🌌 2D Strip Packing Problem - VLSI 🌌

In this project, we try 4 different optimization techniques to solve the very well known 2D Strip Packing problem. To model it in an intuitive way, we think of it as the problem of placing a set of rectangular chips in a silicon plate (which is a bigger rectangle itself) in order to occupy the least possible space. To understand the reasons of our implementations, read the Report.pdf included in this repo.

©Alessandro D’Amico ©Andrea Virgillito ©Sfarzo El Husseini

Requirements

Some general requirements all valid for all the methods, since they use common python packages for the upper bound computation, plotting and parsing of the iinput/output instances:

• python (tested on Python 3.8)
• pandas pip install pandas
• tqdm pip install tqdm
• matplotlib pip install matplotlib
• numpy pip install numpy
• re pip install regex
• gc
• datetime pip install DateTime
• time

The requirements are different across the various modeling techniques:

• cp:

  • Minizinc install & IDE (tested on version 2.5.5)
  • OrTools flatzinc install (tested on the visual studio 2019 64 bit v 9.2.9972) with all the flags checked through the Minizinc IDE (make sure to properly link it)
  • Minizinc Python API (can easily install it with pip: pip install minizinc)

• sat & smt:

  • Z3 Python API (can easily install it with pip: pip install z3-solver)

• lp:

  • OrTools Python API (can easily install it with pip: pip install ortools).
  • Gurobi install (in our case activated with academic license, which can be obtained just through the university network) (tested on version 9.5.2)
  • recompilation of the whole C++ package (which is failing right now 03/12/2022 ) is required if one needs to try other commercial solvers such as CPLEX (of course, after having installed them on the computer in use and having set a system path variable for em) - more info on https://developers.google.com/optimization/install/python

Play with it 🚀

When the corresponding enviroment is set as above,

• cp:
  • run python CP.py in the cp/src folder to process the whole benchmark on Or-Tools or use the functions inside that file to process just a single instance.
• sat:
  • run python SAT.py in the sat/src folder to process the whole benchmark on Z3 or use the functions inside that file to process just a single instance.
• smt:
  • run python SMT.py in the smt/src folder to process the whole benchmark on Z3 or use the functions inside that file to process just a single instance.
• lp:
  • run python LP.py in the lp/src folder to process the whole benchmark on Gurobi or use the functions inside that file to process just a single instance.

Input format

The collections of rectangles to be placed are located in the "instances" folder. Each of them is named "ins-{x}.txt", where {x} is the instance number. Each one of them is of this form:

_____________ ins-{x}.txt _____________  
 W  
 n_rect  
 width(0) height(0)  
 width(1) height(1)  
 ...  
 width(n_rect) height(n_rect)  
 _____________________________________

where we have

• W: the width of the strip
• n_rect: the number of rectangles to be placed in the corresponding instance (collection)
• width(i): the width of the rectangle i
• height(i): the height of the rectangle i

---

Output format

To visualize singular solutions use the notebook 'visualize_solutions.ipynb'

The computed solutions (the placements of the rectangles) are placed in the "out" folder, divided by

• modeling technique: cp, sat, smt, lp
• strategy:
  • base (base version of the problem, no rotations),
  • base-sb (base version with the addition of symmetry breaking techniques)
  • rotations (model allowing the rotation of rectangles)
  • rotations-sb (model allowing rotations, with the addition of symmetry breaking techniques)
• solver (depending on the modeling technique, sometimes different solvers were used)

_____________ ins-{x}.txt _____________  
 W H  
 n_rectangles  
 width(0) height(0) x_(0) y_(0) rot(0)  
 width(1) height(1) x_(1) y_(1) rot(1)  
 ...  
 width(n_rect) height(n_rect) x(n_rect) y(n_rect) rot(n_rect)  
   
 time  
 overtime  
 kind_of_bound  
 _____________________________________

In these output files there are some added numbers (wrt the plain input file described above)

• H: the overall height of the strip
• x(i): the position on the x-axis of the low bottom corner of the rectangle i
• y(i): the position on the x-axis of the low bottom corner of the rectangle i
• rot(i): "rotated" if the rectangle i has been rotated (WARNING: in that case the height and the width are already swapped), "not-rotated" otherwise
• time: the time taken from the solver (in seconds)
• overtime: True if the solver has exceeded the time limit (300s in our tests)
• kind_of_bound:
  • OPTIMAL if the height corresponding to the perfect packaging has been reached
  • NOT_OPTIMAL if at least a valid solution has been computed by the solver within the time limit
  • UPPER_BOUND if no solution from the solver has been computed within the time limit: in this case, we use just the height (and the positioning of the rectangles) computed by the method used to obtain the upper bound (which is )

---