571 research outputs found
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Accelerated Expansion of the Universe in Gauss-Bonnet Gravity
We show that in Gauss-Bonnet gravity with negative Gauss-Bonnet coefficient
and without a cosmological constant, one can explain the acceleration of the
expanding Universe. We first introduce a solution of the Gauss-Bonnet gravity
with negative Gauss-Bonnet coefficient and no cosmological constant term in an
empty -dimensional bulk. This solution can generate a de Sitter
spacetime with curvature . We show that an
-dimensional brane embedded in this bulk can have an expanding feature
with acceleration. We also considered a 4-dimensional brane world in a
5-dimensional empty space with zero cosmological constant and obtain the
modified Friedmann equations. The solution of these modified equations in
matter-dominated era presents an expanding Universe with negative deceleration
and positive jerk which is consistent with the recent cosmological data. We
also find that for this solution, the derivative of the scale factor
with respect to time can be expressed only in terms of Hubble and deceleration
parameters.Comment: 12 pages, no figure, references added, typos corrected, Section 4
ammended, an appndix added, version to be appeared in Phys. Rev.
Asymptotically (anti)-de Sitter solutions in Gauss-Bonnet gravity without a cosmological constant
In this paper we show that one can have asymptotically de Sitter (dS),
anti-de Sitter (AdS) and flat solutions in Gauss-Bonnet gravity without any
need to a cosmological constant term in field equations. First, we introduce
static solutions whose 3-surfaces at fixed and have constant positive
(), negative (), or zero () curvature. We show that for
, one can have asymptotically dS, AdS and flat spacetimes, while for
the case of , one has only asymptotically AdS solutions. Some of these
solutions present naked singularities, while some others are black hole or
topological black hole solutions. We also find that the geometrical mass of
these 5-dimensional spacetimes is , which is different from
the geometrical mass, , of the solutions of Einstein gravity. This feature
occurs only for the 5-dimensional solutions, and is not repeated for the
solutions of Gauss-Bonnet gravity in higher dimensions. We also add angular
momentum to the static solutions with , and introduce the asymptotically
AdS charged rotating solutions of Gauss-Bonnet gravity. Finally, we introduce a
class of solutions which yields an asymptotically AdS spacetime with a
longitudinal magnetic field which presents a naked singularity, and generalize
it to the case of magnetic rotating solutions with two rotation parameters.Comment: 13 pages, no figur
Structured Random Matrices
Random matrix theory is a well-developed area of probability theory that has
numerous connections with other areas of mathematics and its applications. Much
of the literature in this area is concerned with matrices that possess many
exact or approximate symmetries, such as matrices with i.i.d. entries, for
which precise analytic results and limit theorems are available. Much less well
understood are matrices that are endowed with an arbitrary structure, such as
sparse Wigner matrices or matrices whose entries possess a given variance
pattern. The challenge in investigating such structured random matrices is to
understand how the given structure of the matrix is reflected in its spectral
properties. This chapter reviews a number of recent results, methods, and open
problems in this direction, with a particular emphasis on sharp spectral norm
inequalities for Gaussian random matrices.Comment: 46 pages; to appear in IMA Volume "Discrete Structures: Analysis and
Applications" (Springer
Perturbing gauge/gravity duals by a Romans mass
We show how to produce algorithmically gravity solutions in massive IIA (as
infinitesimal first order perturbations in the Romans mass parameter) dual to
assigned conformal field theories. We illustrate the procedure on a family of
Chern--Simons--matter conformal field theories that we recently obtained from
the N=6 theory by waiving the condition that the levels sum up to zero.Comment: 30 page
A practical case of the multiobjective knapsack problem: Design, modelling, tests and analysis
In this paper, we present a practical case of the multiobjective knapsack problem which concerns the elaboration of the optimal action plan in the social and medico-social sector. We provide a description and a formal model of the problem as well as some preliminary computational results. We perform an empirical analysis of the behavior of three metaheuristic approaches: a fast and elitist multiobjective genetic algorithm (NSGA-II), a Pareto Local Search (PLS) algorithm and an Indicator-Based Multi-Objective Local Search (IBMOLS)
Time Scales for transitions between free energy minima of a hard sphere system
Time scales associated with activated transitions between glassy metastable
states of a free energy functional appropriate for a dense hard sphere system
are calculated by using a new Monte Carlo method for the local density
variables. We calculate the time the system,initially placed in a shallow
glassy minimum of the free energy, spends in the neighborhood of this minimum
before making a transition to the basin of attarction of another free energy
minimum. This time scale is found to increase with the average density. We find
a crossover density near which this time scale increases very sharply and
becomes longer than the longest times accessible in our simulation. This scale
shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E,
March 1996 or s
Entropic Origin of the Growth of Relaxation Times in Simple Glassy Liquids
Transitions between ``glassy'' local minima of a model free-energy functional
for a dense hard-sphere system are studied numerically using a
``microcanonical'' Monte Carlo method that enables us to obtain the transition
probability as a function of the free energy and the Monte Carlo ``time''. The
growth of the height of the effective free energy barrier with density is found
to be consistent with a Vogel-Fulcher law. The dependence of the transition
probability on time indicates that this growth is primarily due to entropic
effects arising from the difficulty of finding low-free-energy saddle points
connecting glassy minima.Comment: Four pages, plus three postscript figure
Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory
We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions
and we determine all four-dimensional gauge theories resulting from the
generalized dimensional reduction a la Forgacs-Manton over coset spaces,
followed by a subsequent application of the Wilson flux spontaneous symmetry
breaking mechanism. Our investigation is constrained only by the requirements
that (i) the dimensional reduction leads to the potentially phenomenologically
interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and
(ii) the Wilson flux mechanism makes use only of the freely acting discrete
symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty,
ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C
- …