https://github.com/t-lak/n-queens-solver
Solving the N-Queens Problem using a Genetic Algorithm in combination with Min-Conflicts and bitboards for better performance.
https://github.com/t-lak/n-queens-solver
bitboards genetic-algorithm min-conflict-algorithm min-conflicts n-queens-problem
Last synced: 8 months ago
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Solving the N-Queens Problem using a Genetic Algorithm in combination with Min-Conflicts and bitboards for better performance.
- Host: GitHub
- URL: https://github.com/t-lak/n-queens-solver
- Owner: T-Lak
- License: mit
- Created: 2023-02-03T17:08:45.000Z (over 2 years ago)
- Default Branch: master
- Last Pushed: 2025-02-14T14:33:51.000Z (8 months ago)
- Last Synced: 2025-02-14T14:41:23.129Z (8 months ago)
- Topics: bitboards, genetic-algorithm, min-conflict-algorithm, min-conflicts, n-queens-problem
- Language: Python
- Homepage:
- Size: 88.9 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
## Overview
This project implements a hybrid approach combining a Genetic Algorithm (GA) with the Min-Conflicts heuristic to solve the [**N-Queens Problem**](https://developers.google.com/optimization/cp/queens) efficiently.
The implementation is designed for performance optimization, using [bitboards](https://www.chessprogramming.org/Bitboards)
instead of arrays for representing chessboards, enabling efficient computations via bitwise operations.
## Features
- **🧬 Chromosome Representation:** Bitboards representing queens' positions.
- **🎯 Selection Methods:** Tournament Selection (TM) & Roulette-Wheel Selection (RW).
- **🔀 Crossover:** One-Point (OP) & Two-Point (TP) crossover.
- **🔄 Mutation:** Swap Random (SR) & Swap Neighbor (SN) mutations.
- **📊 Fitness Function:** Based on the number of conflicts between queens.
- **🧩 Min-Conflicts:** To guide solutions towards feasibility.
## Algorithm Workflow
The hybrid approach combines a **Genetic Algorithm (GA)** with the **Min-Conflicts heuristic** to iteratively refine solutions for the N-Queens problem. The process consists of the following steps:
- **Initialization:**
Generate an initial population of random board configurations. Each board is represented as a bitboard, enabling fast state manipulation.
- **Selection:**
Choose parents for the next generation using **`Tournament Selection (10% pool)`** or **`Roulette-Wheel Selection (20% rate)`**.
- **Crossover:**
Apply **`One-Point (90% probability)`** or **`Two-Point crossover`**, exchanging partial board states between parents.
- **Mutation:**
Introduce diversity using **`Swap Random (SR)`** or **`Swap Neighbor (SN)`** mutations, occurring with a **`3% probability`**.
- **Conflict Reduction (Min-Conflicts Heuristic):**
With a **`10% probability`**, the algorithm applies **`Min-Conflicts`** to adjust queen positions toward a conflict-free solution.
- **Termination:**
**`All valid solutions`** (conflict-free board) were found or the maximum limit of **`n generations`** is reached.
## Experimental Results
Three experimental phases were conducted:
- **Phase 1 - Evaluation of different GA configurations on n=8:**
Results showed that Tournament Selection and Two-Point Crossover yielded the best performance. Min-Conflicts significantly improved success rates, achieving up to 100% success rate in some configurations.
- **Phase 2 - Testing the hybrid approach on larger board sizes (n=10, 20, 30, 40, 50):**
The bitboard-based representation allowed the algorithm to scale efficiently, consistently finding solutions in fewer than 5 generations for all tested board sizes.
- **Phase 3 - Assessing the ability to find all possible solutions for n=8–11:**
Results indicated that Roulette-Wheel Selection consistently found 100% of all possible solutions, while Tournament Selection was slightly less consistent for larger n.
## Installation
Ensure you have Python installed. Then, create and activate a virtual environment:
```bash
python -m venv .venv
source .venv/bin/activate # Linux/macOS
.venv\Scripts\activate # Windows
```
Install dependencies:
```bash
pip install -r requirements.txt
```
### Optional Parameters
Customize the algorithm with selection, crossover and mutation strategies:
| Argument | Type | Description |
|-----------------|------------|----------------------------------------------|
| `--n` | int | Size of the chessboard (N-Queens) |
| `--population` | int | Number of individuals in the population |
| `--generations`| int | Number of generations to evolve |
| `--TM size prob` | float, float | Tournament selection (size ratio, probability) |
| `--RW prob` | float | Roulette Wheel selection probability |
| `--RB prob` | float | Rank-based selection probability |
| `--OP prob` | float | One-point crossover probability |
| `--TP prob` | float | Two-point crossover probability |
| `--SN prob` | float | Swap neighbor mutation probability |
| `--SR prob` | float | Swap random mutation probability |
| `--MC prob iter` | float, int | Min-conflicts (probability, max iterations) |
### Example Usage
```bash
python ga_cli.py --n 6 --population 200 --generations 250 --TM 0.2 0.8 --OP 0.9 --SN 0.1
```
### Printed Results
```bash
_ Q _ _ _ _ _ _ _ _ Q _
_ _ _ Q _ _ _ _ Q _ _ _
_ _ _ _ _ Q Q _ _ _ _ _
Q _ _ _ _ _ _ _ _ _ _ Q
_ _ Q _ _ _ _ _ _ Q _ _
_ _ _ _ Q _ _ Q _ _ _ _ ...
```
## Project Structure
```plaintext
│── Genetic_Algorithm # Core GA classes (e.g., chromosome, population)
│ │── Operators # Selection, crossover, mutation strategies
│── Tests # Unit tests for correctness
│── Utilities # Bitboard representations and helper functions
│── ga_cli.py
```
## Dependencies
- Python 3.x
- NumPy
## Future Improvements
- ⚙️ Fine-tuning Parameters - experiment with adaptive selection/mutation rates.
- 🔄 Exploring alternative selection and mutation strategies.
- 📌 Applying the approach to other combinatorial optimization problems.
---
✨ **Contributions welcome!** Feel free to fork and enhance this project.
---
## License
This project is licensed under the MIT License.