Bachelor and Master Theses

Optimization problems arise in many real-world applications, including transportation, logistics, and aviation. These problems involve identifying suitable solutions while satisfying specific constraints and minimizing operational costs. One such application is aircraft conflict resolution, where aircraft trajectories must be adjusted to avoid potential conflicts while maintaining safe separation distances.

Classical optimization techniques, such as Genetic Algorithms (GAs), are widely used to solve complex optimization problems. In recent years, quantum computing has emerged as an alternative computational approach, introducing new methods for addressing optimization problems.

This project aims to explore classical and quantum optimization approaches through a simplified aircraft conflict-resolution problem. The student will implement a classical Genetic Algorithm in Python and investigate a quantum optimization approach using IBM's Qiskit framework. The project will focus on experimental evaluation and comparison of the two approaches.

Problem Statement

Aircraft conflict resolution requires determining suitable maneuvers to prevent potential conflicts between aircraft while minimizing deviations from their intended trajectories. As the number of aircraft and possible maneuvers increases, identifying suitable solutions can become computationally challenging.

Classical optimization methods, such as Genetic Algorithms, provide practical approaches to solving such problems. Quantum optimization algorithms offer alternative methods, but understanding their practical behavior and performance requires further investigation.

This project aims to investigate how classical and quantum optimization approaches perform on a simplified aircraft conflict-resolution problem, particularly in terms of solution quality, convergence behavior, and computational time.

No prior quantum computing experience is required. Introductory training on quantum computing and Qiskit will be provided.

Tools and Technologies

Classical Optimization

• Python
• Genetic Algorithms
• NumPy, Matplotlib

Quantum Computing

• IBM Qiskit
• Quantum circuit simulators
• QUBO-based optimization

The simplified aircraft conflict-resolution problem, QUBO formulation, and quantum circuit design will be provided to the student. Introductory training sessions on quantum computing and Qiskit will also be provided to support the quantum optimization experiments.

• Basic programming knowledge, preferably Python.
• Basic knowledge of algorithms and mathematics.
• Interest in optimization and computational methods.

Tools and Technologies

Classical Optimization

• Python
• Genetic Algorithms
• NumPy, Matplotlib

Quantum Computing

• IBM Qiskit
• Quantum circuit simulators
• QUBO-based optimization