11,968 research outputs found
The Random-bond Potts model in the large-q limit
We study the critical behavior of the q-state Potts model with random
ferromagnetic couplings. Working with the cluster representation the partition
sum of the model in the large-q limit is dominated by a single graph, the
fractal properties of which are related to the critical singularities of the
random Potts model. The optimization problem of finding the dominant graph, is
studied on the square lattice by simulated annealing and by a combinatorial
algorithm. Critical exponents of the magnetization and the correlation length
are estimated and conformal predictions are compared with numerical results.Comment: 7 pages, 6 figure
Multi-layer local optima networks for the analysis of advanced local search-based algorithms
A Local Optima Network (LON) is a graph model that compresses the fitness
landscape of a particular combinatorial optimization problem based on a
specific neighborhood operator and a local search algorithm. Determining which
and how landscape features affect the effectiveness of search algorithms is
relevant for both predicting their performance and improving the design
process. This paper proposes the concept of multi-layer LONs as well as a
methodology to explore these models aiming at extracting metrics for fitness
landscape analysis. Constructing such models, extracting and analyzing their
metrics are the preliminary steps into the direction of extending the study on
single neighborhood operator heuristics to more sophisticated ones that use
multiple operators. Therefore, in the present paper we investigate a twolayer
LON obtained from instances of a combinatorial problem using bitflip and swap
operators. First, we enumerate instances of NK-landscape model and use the hill
climbing heuristic to build the corresponding LONs. Then, using LON metrics, we
analyze how efficiently the search might be when combining both strategies. The
experiments show promising results and demonstrate the ability of multi-layer
LONs to provide useful information that could be used for in metaheuristics
based on multiple operators such as Variable Neighborhood Search.Comment: Accepted in GECCO202
Fast minimum variance wavefront reconstruction for extremely large telescopes
We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the
reconstruction of the optical wavefront from measurements provided by a
wavefront sensor. As our application is adaptive optics on extremely large
telescopes, our algorithm was designed with speed and best quality in mind. The
latter is achieved thanks to a regularization which enforces prior statistics.
To solve the regularized problem, we use the conjugate gradient method which
takes advantage of the sparsity of the wavefront sensor model matrix and avoids
the storage and inversion of a huge matrix. The prior covariance matrix is
however non-sparse and we derive a fractal approximation to the Karhunen-Loeve
basis thanks to which the regularization by Kolmogorov statistics can be
computed in O(N) operations, N being the number of phase samples to estimate.
Finally, we propose an effective preconditioning which also scales as O(N) and
yields the solution in 5-10 conjugate gradient iterations for any N. The
resulting algorithm is therefore O(N). As an example, for a 128 x 128
Shack-Hartmann wavefront sensor, FRiM appears to be more than 100 times faster
than the classical vector-matrix multiplication method.Comment: to appear in the Journal of the Optical Society of America
- …