To solve a multi-objective optimization problem with random parameters using MATLAB, you can use the gamultiobj function from the Global Optimization Toolbox. The gamultiobj function performs multi-objective genetic algorithm optimization.
Here's an example code snippet that demonstrates how to define and solve the multi-objective optimization problem you provided:
matlabCopy code:
% Define the objective functions
fun = @(x) [a*x(1) - b*x(2), b*x(1) + c*x(2)];
% Define the constraints
A = [a, -d; c, a];
b = [b; 1];
lb = [10; 5];
ub = [20; 10];
% Define the bounds for each parameter
lb = [10, 5, 0, 2]; % Lower bounds for [a, b, c, d]
ub = [20, 10, 1, 6]; % Upper bounds for [a, b, c, d]
% Define the options for the genetic algorithm
options = optimoptions('gamultiobj', 'Display', 'final');
% Run the genetic algorithm
[x, fval] = gamultiobj(fun, 2, A, b, [], [], lb, ub, options);
% Display the results
disp('Optimal solutions:');
disp(x);
disp('Objective function values at the optimal solutions:');
disp(fval);
In the above code, fun represents the objective functions as a function handle, and A and b represent the inequality constraints. The lower and upper bounds for the parameters are defined using lb and ub, respectively. The options for the genetic algorithm are set using optimoptions.
After running the gamultiobj function, the optimal solutions and their corresponding objective function values are obtained and displayed.
Make sure you have the Global Optimization Toolbox installed to use the gamultiobj function.
