How to adjust and adapt General code of Metaheuristic algorithm to fit you problem?

Dear all;

I am using a standard algorithm of GWO to implement it of parameters estimation of my problem

The general GWO code is based on Objective function, in my case i do not have the objective function. instead, i have experiment data.

I need the algorithm frameworks (pseaudo code or flowchart ..) in this case to use it for multiple metaheuristic cases.

Here is the general code:

% Grey Wolf Optimizer
function [Alpha_score,Alpha_pos,Convergence_curve]=GWO(SearchAgents_no,Max_iter,lb,ub,dim,fobj)

% initialize alpha, beta, and delta_pos
Alpha_pos=zeros(1,dim);
Alpha_score=inf; %change this to -inf for maximization problems

Beta_pos=zeros(1,dim);
Beta_score=inf; %change this to -inf for maximization problems

Delta_pos=zeros(1,dim);
Delta_score=inf; %change this to -inf for maximization problems

%Initialize the positions of search agents
Positions=initialization(SearchAgents_no,dim,ub,lb);

Convergence_curve=zeros(1,Max_iter);

l=0;% Loop counter

% Main loop
while l<Max_iter
    for i=1:size(Positions,1)  
        
       % Return back the search agents that go beyond the boundaries of the search space
        Flag4ub=Positions(i,:)>ub;
        Flag4lb=Positions(i,:)<lb;
        Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;               
        
        % Calculate objective function for each search agent
        fitness=fobj(Positions(i,:));
        
        % Update Alpha, Beta, and Delta
        if fitness<Alpha_score 
            Alpha_score=fitness; % Update alpha
            Alpha_pos=Positions(i,:);
        end
        
        if fitness>Alpha_score && fitness<Beta_score 
            Beta_score=fitness; % Update beta
            Beta_pos=Positions(i,:);
        end
        
        if fitness>Alpha_score && fitness>Beta_score && fitness<Delta_score 
            Delta_score=fitness; % Update delta
            Delta_pos=Positions(i,:);
        end
    end
    
    
    a=2-l*((2)/Max_iter); % a decreases linearly fron 2 to 0
    
    % Update the Position of search agents including omegas
    for i=1:size(Positions,1)
        for j=1:size(Positions,2)     
                       
            r1=rand(); % r1 is a random number in [0,1]
            r2=rand(); % r2 is a random number in [0,1]
            
            A1=2*a*r1-a; % Equation (3.3)
            C1=2*r2; % Equation (3.4)
            
            D_alpha=abs(C1*Alpha_pos(j)-Positions(i,j)); % Equation (3.5)-part 1
            X1=Alpha_pos(j)-A1*D_alpha; % Equation (3.6)-part 1
                       
            r1=rand();
            r2=rand();
            
            A2=2*a*r1-a; % Equation (3.3)
            C2=2*r2; % Equation (3.4)
            
            D_beta=abs(C2*Beta_pos(j)-Positions(i,j)); % Equation (3.5)-part 2
            X2=Beta_pos(j)-A2*D_beta; % Equation (3.6)-part 2       
            
            r1=rand();
            r2=rand(); 
            
            A3=2*a*r1-a; % Equation (3.3)
            C3=2*r2; % Equation (3.4)
            
            D_delta=abs(C3*Delta_pos(j)-Positions(i,j)); % Equation (3.5)-part 3
            X3=Delta_pos(j)-A3*D_delta; % Equation (3.5)-part 3             
            
            Positions(i,j)=(X1+X2+X3)/3;% Equation (3.7)
            
        end
    end
    l=l+1;    
    Convergence_curve(l)=Alpha_score;
end

Answer 1

[Umang Pandey]

Hi Yasser,

To adapt the Grey Wolf Optimizer (GWO) for parameter estimation using experimental data instead of an explicit objective function, you can create a custom objective function that measures the discrepancy between the model's predictions (based on the current parameters) and the experimental data. This discrepancy can be quantified using a metric such as the mean squared error (MSE).

Here is a pseudo-code framework for the modified GWO algorithm:

1) Initialize Parameters:

• Number of search agents (SearchAgents_no)
• Maximum number of iterations (Max_iter)
• Lower and upper bounds of the parameters (lb, ub)
• Dimension of the parameter space (dim)
• Experimental data (exp_data)

2) Initialize Alpha, Beta, and Delta Positions and Scores:

• Alpha_pos, Beta_pos, Delta_pos as zero vectors of size dim
• Alpha_score, Beta_score, Delta_score as infinity

3) Initialize the Positions of Search Agents:

• Positions matrix with random values within bounds lb and ub

4) Main Loop (Iterate until Max_iter):

• For each search agent:
• Ensure positions are within bounds
• Calculate the fitness of each search agent:
• Use a custom objective function that computes the MSE between model predictions and exp_data
• Update Alpha, Beta, and Delta positions and scores based on fitness
• Update the positions of search agents using GWO equations
• Record the best score in the convergence curve

5) Return Results:

• Best score (Alpha_score)
• Best position (Alpha_pos)
• Convergence curve (Convergence_curve)

You can create a sample Objective function that calculates the MSE between the model's predictions and the experimental data like this:

function mse = customObjectiveFunction(params, exp_data)
    % Model predictions based on current params
    model_predictions = modelFunction(params);
    
    % Calculate Mean Squared Error
    mse = mean((exp_data - model_predictions).^2);
end

function predictions = modelFunction(params)
    % Define your model here using the parameters
    % For example, a simple linear model:
    % predictions = params(1) * x + params(2);
    
    % Replace this with your actual model
    predictions = ...;
end

You can refer to the following File Exchange Submission for GWO implementation:

https://www.mathworks.com/matlabcentral/fileexchange/44974-grey-wolf-optimizer-gwo

Hope this helps!

Best,

Umang