wangmaolin / nd-bin-packing

Environment Setup Through Miniconda

conda activate

pip install cvxpy

conda install -c conda-forge coin-or-cbc

pip install cylp

(Tested on macOS Monteray and Ubuntu 18.04)

Problem Definition

The input is a 2D array($n \times p$) named bit_map $B$. It has $n$ rows and $p=16$ columns. Each element in the array is either 0 or 1. Here is an example of $n=10$:

[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]

[0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0]

[1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0]

[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

[0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0]

[1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0]

[1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0]

[1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1]

[0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0]

[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1]

Objective

Define a box as one row of 16 columns. some rows of $B$ can be put in the same box if the 1s are perfectly interleaved.

In the above example, row 0 and row 1 can't be put into the same box because both 14th columns of these two rows are 1. It's okay to put row 0, 8 and 9 into the same box.

The object is to find a way to pack these rows so the number of boxes is minimized. The way of packing can be described as a 1D array $S$ of size $n$. Assume that box is enumerated from top to down(the first row is box 0). $S_k=t$ means the row $k$ should be put in the box $t$.

Here is an sample packing for the above example:[0, 1, 0, 1, 2, 2, 3, 4, 5, 5].

CVXPY Description

CVXPY modeling of the problem can be found as the cvx_condense function in vector_packing.py. It's based on the following example: https://stackoverflow.com/questions/48866506/binpacking-multiple-constraints-weightvolume

Problem Scale

Current maximum $n$ is about $60,000$ in OSQP benchmarks. The current hardware uses $p=16$. Later $p$ will scaled to $p=16 \times 5$ and $p=16 \times 12$ on larger hardware.