Solving the 0-1 Knapsack Problem Using the LAB Algorithm

This repository contains the implementation of the LAB (Leader Advocate Believer) Algorithm to solve the 0-1 Knapsack Problem.

Overview

The LAB Algorithm is a metaheuristic optimization algorithm inspired by human social behavior. It is used to find optimal or near-optimal solutions for combinatorial problems, such as the 0-1 Knapsack Problem. The repository is divided into two main sections:

1. Single Knapsack Problem
2. Multiple Knapsack Problem

LAB Algorithm

The LAB Algorithm is designed to mimic the decision-making process of a group of individuals classified as leaders, advocates, and believers:

• Leaders: Explore new solutions and set high aspirations.
• Advocates: Evaluate solutions proposed by leaders and advocate for the most promising ones.
• Believers: Follow the solutions proposed by advocates and refine them to find the optimal solution.

This collaborative approach allows the LAB Algorithm to efficiently explore and exploit the solution space.

Repository Structure

• Single Knapsack Problem

  • Single_Knapsack_Problem.ipynb: Jupyter notebook implementing the LAB Algorithm for the single knapsack problem.

• Multiple Knapsack Problem

  • Multiple_Knapsack_Problem.ipynb: Jupyter notebook implementing the LAB Algorithm for multiple knapsacks.

Getting Started

Prerequisites

• Python 3.10
• Jupyter Notebook
• Additional Python libraries: numpy, pandas, statistics (installable via pip)

Installation

1. Clone the repository:

   git clone https://github.com/mustafa-droid18/Solving-the-0-1-Knapsack-Problem-Using-the-LAB-Algorithm.git
   cd Solving-the-0-1-Knapsack-Problem-Using-the-LAB-Algorithm

2. Install required libraries:

   pip install numpy pandas statistics

Single Knapsack Problem

The notebook Single_Knapsack_Problem.ipynb contains:

• Initialization of item weights, values, and knapsack capacity.
• Implementation of the LAB Algorithm to maximize the total value without exceeding the knapsack's capacity.
• Output of the optimal solution and various statistics.

Multiple Knapsack Problem

The notebook Multiple_Knapsack_Problem.ipynb contains:

• Initialization of multiple knapsacks with their respective capacities, weights, and values of items.
• Implementation of the LAB Algorithm to maximize the total value across all knapsacks without exceeding their capacities.
• Output of detailed results and statistics.

Contributing

Contributions are welcome! If you find any issues or have suggestions for improvements, feel free to open an issue or submit a pull request.

Acknowledgments

Inspired by various metaheuristic algorithms and the need to solve optimization problems efficiently.