Output is not as expected

I m trying to do ant colony optimisation based upqc but the out is not as expected

I am getting above output i.e, zeroes but the required one is as shown below

[Torsten]

How should anybody be able to help with the information given ?

[Sahithi Kandhukuri]

sorry..... below are the attached files required

[Sam Chak]

I haven't tested everything yet, but I experimented with a basic quadratic function and observed that the optimal solution obtained through Ant Colony Optimization does not yield the lowest cost. Until this issue is addressed, it does not make sense to proceed with the current optimization problem.

format long g

%% ACO parameters
n_iter  = 5;                   % number of iteration
NA      = 5;                   % Number of Ants
alpha   = 0.8;
beta    = 0.2;
roh     = 0.7;                  % Evaporation rate
n_param = 1;                    % Number of parameters
LB      = 0.1*ones(1,n_param);  % lower band
UB      = 2.0*ones(1,n_param);  % upper band
n_node  = 1000;                 % number of nodes for each param

%% intilalizing some variables
cost_best_prev      = inf;
ant                 = zeros(NA,n_param);
cost                = zeros(NA,1);
tour_selected_param = zeros(1,n_param);
param_mat           = zeros(n_iter,n_param);
Nodes               = zeros(n_node,n_param);
prob                = zeros(n_node,n_param);

%% Generating nodes
T   =  ones(n_node, n_param).*eps;
dT  = zeros(n_node, n_param);
for i = 1:n_param
    Nodes(:,1) = linspace(LB(i), UB(i), n_node);
end

%% iteration loop
for iter = 1:n_iter

    for tour_i = 1:n_param
        prob(:,tour_i) = (T(:,tour_i).^alpha).*((1./Nodes(:,tour_i)).^beta);
        prob(:,tour_i) = prob(:,tour_i)./sum(prob(:,tour_i));
    end

    for A = 1:NA
        for tour_i = 1:n_param
            node_se1 = rand;
            node_ind = 1;
            prob_sum = 0;
            for j = 1:n_node
                prob_sum = prob_sum + prob(j,tour_i);
                if prob_sum >= node_se1
                    node_ind = j;
                    break
                end
            end
            ant(A,tour_i) = node_ind;
            tour_selected_param(tour_i) = Nodes(node_ind, tour_i);
        %% 
        end
        
        %% Put the Cost function here:
        % cost(A) = cost_func(tour_selected_param);
        cost(A) = costume(tour_selected_param);
        
        disp(['Ant number: ' num2str(A)])
        disp(['Ant Cost: ' num2str(cost(A))])
        disp(['Ant parameters: ' num2str(tour_selected_param)])
        if iter~=1
            disp(['iteration:' num2str(iter)])
            disp('________________')
            disp(['Best cost:' num2str(cost_best)])
            for i=1:n_param
                tour_selected_param(i) = Nodes(ant(cost_best_ind,1), i);
            end
            disp(['Best parameters:' num2str(tour_selected_param)])
        end
    
    end
    [cost_best, cost_best_ind] = min(cost);

    % Elistem
    if (cost_best > cost_best_prev) && (iter ~= 1)
        [cost_worst, cost_worst_ind] = max(cost);
        ant(cost_worst_ind,:)        = best_prev_ant;
        cost_best                    = cost_best_prev;
        cost_best_ind                = cost_worst_ind;
    else
        cost_best_prev = cost_best;
        best_prev_ant  = ant(cost_best_ind,:);
    end

    dT = zeros(n_node,n_param); % Change of Phormone
    for tour_i = 1:n_param
        for A = 1:NA
            dT(ant(A, tour_i), tour_i) = dT(ant(A, tour_i), tour_i) + cost_best/cost(A);
        end
    end

    T = roh.*T + dT;
end

Ant number: 1

Ant Cost: 1.4451

Ant parameters: 1.6672

Ant number: 2

Ant Cost: 1.0667

Ant parameters: 1.2583

Ant number: 3

Ant Cost: 1.5524

Ant parameters: 1.7432

Ant number: 4

Ant Cost: 1.9254

Ant parameters: 1.962

Ant number: 5

Ant Cost: 1.7482

Ant parameters: 1.865

Ant number: 1

Ant Cost: 1.5524

Ant parameters: 1.7432

iteration:2

________________

Best cost:1.0667

Best parameters:1.2583

Ant number: 2

Ant Cost: 1.4451

Ant parameters: 1.6672

iteration:2

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 3

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:2

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 4

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:2

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 5

Ant Cost: 1.9254

Ant parameters: 1.962

iteration:2

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 1

Ant Cost: 1.7482

Ant parameters: 1.865

iteration:3

________________

Best cost:1.0667

Best parameters:1.2583

Ant number: 2

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:3

________________

Best cost:1.0667

Best parameters:1.2583

Ant number: 3

Ant Cost: 1.7482

Ant parameters: 1.865

iteration:3

________________

Best cost:1.0667

Best parameters:1.865

Ant number: 4

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:3

________________

Best cost:1.0667

Best parameters:1.865

Ant number: 5

Ant Cost: 1.4451

Ant parameters: 1.6672

iteration:3

________________

Best cost:1.0667

Best parameters:1.865

Ant number: 1

Ant Cost: 1.5524

Ant parameters: 1.7432

iteration:4

________________

Best cost:1.0667

Best parameters:1.2583

Ant number: 2

Ant Cost: 1.4451

Ant parameters: 1.6672

iteration:4

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 3

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:4

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 4

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:4

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 5

Ant Cost: 1.4451

Ant parameters: 1.6672

iteration:4

________________

Best cost:1.0667

Best parameters:1.6672

Ant number: 1

Ant Cost: 1.5524

Ant parameters: 1.7432

iteration:5

________________

Best cost:1.0667

Best parameters:1.2583

Ant number: 2

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:5

________________

Best cost:1.0667

Best parameters:1.2583

Ant number: 3

Ant Cost: 1.9254

Ant parameters: 1.962

iteration:5

________________

Best cost:1.0667

Best parameters:1.962

Ant number: 4

Ant Cost: 1.0667

Ant parameters: 1.2583

iteration:5

________________

Best cost:1.0667

Best parameters:1.962

Ant number: 5

Ant Cost: 1.9254

Ant parameters: 1.962

iteration:5

________________

Best cost:1.0667

Best parameters:1.962

%% ACO Result
k = tour_selected_param

k = 
          1.96196196196196

J = costume(k)

J = 
          1.92537081626171

%% Compare with other Optimizer
[kopt, fval] = fminunc(@costume, 2)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

kopt = 
     1

fval = 
     1

%% Custom Optimization Solution for Targeted User Minimum Equation
function J = costume(k)
    J   = (k - 1)^2 + 1;
end

[Sahithi Kandhukuri]

Sorry I am unbale to understand could you please describ it clearly

[Sam Chak]

Okay, I gave it a shot. I experimented with your Ant Colony Optimization algorithm (ACO) using a basic quadratic function. See the graph below. The minimum value occurs when , and at that point, the cost is . If the ACO works well, it should return after numerous iterations.

J   = @(k) (k - 1).^2 + 1;
k   = 0:0.01:2;
plot(k, J(k)), hold on
plot(1, 1, 'ro', 'markersize', 12, 'linewidth', 2), grid
xlabel k, ylabel J

[Sahithi Kandhukuri]

Can you please suggest me a way forward

How to make that ACO code work fine

[Torsten]

Why not asking the author of the code ?

https://uk.mathworks.com/matlabcentral/fileexchange/52859-ant-colony-optimization-aco

@Sam Chak

I don't know exactly what it means in the code description under the above address:

MATLAB implementation of ACO for Discrete and Combinatorial Optimization Problems

Maybe it's not suited for your (and the OP's) continuous optimization problem.

[Sahithi Kandhukuri]

https://in.mathworks.com/matlabcentral/fileexchange/50873-ant-colony-optimization-for-pid-controller-of-a-dc-motor?s_tid=ta_fx_results

I have taken this ACO algorithm as reference

[Torsten]

Better take a "conventional" optimizer as reference (e.g. fmincon).

[Sahithi Kandhukuri]

https://www.youtube.com/watch?v=HgYYW1TlzyY

just to know..how did he get the output using same ACO algorithm

[Sam Chak]

HI @Torsten,

Upon reviewing the code, Yarpiz developed an iteration of Ant Colony Optimization (ACO) designed for addressing Combinatorial Optimization Problems, such as the well-known Travelling Salesman and Binary Knapsack problems. Overall, I am of the opinion that the ACO concept can be applied to optimize specific control design parameters within continuous-time dynamical systems.

Hi @Sahithi Kandhukuri

This problem involves numerous design factors that impact the solution, especially when there are no error messages. It's not as straightforward as a simple equation like 1 + 2 = 3. For instance, at the 11:40 timestamp in the video, the optimal solution is presented as follows:

If the Simulink parameters are configured appropriately,

%% Best solution by ACO
k   = [77 230 193 30 330 290];

%% Parameters in Simulink
ke  = k(1,1);
kce = k(1,2);
ku  = k(1,3);
X   = k(1,4);
z_a = abs(k(1,5));
v_a = abs(k(1,6));

%% Fuzzy Logic parameters in Simulink
% negative big
NB  = -X;
% negative medium
NM  = -X/2;
% positive medium
PM  = X/2;
% positive big
PB  = X;
% Sam: Zero
Z   = 0;        % set by User

we would anticipate witnessing identical results (for deterministic systems) as demonstrated in the YouTube video:

However, the outcomes (Load Voltage and Injected Voltage) I achieved in R2023b are evidently different.

[Sahithi Kandhukuri]

Will changing the parameters help us in getting those results?

[Sam Chak]

In theory, yes. The keys to achieving the same results lie in your contributions to this work. The test suggests that despite using the same optimal values, your Simulink model may differ from the YouTube version.