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);
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.