how to create function for below objective function.

Iam trying to implement genetic algorithm in suspension design of vehicle.my objective function is

ABS(z1+z2)+MAX(ABS(z2)-9.8,0)+MAX(ABS(z1-z2)-0.13,0)+MAX(w-1,0)

please give me code how to create function with it in matlab.so that i can use it with ga tool.

Answer 1

[arushi]

Hi Simpy,

To implement a genetic algorithm (GA) for optimizing a suspension design in MATLAB, you need to define your objective function and use it with the `ga` function.

% Number of variables
nvars = 3; % [z1, z2, w]

% Set bounds for each variable if needed
lb = [-10, -10, 0]; % Lower bounds for [z1, z2, w]
ub = [10, 10, 5];  % Upper bounds for [z1, z2, w]

% Set options for the genetic algorithm
options = optimoptions('ga', 'Display', 'iter', 'PlotFcn', @gaplotbestf);

% Run the genetic algorithm
[x_optimal, fval] = ga(@suspensionObjective, nvars, [], [], [], [], lb, ub, [], options);

% Display the results
fprintf('Optimal z1: %.4f\n', x_optimal(1));
fprintf('Optimal z2: %.4f\n', x_optimal(2));
fprintf('Optimal w: %.4f\n', x_optimal(3));
fprintf('Minimum Objective Value: %.4f\n', fval);

This setup provides a basic framework for using a genetic algorithm to optimize the suspension design based on your specified objective function. Adjust the bounds and options to suit your specific design constraints and requirements.

Hope this helps.

Answer 2

[John D'Errico]

Your objective function has three unknown variables in it, so z1, z2, and w. But an optimizer MUST have it as a vector of length 3.

So first, I'll write the objective using the three variables as you know them.

yourobj = @(z1,z2,w) abs(z1+z2) + max(abs(z2)-9.8,0) + max(abs(z1-z2)-0.13,0) + max(w-1,0);

And that is exactly as you wrote it. But as I said, a tool like GA needs to use vectors. So we can just create an objective function for GA.

gaobj = @(V) yourobj(V(1),V(2),V(3));

And now GA can use this function as an objective. If you have constraints, etc., they all need to work in terms of a VECTOR of length 3.

Note the use of abs and max make this a problem NOT suitable for most optimizers becaue the result will be an objective function that is not differentiable. However, GA should be able to handle it, so you have made a good choice there.

(Interestingly, I debated suggeting you use an optimproblem to solve this, but abs and max are not defined for optimvars.)