Question about CMA-ES step size sigma

[Kefeng]

Hi everyone,

I am new here. I am working in geophysics and I would like to invert for a simple layered velocity model using CMA-ES optimization method. I downloaded the purecmaes.m code in Matlab here: https://www.lri.fr/~hansen/cmaes_inmatlab.html, and also implemented one in Fortran 90. I successfully ran it for several optimization functions (Rastrigin, Rosenbrock, Styblinski-Tang...) but can't make it work for my inversion problem.
Indeed, I have to invert for the velocity of each layer (ranging from 500 to 6000 m/s) and also their thicknesses (from 10 to 500 meters). Therefore, as the step size sigma is used to generate a normally distributed population around the current generation mean, using the same step size sigma to generate the velocities and the thicknesses will generate unconsistent parameters (e.g. negative thicknesses).
Is there a way to use CMA-ES to invert for parameters of different scales? (not to mention that I would also like to invert for a ratio for each layer, which means that I will have parameters between 0 and 1)...

Thank you in advance for your replies.

 

[lofgran]

Hello,

Thank you for sharing your question and your progress with CMA-ES optimization method. As a fellow geophysicist, I understand the challenges of inverting for layered velocity models.

One solution to your problem could be to use a scaling factor for each parameter during the optimization process. This will allow the algorithm to search within a smaller range for each parameter, making it more efficient and less likely to generate inconsistent values.

Another option could be to use a multi-objective optimization approach, where you optimize for both the velocities and thicknesses simultaneously. This can be achieved by defining a fitness function that takes into account both the misfit between observed and predicted data, as well as the consistency of the model parameters.

Additionally, you may want to consider incorporating prior information or constraints in your inversion process. This can help guide the optimization towards more realistic solutions and reduce the search space for each parameter.

I hope these suggestions are helpful to you. Best of luck with your inversion process!