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

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

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

Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries

We consider the neutrino masses and mixing in the framework of SO(10) GUTs with hidden sector consisting of fermionic and bosonic SO(10) singlets and flavor symmetries. The framework allows to disentangle the CKM physics responsible for the CKM mixing and different mass hierarchies of quarks and leptons and the neutrino new physics which produces smallness of neutrino masses and large lepton mixing. The framework leads naturally to the relation $U_{PMNS} \sim V_{CKM}^{\dagger} U_0$, where structure of $U_0$ is determined by the flavor symmetry. The key feature of the framework is that apart from the Dirac mass matrices $m_D$, the portal mass matrix $M_D$ and the mass matrix of singlets $M_S$ are also involved in generation of the lepton mixing. This opens up new possibilities to realize the flavor symmetries and explain the data. Using $A_4 \times Z_4$ as the flavor group, we systematically explore the flavor structures which can be obtained in this framework depending on field content and symmetry assignments. We formulate additional conditions which lead to $U_0 \sim U_{TBM}$ or $U_{BM}$. They include (i) equality (in general, proportionality) of the singlet flavons couplings, (ii) equality of their VEVs; (iii) correlation between VEVs of singlets and triplet, (iv) certain VEV alignment of flavon triplet(s). These features can follow from additional symmetries or be remnants of further unification. Phenomenologically viable schemes with minimal flavon content and minimal number of couplings are constructed

Structure of CdTe/ZnTe superlattices

The structure of CdTe/ZnTe superlattices has been analyzed through θ/2θ x‐ray diffraction, photoluminescence, and in situ reflection high‐energy electron diffraction (RHEED) measurements. Samples are found to break away from Cd_(x)Zn_(1−x)Te buffer layers as a consequence of the 6% lattice mismatch in this system. However, defect densities in these superlattices are seen to drop dramatically away from the buffer layer interface, accounting for the intense photoluminescence and high‐average strain fields seen in each of our samples. Observed variations in residual strains suggest that growth conditions play a role in forming misfit defects. This could explain discrepancies with calculated values of critical thickness based on models which neglect growth conditions. Photoluminescence spectra reveal that layer‐to‐layer growth proceeded with single monolayer uniformity, suggesting highly reproducible growth. Our results give hope for relatively defect‐free Cd_(x)Zn_(1−x)Te/Cd_(y)Zn_(1−y)Te superlattices with the potential for applications to optoelectronics offered by intense visible light emitters

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

Electric vehicle charging station placement

Transportation electrification is one of the essential components in the future smart city planning and electric vehicles (EVs) will be integrated into the transportation system seamlessly. Charging stations are the main source of energy for EVs and their locations are critical to the accessibility of EVs in a city. They should be carefully situated so that an EV can access a charging station within its driving range and cruise around anywhere in the city upon being recharged. In this paper, we formulate the Electric Vehicle Charging Station Placement Problem, in which we minimize the total construction cost subject to the constraints for the charging station coverage and the convenience of the drivers for EV charging. We study the properties of the problem, especially its NP-hardness, and propose an efficient greedy algorithm to tackle the problem. We perform a series of simulation whose results show that the greedy algorithm can result in solutions comparable to the mixed-integer programming approach and its computation time is much shorter. © 2013 IEEE.Link_to_subscribed_fulltextpostprin

Effects of Three Gorges Reservoir (TGR) water storage in June 2003 on Yangtze River sediment entering the estuary

International audienceThe world-greatest water conservancy project, Three Gorges Reservoir (TGR), stored water for the first time in June 2003, which provides an excellent opportunity to examine its effects on the sediment entering the Yangtze River estuary. A daily record dataset of water discharge and suspended sediment concentration (SSC) of the Yangtze River measured at Datong (the controlling hydrological gauging station into the estuary) from May 15 to July of 2003 spanning the water storage, together with a monthly record dataset of runoff, sediment load and SSC measured at Datong from 1953 to 2003, were used to examine the effects of the TGR water storage in June 2003 on the Yangtze River sediment entering the estuary. The results show that the unnaturally clearer water due to the TGR sedimentation resulted by the water storage in June 2003 brought the Yangtze River markedly decreased SSC and sediment load entering the estuary both during the TGR water storage and in the second half year of 2003. The Yangtze River water and sediment discharges into the estuary from 15 May to 15 July in 2003 spanning the TGR water storage clearly indicated three phases: (1) pre-water storage of the TGR from 15 May to 25 May, during this phase, SSC and sediment load increased with water discharge increasing; (2) water storage of the TGR from 25 May to 10 June (including the preparation phase from 25 May to 31 May), during this phase, SSC and sediment load decreased dramatically with water discharge decreasing; and (3) post-water storage of the TGR, at the beginning, SSC, sediment load and water discharge basically remained at a relatively low value until the end of June, and since then, SSC and sediment load increased gradually with water discharge increasing. In addition, the real total sediment load was reduced by 2456.07×104 t than the estimated total sediment load during the period from 27 May to 2 July in 2003