2,003 research outputs found
From Slater to Mott-Heisenberg physics: The antiferromagnetic phase of the Hubbard model
We study the optical conductivity of the one-band Hubbard model in the N\'eel
state at half filling at T=0 using the dynamical mean-field theory. For small
values of the Coulomb parameter clear signatures of a Slater insulator expected
from a weak-coupling theory are found, while the strongly correlated system can
be well described in terms of a Mott-Heisenberg picture. However, in contrast
to the paramagnet, we do not find any evidence for a transition between these
two limiting cases but rather a smooth crossover as a function of the Coulomb
interaction.Comment: 8 pages, 9 figure
R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection
short paperInternational audienceAn indicator-based evolutionary multiobjective optimization algorithm (EMOA) is introduced which incorporates the contribution to the unary R2-indicator as the secondary selection criterion. First experiments indicate that the R2-EMOA accurately approximates the Pareto front of the considered continuous multiobjective optimization problems. Furthermore, decision makers' preferences can be included by adjusting the weight vector distributions of the indicator which results in a focused search behavior
Magnetism and Phase Separation in the Ground State of the Hubbard Model
We discuss the ground state magnetic phase diagram of the Hubbard model off
half filling within the dynamical mean-field theory. The effective
single-impurity Anderson model is solved by Wilson's numerical renormalization
group calculations, adapted to symmetry broken phases. We find a phase
separated, antiferromagnetic state up to a critical doping for small and
intermediate values of U, but could not stabilise a Neel state for large U and
finite doping. At very large U, the phase diagram exhibits an island with a
ferromagnetic ground state. Spectral properties in the ordered phases are
discussed.Comment: 9 pages, 11 figure
A New Mechanism for Maintaining Diversity of Pareto Archive in Multiobjective Optimization
The article introduces a new mechanism for selecting individuals to a Pareto
archive. It was combined with a micro-genetic algorithm and tested on several
problems. The ability of this approach to produce individuals uniformly
distributed along the Pareto set without negative impact on convergence is
demonstrated on presented results. The new concept was confronted with NSGA-II,
SPEA2, and IBEA algorithms from the PISA package. Another studied effect is the
size of population versus number of generations for small populations.Comment: 51 pages, 28 figure
Approximating the least hypervolume contributor: NP-hard in general, but fast in practice
The hypervolume indicator is an increasingly popular set measure to compare
the quality of two Pareto sets. The basic ingredient of most hypervolume
indicator based optimization algorithms is the calculation of the hypervolume
contribution of single solutions regarding a Pareto set. We show that exact
calculation of the hypervolume contribution is #P-hard while its approximation
is NP-hard. The same holds for the calculation of the minimal contribution. We
also prove that it is NP-hard to decide whether a solution has the least
hypervolume contribution. Even deciding whether the contribution of a solution
is at most (1+\eps) times the minimal contribution is NP-hard. This implies
that it is neither possible to efficiently find the least contributing solution
(unless ) nor to approximate it (unless ).
Nevertheless, in the second part of the paper we present a fast approximation
algorithm for this problem. We prove that for arbitrarily given \eps,\delta>0
it calculates a solution with contribution at most (1+\eps) times the minimal
contribution with probability at least . Though it cannot run in
polynomial time for all instances, it performs extremely fast on various
benchmark datasets. The algorithm solves very large problem instances which are
intractable for exact algorithms (e.g., 10000 solutions in 100 dimensions)
within a few seconds.Comment: 22 pages, to appear in Theoretical Computer Scienc
Phase diagram of the frustrated Hubbard model
The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the
one-band Hubbard model has long been used to describe similar features in real
materials like VO. Here we show that this transition is hidden inside a
rather robust antiferromagnetic insulator even in the presence of comparatively
strong magnetic frustration. This result raises the question of the relevance
of the Mott-Hubbard metal-insulator transition for the generic phase diagram of
the one-band Hubbard model.Comment: 4 pages, 6 figure
Hybridizing Non-dominated Sorting Algorithms: Divide-and-Conquer Meets Best Order Sort
Many production-grade algorithms benefit from combining an asymptotically
efficient algorithm for solving big problem instances, by splitting them into
smaller ones, and an asymptotically inefficient algorithm with a very small
implementation constant for solving small subproblems. A well-known example is
stable sorting, where mergesort is often combined with insertion sort to
achieve a constant but noticeable speed-up.
We apply this idea to non-dominated sorting. Namely, we combine the
divide-and-conquer algorithm, which has the currently best known asymptotic
runtime of , with the Best Order Sort algorithm, which
has the runtime of but demonstrates the best practical performance
out of quadratic algorithms.
Empirical evaluation shows that the hybrid's running time is typically not
worse than of both original algorithms, while for large numbers of points it
outperforms them by at least 20%. For smaller numbers of objectives, the
speedup can be as large as four times.Comment: A two-page abstract of this paper will appear in the proceedings
companion of the 2017 Genetic and Evolutionary Computation Conference (GECCO
2017
Dual guidance in evolutionary multi-objective optimization by localization
In this paper, we propose a framework using local models for multi-objective optimization to guide the search heuristic in both the decision and objective spaces. The localization is built using a limited number of adaptive spheres in the decision space. These spheres are usually guided, using some direction information, in the decision space towards the areas with non-dominated solutions. We use a second mechanism to adjust the spheres to specialize on different parts of the Pareto front using the guided dominance technique in the objective space. With this dual guidance, we can easily guide spheres towards different parts of the Pareto front while also exploring the decision space efficiently
Preference Articulation by Means of the R2 Indicator
International audienceIn multi-objective optimization, set-based performance indicators have become the state of the art for assessing the quality of Pareto front approximations. As a consequence, they are also more and more used within the design of multi-objective optimization algorithms. The R2 and the Hypervolume (HV) indicator represent two popular examples. In order to understand the behavior and the approximations preferred by these indicators and algorithms, a comprehensive knowledge of the indicator's properties is required. Whereas this knowledge is available for the HV, we presented a first approach in this direction for the R2 indicator just recently. In this paper, we build upon this knowledge and enhance the considerations with respect to the integration of preferences into the R2 indicator. More specifically, we analyze the effect of the reference point, the domain of the weights, and the distribution of weight vectors on the optimization of μ solutions with respect to the R2 indicator. By means of theoretical findings and empirical evidence, we show the potentials of these three possibilities using the optimal distribution of μ solutions for exemplary setups
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