A new evolutionary search strategy for global optimization of high-dimensional problems

Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SP-UCI is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population's capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SP-UCI surpasses two popular algorithms, particle swarm optimizer (PSO) and differential evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones. © 2011 Elsevier Inc. All rights reserved

A solution to the crucial problem of population degeneration in high-dimensional evolutionary optimization

Three popular evolutionary optimization algorithms are tested on high-dimensional benchmark functions. An important phenomenon responsible for many failures - population degeneration - is discovered. That is, through evolution, the population of searching particles degenerates into a subspace of the search space, and the global optimum is exclusive from the subspace. Subsequently, the search will tend to be confined to this subspace and eventually miss the global optimum. Principal components analysis (PCA) is introduced to discover population degeneration and to remedy its adverse effects. The experiment results reveal that an algorithm's efficacy and efficiency are closely related to the population degeneration phenomenon. Guidelines for improving evolutionary algorithms for high-dimensional global optimization are addressed. An application to highly nonlinear hydrological models demonstrates the efficacy of improved evolutionary algorithms in solving complex practical problems. © 2011 IEEE

Handling boundary constraints for particle swarm optimization in high-dimensional search space

Despite the fact that the popular particle swarm optimizer (PSO) is currently being extensively applied to many real-world problems that often have high-dimensional and complex fitness landscapes, the effects of boundary constraints on PSO have not attracted adequate attention in the literature. However, in accordance with the theoretical analysis in [11], our numerical experiments show that particles tend to fly outside of the boundary in the first few iterations at a very high probability in high-dimensional search spaces. Consequently, the method used to handle boundary violations is critical to the performance of PSO. In this study, we reveal that the widely used random and absorbing bound-handling schemes may paralyze PSO for high-dimensional and complex problems. We also explore in detail the distinct mechanisms responsible for the failures of these two bound-handling schemes. Finally, we suggest that using high-dimensional and complex benchmark functions, such as the composition functions in [19], is a prerequisite to identifying the potential problems in applying PSO to many real-world applications because certain properties of standard benchmark functions make problems inexplicit. © 2011 Elsevier Inc. All rights reserved

Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA

Coexistence of Wi-Fi and Heterogeneous Small Cell Networks Sharing Unlicensed Spectrum

As two major players in terrestrial wireless communications, Wi-Fi systems and cellular networks have different origins and have largely evolved separately. Motivated by the exponentially increasing wireless data demand, cellular networks are evolving towards a heterogeneous and small cell network architecture, wherein small cells are expected to provide very high capacity. However, due to the limited licensed spectrum for cellular networks, any effort to achieve capacity growth through network densification will face the challenge of severe inter-cell interference. In view of this, recent standardization developments have started to consider the opportunities for cellular networks to use the unlicensed spectrum bands, including the 2.4 GHz and 5 GHz bands that are currently used by Wi-Fi, Zigbee and some other communication systems. In this article, we look into the coexistence of Wi-Fi and 4G cellular networks sharing the unlicensed spectrum. We introduce a network architecture where small cells use the same unlicensed spectrum that Wi-Fi systems operate in without affecting the performance of Wi-Fi systems. We present an almost blank subframe (ABS) scheme without priority to mitigate the co-channel interference from small cells to Wi-Fi systems, and propose an interference avoidance scheme based on small cells estimating the density of nearby Wi-Fi access points to facilitate their coexistence while sharing the same unlicensed spectrum. Simulation results show that the proposed network architecture and interference avoidance schemes can significantly increase the capacity of 4G heterogeneous cellular networks while maintaining the service quality of Wi-Fi systems

An energy saving small cell sleeping mechanism with cell range expansion in heterogeneous networks

In recent years, the explosion of wireless data traffic has resulted in a trend of large scale dense deployment of small cells, with which the rising cost of energy has attracted a lot of research interest. In this paper, we present a novel sleeping mechanism for small cells to decrease the energy consumption of heterogeneous networks. Specifically, in the cell-edge area of a macrocell, the small cells will be put into sleep where possible and their service areas will be covered by the range-expanded small cells nearby and the macrocell; in areas close to the macrocell, the user equipments associated with a sleeping small cell will be handed over to the macrocell. Furthermore, we use enhanced inter-cell interference coordination techniques to support the range expanded small cells to avoid QoS degradation. Using a stochastic geometry-based network model, we provide the numerical analysis of the proposed approach, and the results indicate that the proposed sleeping mechanism can significantly reduce the power consumption of the network compared with the existing sleeping methods while guaranteeing the QoS requirement

Magnetodielectric effect of Bi6Fe2Ti3O18 film under an ultra-low magnetic field

Good quality and fine grain Bi6Fe2Ti3O18 magnetic ferroelectric films with single-phase layered perovskite structure have been successfully prepared via metal organic decomposition (MOD) method. Results of low-temperature magnetocapacitance measurements reveal that an ultra-low magnetic field of 10 Oe can produce a nontrivial magnetodielectric (MD) response in zero-field-cooling condition, and the relative variation of dielectric constants in magnetic field is positive, i.e., MD=0.05, when T<55K, but negative with a maximum of MD=-0.14 when 55K<T<190K. The magnetodielectric effect appears a sign change at 55K, which is due to transition from antiferromagnetic to weak ferromagnetic; and vanishes abruptly around 190K, which is thought to be associated with order-disorder transition of iron ion at B site of perovskite structures. The ultra-low-field magnetodielectric behaviour of Bi6Fe2Ti3O18 film has been discussed in the light of quasi-two-dimension unique nature of local spin order in ferroelectric film. Our results allow expectation on low-cost applications of detectors and switches for extremely weak magnetic fields in a wide temperature range 55K-190K.Comment: 10 pages 4 figures, planned to submit to J. Phys.: Condensed Matte