arXiv subjects

Matthias Klar

Publications and source records attributed to Matthias Klar.

5 recordsLinked to original sources

arXiv2024

Evaluation of Quantum Annealing-based algorithms for flexible job shop scheduling

A flexible job shop scheduling problem (FJSSP) poses a complex optimization task in modeling real-world process scheduling tasks with conflicting objectives. To tackle FJSSPs, approximation methods are employed to ensure solutions are within acceptable timeframes. Quantum Annealing, a metaheuristic leveraging quantum mechanical effects, demonstrates superior solution quality in a shorter time compared to classical algorithms. However, due to hardware limitations of quantum annealers, hybrid algorithms become essential for solving larger FJSSPs. This paper investigates the threshold problem sizes up to which quantum annealers are sufficient and when hybrid algorithms are required, highlighting the distribution of computing power in hybrid methods.

quant-ph↗

arXiv2024

Dynamic Spectrum Management for 6G Network-in-Network Concepts

Flexible, self-organizing communication networks will be a key feature in the next mobile communication standard. Network-in-Network (NiN) is one important concept in 6G research, introducing sub-networks tailored to specific application requirements. These sub-networks may be dynamic, i.e., they may appear, disappear, or even move throughout the network. Moreover, sub-networks may operate within a shared frequency spectrum, thereby requiring coordination among them. We demonstrate the concept of Dynamic Spectrum Management (DSM) for future 6G networks that dynamically (re-)allocates spectrum according to active sub-networks in the shared spectrum domain. Resilient control plane connectivity between sub-networks and the DSM is provided by the self-organizing routing protocol KIRA, enabling the aforementioned coordination. This demonstration presents an integrated solution of the DSM concept, providing increased flexibility to support diverse industrial applications and their individual performance requirements simultaneously within the context of a cyber-physical production system (CPPS). For the sub-networks, we use specifically designed hardware for wireless real-time communication and couple them with a network emulation. By switching sub-networks on and off, one can see that the DSM dynamically manages the spectrum allocations for them and that KIRA provides the required connectivity.

cs.NI↗

arXiv2023

Multi-objective Quantum Annealing approach for solving flexible job shop scheduling in manufacturing

Flexible Job Shop Scheduling (FJSSP) is a complex optimization problem crucial for real-world process scheduling in manufacturing. Efficiently solving such problems is vital for maintaining competitiveness. This paper introduces Quantum Annealing-based solving algorithm (QASA) to address FJSSP, utilizing quantum annealing and classical techniques. QASA optimizes multi-criterial FJSSP considering makespan, total workload, and job priority concurrently. It employs Hamiltonian formulation with Lagrange parameters to integrate constraints and objectives, allowing objective prioritization through weight assignment. To manage computational complexity, large instances are decomposed into subproblems, and a decision logic based on bottleneck factors is used. Experiments on benchmark problems show QASA, combining tabu search, simulated annealing, and Quantum Annealing, outperforms a classical solving algorithm (CSA) in solution quality (set coverage and hypervolume ratio metrics). Computational efficiency analysis indicates QASA achieves superior Pareto solutions with a reasonable increase in computation time compared to CSA.

quant-ph↗

arXiv2022

Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system

This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging method, as well as modern techniques, such as the GENERIC formalism. The main part of this article combines ideas of some of these techniques and addresses the problem of deriving a reduced system for the slow degrees of freedom (DOF) of a fast-slow Hamiltonian system. In the first part, we derive an asymptotic expansion of the averaged evolution of the fast-slow system up to second-order, using weak convergence techniques and two-scale convergence. In the second part, we determine quantities which can be interpreted as temperature and entropy of the system and expand these quantities up to second-order, using results from the first part. The results give new insights into the thermodynamic interpretation of the fast-slow system at different scales.

math-ph↗

arXiv2021

Second-order fast-slow dynamics of non-ergodic Hamiltonian systems: Thermodynamic interpretation and simulation

A class of fast-slow Hamiltonian systems with potential $U_\varepsilon$ describing the interaction of non-ergodic fast and slow degrees of freedom is studied. The parameter $\varepsilon$ indicates the typical timescale ratio of the fast and slow degrees of freedom. It is known that the Hamiltonian system converges for $\varepsilon\to0$ to a homogenised Hamiltonian system. We study the situation where $\varepsilon$ is small but positive. First, we rigorously derive the second-order corrections to the homogenised (slow) degrees of freedom. They can be decomposed into explicitly given terms that oscillate rapidly around zero and terms that trace the average motion of the corrections, which are given as the solution to an inhomogeneous linear system of differential equations. Then, we analyse the energy of the fast degrees of freedom expanded to second-order from a thermodynamic point of view. In particular, we define and expand to second-order a temperature, an entropy and external forces and show that they satisfy to leading-order, as well as on average to second-order, thermodynamic energy relations akin to the first and second law of thermodynamics. Finally, we analyse for a specific fast-slow Hamiltonian system the second-order asymptotic expansion of the slow degrees of freedom from a numerical point of view. Their approximation quality for short and long time frames and their total computation time are compared with those of the solution to the original fast-slow Hamiltonian system of similar accuracy.

math-ph↗