https://github.com/jaantollander/lockpatterncomplexity.jl
Solving the most complex lock patterns with Julia Language, MiniZinc, and Google OR-Tools.
https://github.com/jaantollander/lockpatterncomplexity.jl
combinatorial-optimization computational-science constraint-programming google-or-tools julia-language minizinc
Last synced: 8 months ago
JSON representation
Solving the most complex lock patterns with Julia Language, MiniZinc, and Google OR-Tools.
- Host: GitHub
- URL: https://github.com/jaantollander/lockpatterncomplexity.jl
- Owner: jaantollander
- License: mit
- Created: 2021-12-01T10:58:05.000Z (almost 4 years ago)
- Default Branch: master
- Last Pushed: 2021-12-19T13:51:42.000Z (almost 4 years ago)
- Last Synced: 2024-12-29T02:52:03.758Z (9 months ago)
- Topics: combinatorial-optimization, computational-science, constraint-programming, google-or-tools, julia-language, minizinc
- Language: Julia
- Homepage: https://jaantollander.github.io/LockPatternComplexity.jl/dev/
- Size: 2.91 MB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
- Citation: CITATION.cff
Awesome Lists containing this project
README
# Solving the Most Complex Lock Patterns
3×3 | 4×4
:-:|:-:
 | 
distance: 22* | distance: 61*
5×5 | 6×6
:-:|:-:
 | 
distance: 119 | distance: 207
7×7 | 7×7
:-: | :-:
 | 
distance=315 | distance=317
[](https://jaantollander.github.io/LockPatternComplexity.jl/dev)
[](https://github.com/jaantollander/LockPatternComplexity.jl/actions)
[](https://zenodo.org/badge/latestdoi/433790288)
## About
In this repository, we present solutions for the most complex lock patterns using the [MiniZinc](https://www.minizinc.org/) modeling language and the powerful [Google OR-Tools](https://developers.google.com/optimization/) solver. Additionally, we use the [Julia Language](https://julialang.org/) to generate the input data and analyze the results.
This repository was inspired by the video [*What Is The Most Complicated Lock Pattern?*](https://www.youtube.com/watch?v=PKjbBQ0PBCQ) by *Dr. Zye*. I highly recommend watching it! Also, you can try out lock patterns with [lock pattern demo](https://tympanix.github.io/pattern-lock-js/) by @tympanix.
We use a generalized definition of maximum complexity for a lock pattern, presented in *Dr. Zye*'s video, such that it has solutions for all n×n grids while preserving the original solutions. Our definition requires all lines in the pattern to have a unique "type" (slope), and we maximize the total ["taxicab" distance](https://en.wikipedia.org/wiki/Taxicab_geometry) of the pattern, which results in greater visual complexity for the patterns. The problem is a **combinatorial optimization** problem. The [**documentation**](https://jaantollander.github.io/LockPatternComplexity.jl/dev/) covers the theoretical aspect of the problem.
## Structure
The source code in this repository is structured as follows.
* The [`src/`](./src/) directory contains Julia code.
* The [`models/`](./models/) directory contains the MiniZinc models.
* The [`models/instances/`](./models/instances/) contains the datafiles for different grid sized instances of the model.
* The [`models/fzn/`](./models/fzn/) contains FlatZinc files generated from each model instances. These are useful to understand the size of a model instance and verify that variables have sensible bounds.
* The [`scripts/`](./scripts/) directory contains scripts for generating data files for instances, running the model, and plotting the results.
The output is located in the following directories.
* The [`results/`](./results/) directory contains the text output from the models.
* The [`plots/`](./plots/) directory contains the generated SVG plots for each grid size and taxicab distance in format `//.svg`. The `` is a unique identified generated using hash of the pattern.
## Instructions
To begin, we need to install MiniZinc and Google OR-Tools. On Linux, we can use the following [**shell scripts**](https://github.com/jaantollander/install-minizinc-ortools) for the installation. After the installation, we can run shell scripts from the `scripts` directory and write the output to the `results/3x3.txt` file. For example, we can run the optimization model using the following command.
```bash
./scripts/nxn_opt.sh 3 results/3x3.txt
```
The output generated by the solver will appear to the `results/` directory.
## Open Questions
~~Can we find a max complexity pattern for a 4×4 grid that provably maximizes the taxicab distance?~~
Can we find a max complexity pattern for a 5×5 grid that provably maximizes the taxicab distance?
~~Can we find a max complexity pattern for a 7×7 grid?~~