The problem appears very simliar with anthor problem in silicon industry, how to optimize dies distribute on a wafer?

https://www.waferworld.com/post/what-is-a-die

http://www.silicon-edge.co.uk/j/index.php/resources/die-per-wafer

https://anysilicon.com/die-per-wafer-formula-free-calculators/

There are similarities between the problem of optimizing the distribution of dies on a wafer and the problem of optimizing the allocation of resources in a computer cluster. In both cases, the goal is to maximize efficiency and minimize waste, while taking into account constraints such as physical space, processing power, and communication bandwidth.

In silicon industry, the problem of optimizing dies distribution on a wafer involves placing a large number of tiny dies onto a single wafer so as to maximize yield (i.e., the number of good chips produced) and minimize manufacturing costs. This is a complex optimization problem that involves many variables, such as the size and shape of the dies, the spacing between them, and the orientation of the wafer. Various mathematical models and algorithms have been developed to solve this problem, including linear programming, simulated annealing, and genetic algorithms.