How to optimize only 2 variables in an objective function with 3 variables?
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I am trying to solve a multiobjective optimization problem.
I have 4 objective functions each of which is a function in 3 variables. Among the 3 variables, 2 variables need to be optimized and are to be used to calculate the 3rd variable using a closed form equation. However, I am unable to figure out how to optimize only 2 of the 3 variables.
Description of overall problem
Each objective function is derived from different inputs which are known. Lets assume inputs as "input_1", "input_2", "input_3", "input_4"
Let's assume the variables to be optimized are "x", "y" and the variables to be calculated are "theta_i", where i=1,2,3,4.
objective function 1 = function (input_1, x,y, theta_1)
objective function 2 = function (input_2, x,y, theta_2)
objective function 3 = function (input_3, x,y, theta_3)
objective function 4 = function (input_4, x,y, theta_4)
optimization solution = gamultiobj([ob1, ob2, ob3, ob4],.....,options);
also
theta_1 = different_function(input_1,x,y)
theta_2 = different_function(input_2,x,y)
theta_3 = different_function(input_3,x,y)
theta_4 = different_function(input_4,x,y)
different_function is not known and needs to be calculated but is generally of the form as stated above.
Any advice on how to proceed with this problem is highly appreciated.
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采纳的回答
Fabio Freschi
2020-6-9
Why don't you remove theta from your objective function definition and call different_function inside function?
function objective_function_1 = objfunction1(input_1, x,y)
theta_1 = different_function(input_1,x,y);
% interesting stuff with input_1, x,y, theta_1
...
end
更多回答(1 个)
Fabio Freschi
2020-6-9
In this case you can set the upper and lower bound for that specific variable to the same value. Maybe it is not efficient but it works. Look the code below
% objective functions
fun = @(x)[x(:,1).^2+x(:,2).^2; (x(:,1)-1).^2+x(:,2).^2];
% number of vars
nvars = 2;
% upper and lower bounds
lb = [-2; -2], ub = [2; 2];
% run optimization
x = gamultiobj(fun,nvars,[],[],[],[],lb,ub);
% set x(:,2) to 0 with same lower and upper bounds
lb = [-2; 0], ub = [2; 0];
% run optimization
x = gamultiobj(fun,nvars,[],[],[],[],lb,ub)
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