15,398 research outputs found
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
Faithful fermionic representations of the Kondo lattice model
We study the Kondo lattice model using a class of canonical transformations
that allow us to faithfully represent the model entirely in terms of fermions
without constraints. The transformations generate interacting theories that we
study using mean field theory. Of particular interest is a new manifestly
O(3)-symmetric representation in terms of Majorana fermions at half-filling on
bipartite lattices. This representation suggests a natural O(3)-symmetric trial
state that is investigated and characterized as a gapped spin liquid.Comment: 11 pages, 2 figures, minor update
The Metric Nearness Problem
Metric nearness refers to the problem of optimally restoring metric properties to
distance measurements that happen to be nonmetric due to measurement errors or otherwise. Metric
data can be important in various settings, for example, in clustering, classification, metric-based
indexing, query processing, and graph theoretic approximation algorithms. This paper formulates
and solves the metric nearness problem: Given a set of pairwise dissimilarities, find a “nearest” set
of distances that satisfy the properties of a metric—principally the triangle inequality. For solving
this problem, the paper develops efficient triangle fixing algorithms that are based on an iterative
projection method. An intriguing aspect of the metric nearness problem is that a special case turns
out to be equivalent to the all pairs shortest paths problem. The paper exploits this equivalence and
develops a new algorithm for the latter problem using a primal-dual method. Applications to graph
clustering are provided as an illustration. We include experiments that demonstrate the computational
superiority of triangle fixing over general purpose convex programming software. Finally, we
conclude by suggesting various useful extensions and generalizations to metric nearness
Quark and Lepton Masses from Deconstruction
We propose a supersymmetric SU(5)xSU(5) model, where the quarks and leptons
live in a U(1) product group theory space that is compactified on the real
projective plane RP^2. The fermion generations are placed on different points
in the deconstructed manifold by assigning them SO(10) compatible U(1) charges.
The observed masses and mixing angles of quarks and leptons emerge from
non-renormalizable operators involving the chiral link fields. The link fields
introduce a large atmospheric neutrino mixing angle \theta_23 via a dynamical
realization of the seesaw mechanism, which sets the deconstruction scale to a
value of the order the B-L breaking scale 10^14 GeV. Supersymmetry breaking can
be achieved through topological effects due to a non-trivial homology group
Z_2. The mixed anomalies of the link fields are canceled by Wess-Zumino terms,
which are local polynomials in the gauge and link fields only. We also comment
on the construction of Chern-Simons couplings from these fields.Comment: 22 pages, 2 figures, typos in neutrino mass squared differences
correcte
Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression
We present an exact method, based on an arc-flow formulation with side
constraints, for solving bin packing and cutting stock problems --- including
multi-constraint variants --- by simply representing all the patterns in a very
compact graph. Our method includes a graph compression algorithm that usually
reduces the size of the underlying graph substantially without weakening the
model. As opposed to our method, which provides strong models, conventional
models are usually highly symmetric and provide very weak lower bounds.
Our formulation is equivalent to Gilmore and Gomory's, thus providing a very
strong linear relaxation. However, instead of using column-generation in an
iterative process, the method constructs a graph, where paths from the source
to the target node represent every valid packing pattern.
The same method, without any problem-specific parameterization, was used to
solve a large variety of instances from several different cutting and packing
problems. In this paper, we deal with vector packing, graph coloring, bin
packing, cutting stock, cardinality constrained bin packing, cutting stock with
cutting knife limitation, cutting stock with binary patterns, bin packing with
conflicts, and cutting stock with binary patterns and forbidden pairs. We
report computational results obtained with many benchmark test data sets, all
of them showing a large advantage of this formulation with respect to the
traditional ones
Anisotropic selection in cellular genetic algorithms
In this paper we introduce a new selection scheme in cellular genetic
algorithms (cGAs). Anisotropic Selection (AS) promotes diversity and allows
accurate control of the selective pressure. First we compare this new scheme
with the classical rectangular grid shapes solution according to the selective
pressure: we can obtain the same takeover time with the two techniques although
the spreading of the best individual is different. We then give experimental
results that show to what extent AS promotes the emergence of niches that
support low coupling and high cohesion. Finally, using a cGA with anisotropic
selection on a Quadratic Assignment Problem we show the existence of an
anisotropic optimal value for which the best average performance is observed.
Further work will focus on the selective pressure self-adjustment ability
provided by this new selection scheme
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