Problem in ant colony optimization code.

hey there!

i have a function

function t=strength(x)

t(1) = -0.804-0.001.*x(1)-0.001.*x(2)+0.0.*x(3)+0.0.*x(4)-0.031.*x(5)+0.005.*x(6)-0.002.*x(7)+0.001.*x(8)-0.735.*x(9)+0.097.*x(10)+0.012.*x(11)+0.078.*x(12)-0.220.*x(13);

end

with 13 variables and their lower and upper bounds are

lb = [490 0 0 19 0 170 700 990 0.35 1.5 16.8 18.5 1]

ub = [500 0 0 22 0 180 710 1000 0.35 1.5 16.8 18.5 1]

i need to perform ACO to minimize the function and get t(1).

this is my code so far. it may be complete wrong or half wrong. I have just started learning matlab and its not been easy for me. it would be very helpful if you guys could help me completing the code.

clear all
close all
% problem definition

obj = @(x)strength(x)

obj = function_handle with value:
    @(x)strength(x)

nVar = 13; % number of parameter
min = [490 0 0 19 0 170 700 990 0.35 1.5 16.8 18.5 1] 

min = 1×13

490.0000 0 0 19.0000 0 170.0000 700.0000 990.0000 0.3500 1.5000 16.8000 18.5000 1.0000

max = [500 0 0 22 0 180 710 1000 0.35 1.5 16.8 18.5 1]

max = 1×13

1.0e+03 * 0.5000 0 0 0.0220 0 0.1800 0.7100 1.0000 0.0003 0.0015 0.0168 0.0185 0.0010

%parameters of ACO
MaxIt=500;      % Maximum Number of Iterations
nAnt=50;        % Number of Ants (Population Size)
Q=1;
tau0=10;        % Initial Phromone
alpha=0.3;      % Phromone Exponential Weight
rho=0.1; 
tau = tau0 * ones(nVar); % Phromone matirx 
Bestfitness=zeros(MaxIt,1);
% Empty Ant
empty_ant.Tour=[];
empty_ant.fitness=[];
% Ant Colony Matrix
ant=repmat(empty_ant,nAnt,1);
BestSol.fitness=inf;

% Main loop of ACO 

for it=1:MaxIt
    
    % Move Ants
    for k=1:nAnt
        
        ant(k).Tour=[];
        
        for l=1:nVar
            
            P=tau(:,l).^alpha;
            
            P(ant(k).Tour)=0;
            
            P=P/sum(P);
            
            j=RouletteWheelSelection(P);
            
            ant(k).Tour=[ant(k).Tour j];
            
        end
        
        ant(k).fitness=fitnessFunction(ant(k).Tour);
        
        if ant(k).fitness<BestSol.fitness
            BestSol=ant(k);
        end
        
    end
    
    % Update Phromones
    for k=1:nAnt
        
        tour=ant(k).Tour;
        
        for l=1:nVar
            
            tau(tour(l),l)=tau(tour(l),l)+Q/ant(k).fitness;
            
        end
        
    end
      % Evaporation
    tau=(1-rho)*tau;
    
    % Store Best Cost
    Bestfitness(it)=BestSol.fitness;
    
    % Show Iteration Information
    disp(['Iteration ' num2str(it) ': Best fitness = ' num2str(Bestfitness(it))]);
    % Plot Solution
    figure(1);
    PlotSolution(BestSol.Tour,model);
    pause(0.01);
    

% Results
figure;
plot(BestCost,'LineWidth',2);
xlabel('Iteration');
ylabel('Best fitness');
grid on;
end

Unrecognized function or variable 'RouletteWheelSelection'.

Answer 1

[Brahmadev]

Hi @harsh Brar,

I understand that you would like to apply “Ant Colony Optimization” but are facing the error "Unrecognized function or variable 'RouletteWheelSelection'. This is because the function  "RouletteWheelSelection" is not defined in your MATLAB path.

The Roulette Wheel Selection is a method used in genetic algorithms for selecting potentially useful solutions for recombination. Here's a simple implementation of the Roulette Wheel Selection:

function j = RouletteWheelSelection(P)
    r = rand;
    C = cumsum(P);
    i = find(r <= C, 1, 'first');
    if isempty(i)
        j = length(P); 
    else
        j = i;
    end
end

You can add this function to your code, and it should resolve the error. Make sure to add it outside your main function, at the end of your script.

Also, your code seems to be incomplete. The function "fitnessFunction" is not defined, and the function "PlotSolution" is also missing. You need to define these functions or replace them with appropriate MATLAB functions.

An example of the aforementioned functions is attached below. Note that these functions should be changed according to the need.

function fit = fitnessFunction(x)
    fit = strength(x); % Edit the fitnessFunction according to need
end

function PlotSolution(Bestfitness)
    plot(Bestfitness, 'LineWidth', 2); % Edit the PlotSolution function according to need
    xlabel('Iteration');
    ylabel('Best Fitness');
    grid on;
end

You would call this function after your main optimization loop, like this:

% After your main ACO loop:
PlotSolution(Bestfitness);

Please refer to the following documentation for more information on the functions used in "Roulette Wheel Selection":

1. https://www.mathworks.com/help/matlab/ref/cumsum.html
2. https://www.mathworks.com/help/matlab/ref/find.html

Hope this helps in resolving your issue!