Matlab Code Assistance for Multistart or GA

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Temesgen 2023-4-5

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评论： Alan Weiss 2023-4-20

I want to apply MultiStart global optimization technique for curve fitting and parameter estimation from data set and system of ordinary differential equation. I am new for that concept. I have Number of infected cases for time serious data and want to fit with my model. I am wondering if you could assist me how to estimate using that technique? I will be very happy if you send me any prototype matlabcode!

Any help is appreciated!

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Answer 1

Nihal Reddy 2023-4-13

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I understand you require resources and reference examples for implementing MultiStart optimization technique in MATLAB.

Please refer to the following MATLAB documentation for more information and examples-

Hope this helps!

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Temesgen 2023-4-15

Dear Nihal Readdy, I will refer these marials. Thank you very much!!

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Answer 2

Alan Weiss 2023-4-14

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Perhaps more relevant documentation is here:

MultiStart with lsqnonlin, Problem-Based

MultiStart Using lsqcurvefit or lsqnonlin

Fit ODE Parameters Using Optimization Variables

Fit an Ordinary Differential Equation (ODE)

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

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Alan Weiss 2023-4-18

编辑：Alan Weiss 2023-4-18

I tried looking at your code but I got confused at what you are trying to do.

The idea should be as follows.

Read the data and get a bunch of known, unchanging parameters.
Put all the parameters that you want to fit into a vector x. How many components are in this vector? That should be exactly the same as the number of components in the vector x0. Also in the vector lb.
Write an ODE function. This needs to have the syntax dydt = odefun(t,y). Include the data in this function. See Passing Extra Parameters.
Write an ODE solver function. This is something like function fout = myfun(@odefun,tspan,y0), where myfun calls ode45 and where tspan is the set of times for your ODE, and y0 has the same number of elements as x0. The output fout is a matrix with one row per time step and one column for each component of the ODE. You might need to pass data into this function as well.
After you have debugged the ODE, so that it gives you the expected output for given inputs, you can try to optimize the ODE. Really, you need to take things one step at a time, and make sure that you know how to pass the data around. Get the ODE solver working before you try to optimize anything.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

Temesgen 2023-4-19

Dear Alan, sorry for sending such a wrong code and confusing you, it is due to luck of exposure.

To make it more clear, I have a systems of differential equation with 10 equations (10 state variables with known initial values). The model have 21 parameters and from these 8 of them have fixed values. I want to estimate the remaining 13 parameters. These 13 parameters have inital gues. I have data in excel with time in the first column and infected cases in the second column.

My objective is to minimize the square of the total error which is the difference between the data in the second column with the solution of infected cases at fourth system and estimate model parameters by finding the global solution. I choose use MultiStart method.

Hence, I tryied to write the code as attached herewith. I try to put titles for parts of the code to be more clear. Could you please try to correct and send me the correct code my dear?

Temesgen 2023-4-20

编辑：Temesgen 2023-4-20

Dear Alan, really I appreciate your effort, thank you so much. here are some thing I want to say.

I want to estimate the following (13) model parameters. Keep in mind, there are 8 fixed model paraeters in addition to another 10 state variables. I gave these initial values for simulation purpose.

x(1) = 0.000548 ; % x(1)=Lambdaa

x(2) = 0.004626; % x(2)= phia

x(3) = 0.00227; % x(3)=gammah

x(4) = 0.295; % x(4)=gammaa

x(5) = 0.0002857; % x(5)=mua

x(6) = 0.0014; % x(6)= deltaa

x(7) = 0.001; % x(7)=q

x(8) =0.003189 ; % x(8)=betah

x(9) = 0.000178; % x(9)=betaaa

x(10) = 0.09; % x(10)=betahe

x(11) = 0.0009; % x(11)=betaah

x(12) = 0.175;% x(12)=alphah

x(13) = 0.285; % x(13)=alphaa

2. the estimated values as indicated in ''yout'' shows for the ten state variables (y(1), y(2), ......y(10)). Am I right? But, the program should use those initial values and estimate those 13 parameters and since most of the values will be in between 0 and 1 since ther are rates except some parametes like x(1).

3. The lower and upper bounds should be for these 13 parameters not for the 10 state variables.

you can use these bounds for those parameters

%[Lama betah betaah betahe betaaa gammah gammaa alphah alphaa mua deltaa q phia];

lb=[1 0.14 0.01 0.01 0.01 0 0.01 0.01 0 0.5 0.5 0.01 0.1];

ub=[1000 0.428 0.95 0.95 0.95 0.95 0.75 0.95 0.5 0.85 0.85 0.75 0.9];

Dear, I am very greatful and I can't wait to see the result after you consider and incorporate these ideas into the program.

Alan Weiss 2023-4-20

OK, I clearly misunderstood what are the parameters to vary in your problem. And I am not sure that I understood correctly what you are trying to match, meaning which data are you trying to fit and which output of the ODE you want to match.

Once more I ask you to perform the following.

Give a function F(x) that is the ODE solver, taking your parameters x to a solution y(t). Obviously, I am not sure what that function is in the code that you gave me.
After that we can try to identify the data that you want F(x) to fit. We will call an optimizer and minimize the sum of squares of some parts of y(t) minus some data d(t).

So I am asking you to give F(x). Not to optimize it, just give clear, unambiguous, working code that takes an input set of parameters x and returns an ODE solution y(t).

Alan Weiss

MATLAB mathematical toolbox documentation

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