You can try differential evolution optimization to perform shape optimization. You have to decide the number of parameters you would like to vary and come up with constraints and objective function. 

To write the code, Matlab has some built in functions which can found here. 

https://www.mathworks.com/matlabcentral/fileexchange/18593-differential-evolution

Thank you so much for this timely information, Sai Sudheer Reddy Bonthu. Please, let us connect on email. My email address: [email protected]. I will be awaiting your email. Thank you.

Hi Samuel

Are you familiar with these publications:

Topology optimization with a level set approach in Matlab [1]

Topology optimization with a density-based approach in Matlab [2] 

I think it provides, what you are looking for.

[1] https://link.springer.com/content/pdf/10.1007%2Fs00158-009-0430-0.pdf

[2] Article Sigmund, O.: A 99 Line Topology Optimization Code Written in...

Hello Samuel

Responding to the question lately..Don't know how useful this information would be now..anyways, following are the few important things for shape optimization in matlab:

- Geometry description and modification through design variables

- Structural analysis through numerical technique

- Optimization algorithm to determine optimum geometry through iterations

In order to automate the entire shape optimization process, it is important to setup tight link between above said attributes...

Hi Samuel,

for efficient shape optimization shape algorithms coded in Matlab, I will be so frank to refer to some of my papers:

- Robust shape optimization of electric devices based on deterministic optimization methods and finite-element analysis with affine parametrization and design elements DOI: · 10.1007/s00202-018-0716-6

- Optimization of a Stern-Gerlach Magnet by Magnetic Field-Circuit Coupling and Isogeometric Analysis DOI: · 10.1109/TMAG.2015.2462806

I hope it helps.

Regards,

Zeger