How to calculate packing density for mixed spheres/polyhedra with different sizes at optimal packing?

[Wodnerstruck]

I would like to use this program to solve a specific packing problem and would appreciate your guidance on which features to use and how to approach the calculation.
My Problem:
I want to calculate the packing density when spheres or polyhedra of different diameters are mixed in certain proportions and arranged to achieve maximum packing density (densest packing).
Specific Requirements:
Mixed particles with different sizes (spheres or polyhedra)
Particles mixed in specified ratios/proportions
Need to find the optimal/densest packing arrangement
Calculate the final packing density of this mixed system
My Questions:
Which specific functions or modules in this program should I use for this type of mixed-size packing problem?
Does the program support automatic optimization to find the densest packing configuration?
Are there any example scripts or tutorials for similar mixed packing calculations?

[joaander]

Which specific functions or modules in this program should I use for this type of mixed-size packing problem?

HPMC.

Does the program support automatic optimization to find the densest packing configuration?

No.

Are there any example scripts or tutorials for similar mixed packing calculations?

No.

There are many journal articles that discuss strategies that find dense packings of shapes. Here are two:

• http://doi.org/10.1103/PhysRevX.4.011024
• https://pubs.acs.org/doi/10.1021/nn204012y

To find the densest packing, you will need to construct a mathematical proof. Wolfram MathWorld summarizes the literature on the densest packing of spheres.

[Wodnerstruck]

Thank you for your answer! My calculation purpose is to optimize some product manufacturing processes, and I don't need to strictly prove that it's theoretically the densest. What I want to know is:

1. can HPMC achieve sufficiently dense packing with more iteration steps and longer time?
2. When I need to compare the packing density of different spherical particle combination formulations to see which is greater, what are the conditions that allow for comparison (runtime/iteration steps/or other conditions)?
3. Do I need to add pressure to the system during the simulation process?

[joaander]

Those journal articles explain the process in far more detail than I can repeat here. The general strategy is to test many small 1, 2, 4, ... particle simulations using QuickCompress and/or BoxMC with pressures that increase over time. Allow all types of box moves (shear, aspect, etc...). Examine the highest density results you get and determine the parameters of the unit cell, then numerically optimize to achieve the local densest packing subject to the identified symmetries.

Trying to compress larger simulations (e.g. 4,000 particles) will typically max out at random close packing densities which is far from the densest possible.