optimization by changing input variables

Hello community,

I have a problem where i solve for 7 variables using an ode. The ode takes 4 input variables (changing with ime) and solves the equations. Now I am looking for develping an optimization problem where the 4 input variables has to be manipulated such that 1 varaible among this 7 has to be optimized (minima/maxima).

I have the following main function which calls other functions to solve the equations (not given completely and left few blanks). It has 4 input datasets (which i am currently acquring from the excel sheet). These 4 inputs has to be manipulated by the GA optimizer such that 1 varaiable- z (: ,3) has to be optimized (minimized/maximized).

Please give me your valuable suggestions/ ideas on how to proceed this.

function RF = gatrial (ip1,ip2,ip3,ip4)
%% Section 1: Input data: 
tspan1 = (---)';        
tspan2 = (---)';  
tspan3 = (---)';     
dataset = xlsread('---.csv'); % data acquiring from excel file
Data_1 = dataset(:,4);
Data_2 = dataset(:,2);
Data_3 = dataset(:,5);
Data_4 = dataset(:,3);
 
%% ip3 and ip4 used to calculate p7

%% Section 2:  ode call 
%initial values 
------
z0=[--]
%num interval defining and num vars
----

%for substituting different values for each iteration
for j = 1 : num_interval
    %%calling parameters which change each iteration and calling ode function
    p7 = ---(j);
    ip1 = Data_1(j);
    ip2 = Data_2(j);
    ip3 = Data_3(j);
    [t2,z2] = ode45(@(t,z) eqns (t,z,p7,ip1,ip2,ip3),...
                  tspan1(j:j+1), z0);
    t(j) = t2(end);
    z0 = z2(end,:);
    z(j,:) = z0;
end
%%final solved values
t = [tspan(1); t];
z = [z0init; z]; 
res1 = [z];

%% 2 more similar sections
--
---
----
%Final result compiled
Time = [tspan1; tspan2; tspan3];
Result_Final = [res1; res2 ; res3];
RF = [Time Result_Final];
end

[Nivedhitha S]

Update:

I have modified the function as follows:

function obj = gatrial (ip1,ip2,ip3,ip4)
% --------all eqns and ode call-------------
obj = Result_Final (end,2);
end

And also defined a GA optimization function as follows:

options = gaoptimset ('UseParallel', true, 'PopulationSize', 200)
lb=[- - - -];
ub=[- - - -];
[X fval] = ga(@gatrial,4,[],[],[],[], [lb],[ub],[], options); 

Now how to get the optimal results for ip1- ip4 such that obj could be minimized?

Though ip1-4 are used ultimately in calculation of obj value, i can't write a simple straightforward equation like obj = ----*ip1+---*ip2... etc., as shown in most of the examples. I am kinda confused on how to solve this kind of problem through optimization. should i create a matrix with obj and also the 4 ips?

Any help will be appreciated.

Thanks.

[Rachit Raj Rajput]

Have you found the solution yet?

Answer 1

[Roshan Hingnekar]

Refer to the following link on optimisation toolbox

https://in.mathworks.com/products/optimization.html