Research Repository: Complexity Theory and NP-Hard Problems

Overview

This repository contains research on various NP-hard problems as part of our study in complexity theory. Specifically, it includes work on the Vehicle Routing Problem (VRP) and the Knapsack Problem.

Structure

The repository is organized into the following main directories:

• VRP/:By Vincnet. Contains all the resources, code, and documentation related to the Vehicle Routing Problem.
• Knapsack/:By Chenyun. Contains all the resources, code, and documentation related to the Knapsack Problem.

Each directory includes subdirectories for data, algorithms, results, and reports.

Vehicle Routing Problem (VRP)

Description

The Vehicle Routing Problem (VRP) is a combinatorial optimization and integer programming problem which seeks to service a number of customers with a fleet of vehicles. The goal is to determine the optimal routes for a fleet of vehicles to traverse in order to deliver to a given set of customers.

Contents

• data/: Contains datasets used for VRP experiments.
• algorithms/: Contains implementations of various VRP algorithms, including heuristic and exact methods.
• results/: Contains results from VRP experiments, including performance metrics and analysis.
• report/: Contains the research report detailing the methods, experiments, and findings related to VRP.

Usage

1. Navigate to the VRP/ directory.
2. Follow the instructions in the README.md file within the VRP/ directory for setting up and running the VRP algorithms.
3. Use the scripts in the algorithms/ directory to execute specific VRP algorithms and analyze the results in the results/ directory.

Knapsack Problem

Description

The Knapsack Problem is a problem in combinatorial optimization where the objective is to maximize the total value of items placed in a knapsack without exceeding its capacity. This problem has many variations and is a fundamental problem in theoretical computer science.

Contents

• data/: Contains datasets used for Knapsack Problem experiments.
• algorithms/: Contains implementations of various Knapsack Problem algorithms, including dynamic programming and greedy methods.
• results/: Contains results from Knapsack Problem experiments, including performance metrics and analysis.
• report/: Contains the research report detailing the methods, experiments, and findings related to the Knapsack Problem.

Usage

1. Navigate to the Knapsack/ directory.
2. Follow the instructions in the README.md file within the Knapsack/ directory for setting up and running the Knapsack Problem algorithms.
3. Use the scripts in the algorithms/ directory to execute specific Knapsack Problem algorithms and analyze the results in the results/ directory.

Getting Started

To get started with this repository:

1. Clone the repository to your local machine:

   git clone https://github.com/your-repo/research-complexity-theory.git

2. Navigate to the relevant directory (VRP or Knapsack) depending on your area of interest.
3. Follow the setup instructions in the respective README.md files.

Contact

For any questions or inquiries, please contact the research team at [Vincent.yelpen#Gmail.com].