, dim, var_down, var_up, var_niter, var_n_gases, var_n_types)

Algorithm Flow:
1. Check the number of input arguments: if fewer than 5 inputs are provided, call `fun_getDefaultOptions()` to set default values for `var_n_gases`, `var_n_types`, and `var_niter`.
2. Initialize algorithm parameters: `l1=5E-03`, `l2=100`, `l3=1E-02`, `alpha=1`, `beta=1`, `M1=0.1`, `M2=0.2`.
3. Generate random vectors `K`, `P`, and `C` using `rand()` with dimensions `var_n_types×1`, `var_n_gases×1`, and `var_n_types×1` respectively, scaled by `l1`, `l2`, and `l3`.
4. Initialize the population matrix `X` with size `var_n_gases×dim` using uniform random numbers between `var_down` and `var_up`.
5. Create groups from the population using `Create_Groups(var_n_gases, var_n_types, X)`.
6. Evaluate each group using `Evaluate()` to get the initial `best_fit` (best objective value for each group) and `best_pos` (best solution vector for each group).
7. Find the initial global best: compute `var_Gbest` (minimum value in `best_fit`) and `vec_Xbest` (corresponding `best_pos` entry).
8. Iterate for `var_niter` times:
   a. Update variables `S` using `update_variables(var_iter, var_niter, K, P, C, var_n_types, var_n_gases)`.
   b. Update the positions of agents in each group to `Groupnew` using `update_positions(Group, best_pos, vec_Xbest, S, var_n_gases, var_n_types, var_Gbest, alpha, beta, dim)`.
   c. Check and correct positions using `fun_checkpoisions(dim, Groupnew, var_n_gases, var_n_types, var_down, var_up)` to ensure they are within bounds.
   d. Evaluate each updated group (`Groupnew`) using `Evaluate()` to update `Group`, `best_fit`, and `best_pos`.
   e. Replace the worst agents in each group using `worst_agents(Group{i}, M1, M2, dim, var_up, var_down, var_n_gases, var_n_types)`.
   f. Compute the current best objective value `var_Ybest` (minimum of `best_fit`) and store it in `vec_Gbest_iter` at the current iteration index.
   g. Update the global best: if `var_Ybest` is less than `var_Gbest`, update `var_Gbest` to `var_Ybest` and `vec_Xbest` to the corresponding `best_pos` entry.

Note: The functions `fun_getDefaultOptions`, `Create_Groups`, `Evaluate`, `update_variables`, `update_positions`, `fun_checkpoisions`, and `worst_agents` called in the code are assumed to be pre-defined and do not need to be re-implemented.
function_header: function [vec_Xbest, var_Gbest,vec_Gbest_iter] = HGSO(objfunc, dim,var_down,var_up,var_niter,var_n_gases,var_n_types)

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

objfunc = @sumsqu;
dim = 2;
var_down = -5;
var_up = 5;
var_niter = 3;
var_n_gases = 6;
var_n_types = 2;
[vec_Xbest, var_Gbest, vec_Gbest_iter] = HGSO(objfunc, dim, var_down, var_up, var_niter, var_n_gases, var_n_types);
val = var_Gbest + sum(vec_Xbest) + sum(vec_Gbest_iter);
correct = 0.768859;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

objfunc = @sumsqu;
dim = 4;
var_down = -6;
var_up = 3;
var_niter = 3;
var_n_gases = 6;
var_n_types = 6;
[vec_Xbest, var_Gbest, vec_Gbest_iter] = HGSO(objfunc, dim, var_down, var_up, var_niter, var_n_gases, var_n_types);
val = var_Gbest + sum(vec_Xbest) + sum(vec_Gbest_iter);
correct = 4.798335;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end

objfunc = @sumsqu;
dim = 3;
var_down = -4;
var_up = 4;
var_niter = 6;
var_n_gases = 8;
var_n_types = 4;
[vec_Xbest, var_Gbest, vec_Gbest_iter] = HGSO(objfunc, dim, var_down, var_up, var_niter, var_n_gases, var_n_types);
val = var_Gbest + sum(vec_Xbest) + sum(vec_Gbest_iter);
correct = 13.907969;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 10
step_description_prompt: Please write MATLAB code that defines a function named HGSO which implements the Henry Gas Solubility Optimization algorithm for minimizing a given fitness function. Then, create a main script that uses this function to perform optimization and visualize the convergence curve. The HGSO function must be defined with the input parameters (fitfun, dim, Lb, Ub) and output parameters (xf, fval, vec_Gbest_iter), where: - fitfun: The fitness function to be minimized (assumed pre-defined). - dim: The number of dimensions of the search space. - Lb: The lower bound of the search space (scalar, applied to all dimensions). - Ub: The upper bound of the search space (scalar, applied to all dimensions). - xf: The best solution vector found by the optimization. - fval: The fitness value of the best solution xf. - vec_Gbest_iter: A 1D vector where each element is the best fitness value obtained at each iteration (length equal to the number of iterations, var_niter). The main script must perform the following steps in order: 1. Execute clc to clear the command window. 2. Execute clear all to remove all variables from the workspace. 3. Execute rng(42) to set the random number generator seed for reproducibility. 4. Execute close all to close all open figures. 5. Define the fitness function as fitfun = @sumsqu (the sumsqu function is assumed to be pre-defined and does not need to be redefined). 6. Set dim = 30, var_niter = 1000, Lb = -10, Ub = 10. 7. Call the HGSO function: [xf, fval, vec_Gbest_iter] = HGSO(fitfun, dim, Lb, Ub). 8. Create a new figure with figure. 9. Plot the convergence curve using semilogy(vec_Gbest_iter, 'r'). 10. Set the x-axis limits to [0 var_niter] with xlim([0 var_niter]).
test_cases: rng(42)
val = fval + sum(xf) + sum(vec_Gbest_iter);
correct = 2642.186542;
tol = abs(val-correct);
if tol>1e-4
    error('Wrong!')
end
disp('Completely right!')

step_number: 11
step_description_prompt: Please write a MATLAB function named get_nan that returns a NaN scalar.
Function definition: function y = get_nan()
Algorithm flow: 1. Return a NaN scalar directly using the built-in `nan` function by assigning it to the output variable `y`.

General solution:

General tests: