Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9706141

Airline Crew Scheduling Using Potts Mean Field Techniques

M. Lagerholm·C. Peterson·B. Söderberg
View original source ↗Read source document ↗Export metadata ↓

Abstract

A novel method is presented and explored within the framework of Potts neural networks for solving optimization problems with a non-trivial topology, with the airline crew scheduling problem as a target application. The key ingredient to handle the topological complications is a propagator defined in terms of Potts neurons. The approach is tested on artificial problems generated with two real-world problems as templates. The results are compared against the properties of the corresponding unrestricted problems. The latter are subject to a detailed analysis in a companion paper [LU TP 97-11]. Very good results are obtained for a variety of problem sizes. The computer time demand for the approach only grows like (number of flights)^3. A realistic problem typically is solved within minutes, partly due to a prior reduction of the problem size, based on an analysis of the local arrival/departure structure at the single airports. To facilitate the reading for audiences not familiar with Potts neurons and mean field techniques, a brief review is given of recent advances in their application to resource allocation problems.

Explore related subjects

cond-mat.dis-nnhep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. Lagerholm, C. Peterson, B. Söderberg. 1997-06-13. Airline Crew Scheduling Using Potts Mean Field Techniques. https://arxiv.org/abs/cond-mat/9706141

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Transition path sampling in Ising models on heterogeneous graphs

Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here, we use transition path sampling to evaluate transition probabilities between ferromagnetic states in the Ising model on finite sparse random graphs, which are perhaps the simplest example of a disordered system with metastable states. To interpret the transient onset of the transition probability curve, we introduce a minimal three-state kinetic description that highlights the role of intermediate configurations. We validate the method on the heterogeneous Zachary Karate Club network, where distinct dynamical regimes emerge as temperature varies. We then apply the method to random regular graphs and Erdős-Rényi graphs, showing that sample-to-sample fluctuations are weak in the former but that quenched topological disorder induces sizable instance variability in the latter. For Erdős-Rényi graphs, we introduce an instance-dependent temperature rescaling that restores a consistent finite-size scaling of dynamical rates and enables a direct comparison with the corresponding static free-energy barrier.

cond-mat.dis-nn↗
arXiv2026

Estimates of ground state energies for the quantum SK and 2D-EA models, using deGennes-Suzuki-Kubo mean-field annealing dynamics

We perform large scale quantum annealing of the Sherrington-Kirkpatrick (SK) spin glass up to a system size $N=40000$ to estimate its ground state energy using the deGennes-Suzuki-Kubo mean-field quantum Ising dynamics, extending the earlier results (reported in Eur. Phys. J. B {\bf 98}, 226 (2025)). Here we numerically solve the deGennes-Suzuki-Kubo annealing dynamics to obtain the spin configurations and subsequently the ground state energy for a given system size at the end of the annealing, starting from a quantum paramagnetic state. The method shows high efficiency, with an overall algorithmic cost of $O(N^3)$ in estimating the energy of the ground state. We later extend this quantum annealing study to estimate the ground state energies (starting again from the quantum paramagnetic phase, annealing down to any desired low value of the transverse field) for the Edwards-Anderson (EA) spin glass model on a square lattice.

cond-mat.dis-nn↗
arXiv2026

Perfect resonance and fragile localization suppression in correlated disordered chains

Spatial correlations can suppress scattering in disordered chains and produce perfectly transmitting resonances. The practical value of this protection, however, depends not on the resonance peak itself but on the width of the surrounding transmission window and its sensitivity to local ordering errors. We show that a resonance can remain exactly transparent at its center while arbitrarily rare adjacent-swap errors restore an inverse localization length proportional to the square of the energy detuning. For lossless single-channel chains assembled from independent blocks of fixed length and composition, this positive quadratic term is guaranteed by a local scattering invariant and holds for every arrangement and every fixed swap probability between zero and one. With exact tuning and matched contacts, the central transmission remains unity. A microscopic quantum chain exhibits both higher-order suppression of scattering in the ideal recursive arrangement and the predicted response to local exchanges. These results reveal a limitation of spatial ordering that is invisible to a measurement at the resonance alone: spatial ordering protects the resonance peak, not the transport around it. The effect can therefore be tested experimentally by measuring transmission spectra before and after exchanges, without identifying microscopic defects.

cond-mat.dis-nn↗