I need help for optimization using Ga

I want to make optimization using genetic algorithm to minimize error between force and displacement (simulated and desired ) . I have 3 numbers of variables (height , depth , width) .. can anyone help me for the coding please

[Sam Chak]

Hi @noura

What do you mean by "to minimize the error between force and displacement"? The reason I ask is that force and displacement do not have the same physical unit dimension. Although it is possible to compute the error between two variables of different units, does the optimal result retain interpretable meaning in the sense of human reasoning?

[noura]

I mean to minimize the error between the chart that obtained from ansys and the desired chart

Note : chart between force and displacement

[Sam Chak]

Hi @noura, Could you please provide a sketch of the "charting error" and evaluate how you plan to make effective use of the code snippet in the Answer below? Your feedback is essential for implementing the given code correctly.

[noura]

I need to make optimization using ga to minimize the error between simulated and desired chart as mentioned. The parameters ( height , depth , width ) of a cuboid

[Sam Chak]

Since you already have the code to run the sim, getting the "Simulated Displacement" points and the "Desired Displacement" points into the "data" array in @Walter Roberson's code should be a relatively easy thing to do.

Since the cuboid's dimension cannot be zero or infinity, estimate some realistic values for the lower and upper bounds for the GA to search within these bounded regions.

Answer 1

[Walter Roberson]

data = Something Appropriate to set up data

numvar = 3;
A = []; b = [];
Aeq = []; beq = [];
lb = [0, 0, 0];
ub = [inf, inf, inf];

best = ga(@(x)Simulate_force(x, data), numvar, A, b, Aeq, beq, lb, ub);

function val = Simulate_force(x, data)
   force = something appropriate using data
   displacement = something else appropriate using data
   val = sum((force - displacement).^2);
end

Answer 2

[Star Strider]

Perhaps something like this —

figure
imshow(imread('Messenger_crea...ef71aba6.jpeg'))

x = [1 2.5 10:10:100];
simulated = 0.007 * x;
desired = 0.021 * x;

objfcn = @(b,x) b(1) + b(2).*x;                                     % Objective Function
ftns = @(b) norm(desired - objfcn(b,simulated));                    % Fitness Function

% PopSz = 500;
% Parms = 2;

% optsAns = optimoptions('ga', 'PopulationSize',PopSz, 'InitialPopulationMatrix',randi(1E+4,PopSz,Parms)*1E-3, 'MaxGenerations',5E3, 'FunctionTolerance',1E-10);                                                                  % Options Structure For 'Answers' Problems
% t0 = clock;
% fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
% [B,fval,exitflag,output,population,scores] = ga(ftns, Parms, [],[],[],[],zeros(Parms,1),Inf(Parms,1),[],[],optsAns);
% t1 = clock;
% fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
% GA_Time = etime(t1,t0)
% DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
% fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
% 
% fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval,output.generations)
% 
% fprintf(1,'\tRate Constants:\n')
% for k1 = 1:length(B)
%     fprintf(1, '\t\tB(%2d) = %8.5f\n', k1, theta(k1))
% end

B = ga(ftns, 2)

ga stopped because the average change in the fitness value is less than options.FunctionTolerance.

B = 1x2

0.0106 2.9520

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figure
plot(x, simulated, 'o-', 'DisplayName','Simulated Displacement')
hold on
plot(x, desired, 'x-', 'DisplayName','Desired Displacement')
plot(x, objfcn(B, simulated), 'sr-', 'DisplayName','Optimised Result')
hold off
grid
legend('Location','best')

The ‘B’ vector here are the intercept and slope transformation required to transform ‘simulated’ to ‘desired’. Using ga may be a bit of ‘overkill’ for this problem, however it can be done, assuming I understand what you want to do.

(I’m getting some sort of weird error with respect to declaring the options structure, so I commented-out that code example. That error is ‘The 'ga' function requires the Global Optimization Toolbox’ so I ran it without the options structure and the code I usually use for ga problems, and it worked.)

.

[Sam Chak]

For static optimization problems involving linear graphs, using a ga() may indeed be considered excessive. However, it appears that the OP intends to determine the dimensions of a cuboid (length × width × height) such that, when a certain magnitude of force F is applied, the cuboid of mass m is displaced by a specific distance x. While the 2nd-order motion model is certainly available, the OP has not provided it.

[Star Strider]

Noted. That is the reason I used what has been provided to create an example.