Tracking the variation of the distance between optimization variable and the optimal solution over the iteration time

I have written a code as:

function x_opt = locao2(h, C, BS_positions, alpha,x0)
objective = @(x) -calculatePDF(x(1), x(2), h, C, BS_positions, alpha);

% Constraints: x and y must be within [xb, xf] and [yb, yf] range
lb = [0, 0]; % Adjust based on the actual range
ub = [500, 500]; % Adjust based on the actual range
% Using genetic algorithm for optimization
x_opt = ga(objective,2, [], [], [], [], lb, ub, []);
end

objective and calculatePDF are functions selfmade. I want to track the variation of the distance between optimization variable and the optimum x0 over the iteration time. So who can provide me a total code, thanks very much!

Answer 1

[Matt J]

function x_opt = locao2(h, C, BS_positions, alpha,x0)

    objective = @(x) -calculatePDF(x(1), x(2), h, C, BS_positions, alpha);
    
    % Constraints: x and y must be within [xb, xf] and [yb, yf] range
    lb = [0, 0]; % Adjust based on the actual range
    ub = [500, 500]; % Adjust based on the actual range
    % Using genetic algorithm for optimization
    
    options = optimoptions('ga', 'PlotFcn', {@plotdistx0});
    
    x_opt = ga(objective,2, [], [], [], [], lb, ub, [], options);


        function state = plotdistx0(options, state, flag)

            if(strcmp(flag,'init')) % Set up the plot
                xlim([1,options.MaxGenerations]);
                axx = gca;
                axx.YScale = 'log';
                hold on;
                xlabel Generation
                title('Distance to x0')
            end
            
           plot(state.Generation,norm(state.Best(:)-x0(:)),'xr');
           
        end


end

[世轩 张]

Thank you so much for your solution, but I found that it's not so accurate, I limit the optimum and variable in 500*500, so it's unlikely that error can reach 10^5 and even goes higher as the iteration continue, which is impossible.

I have edit some places in your code as:

function x_opt = locao2(h, C, BS_positions, alpha,user)

x0=user';

objective = @(x) -calculatePDF(x(1), x(2), h, C, BS_positions, alpha);

% Constraints: x and y must be within [xb, xf] and [yb, yf] range

lb = [0, 0]; % Adjust based on the actual range

ub = [500, 500]; % Adjust based on the actual range

% Using genetic algorithm for optimization

options = optimoptions('ga', 'PlotFcn', {@plotdistx0});

x_opt = ga(objective,2, [], [], [], [], lb, ub, [], options);

function state = plotdistx0(options, state, flag)

if(strcmp(flag,'init')) % Set up the plot

xlim([1,options.MaxGenerations]);

axx = gca;

axx.YScale = 'log';

hold on;

xlabel Generation

title('Distance to x0')

end

plot(state.Generation,norm(state.Best-x0),'xr');

end

end

Aboving is after the final iteration the distance between x_opt and x0 and the time consume.

Also, the best result I need is actually error-comsuming time, better than error-iteration times, look forward your reply, thanks!

[Torsten]

Check norm(x_opt - x0) and compare with the plot.

What is p* ? I don't see a variable p in your code.

[世轩 张]

x* is the optimum of the varible, p* is the optimum of the dependent variable, just terms.

[Torsten]

And what about the last point in the plot and norm(x_opt - x0) ? Do they agree ?

[世轩 张]

Sorry I can't get you, the last point? I have put the results on the previous comment.

[世轩 张]

It should be 1.0004

[Torsten]

Thus the last value in the plot is around 7e5 and norm(x_opt - x0) is 1.0004 - thus the two values don't agree ?

[世轩 张]

Yeah, also as the iteration continue, x should be more and more close to x0, x0 is the x* which I'm sure about. So the distance should be less and less.

[Torsten]

And what do you get for norm(x_opt-x0) after ga has finshed ?

Just insert the line

norm(x_opt-x0)

after

x_opt = ga(objective,2, [], [], [], [], lb, ub, [], options);

[世轩 张]

Yes I have.

[Torsten]

And where is the result ?

[世轩 张]

user is the x*, ue is the x_opt,

[世轩 张]

My code is an algorithm of localization, to estimate where the user is

[世轩 张]

I found where the wrong from , the state.best is not the 2*1 matrix, it's not the variable I want . It should be a point in a 2D plot.

[Matt J]

Show us both objective(x_opt) and objective(x0).

[Matt J]

Change the plot function to,

        function state = plotdistx0(options, state, flag)
            if(strcmp(flag,'init')) % Set up the plot
                xlim([1,options.MaxGenerations]);
                axx = gca;
                axx.YScale = 'log';
                hold on;
                xlabel Generation
                title('Distance to x0')
            end
            
            
           [~,imin]=min(state.Score);
           xbest=state.Population(imin,:);
           dist= norm( xbest(:) - x0(:);
           
           plot(state.Generation, dist,'xr');
           
        end