I want to compare metaheuristics on the optimizattion of Lennard-Jones clusters. There are many papers available that optimize Lennard-Jones clusters. Unfortunately, none of them provide the upper and lower bounds of the search space. In order to conduct a fair comparison, all metaheuristics should search in the same bounds of the search space. I found the global minima here: http://doye.chem.ox.ac.uk/jon/structures/LJ/tables.150.html but the search space is not defined.
Can anyone please tell me what are the recommended upper and lower bounds of the search space?
Dear Miha Ravber,
For a global optimization of Lennard-Jones clusters we can have a space between 5 ≤ N ≤ 50 and for other types of optimization this can change.
For more information about this subject, I suggest you to see links and attached files on topic.
Preprint A fast and reliable hybrid algorithm for numerical nonlinear...
https://www-wales.ch.cam.ac.uk/pdf/JPCA.101.5111.1997.pdf
https://warwick.ac.uk/study/csde/gsp/eportfolio/directory/pg/ccrkac/bibliography/northby_lj_potential.pdf
https://arxiv.org/pdf/2001.11465.pdf
Article Global Optimization of Binary Lennard-Jones Clusters Using T...
Article Global Optimization by Basin-Hopping and the Lowest Energy S...
Best regards
That's a good question. Most of the solutions that are presented in the literature are indeed hard to interpret. Besides, there are symmetries (a solution is invariant under rotation and translation).
In chapter 7 of my PhD thesis (https://www.researchgate.net/publication/337947149), I broke symmetries by fixing some of the variables/directions and proved the global optimality of the solution for N = 5, even in the presence of roundoff errors.
The solution roughly lies within [-2, 2]^N. You can expand it a bit for your work.
Dear Charlie Vanaret
Thank you for the answer! But isn't then the search space too large? When I was checking the global optima, most of the solutions are in the range [-4, 4]. To make the search a bit more challenging I would put it in the range [-10, 10]. But for a fair comparison, everyone should use the same search space or at least mention it in their paper.
Miha Ravber : for me, [-2, 2] was enough because I fixed the first atom at (0, 0, 0), the second at (>= 0, 0, 0), etc. If you don't, you get free coordinates between your bounds.
You can definitely start at [-10, 10] and see what the results are, then adjust.
I would like to invite you to have a look on the following links.
SSO: https://www.mathworks.com/matlabcentral/fileexchange/92150-sperm-swarm-optimization-sso
HSSOGSA: https://www.mathworks.com/matlabcentral/fileexchange/92130-hssogsa?s_tid=srchtitle
MOSFP: https://github.com/sh7adeh1990/MOSFP
Thank you very much for your time and efforts.
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