Generalized Benders’ Decomposition for topology optimization problems

This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.     

Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces

Computational Optimization and Applications - We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose...     

Test driving three 1995 genetic algorithms: New test functions and geometric matching

Genetic algorithms have attracted a good deal of interest in the heuristic search community. Yet there are several different types of genetic algorithms with varying performance and search characteristics. In this article we look at three genetic algorithms: an elitist simple genetic algorithm, the CHC algorithm and Genitor. One problem in comparing algorithms is that most test problems in the genetic algorithm literature can be solved using simple local search methods. In this article, the three algorithms are compared using new test problems that are not readily solved using simple local search methods. We then compare a local search method to genetic algorithms for geometric matching and examine a hybrid algorithm that combines local and genetic search. The geometric matching problem matches a model (e.g., a line drawing) to a subset of lines contained in a field of line fragments. Local search is currently the best known method for solving general geometric matching problems.     

Misfit driven azimuthal orientation of NaCl domains on Ag(1 0 0)

We investigated the growth of thin NaCl films on Ag(1 0 0) by spot-profile-analysis low energy electron diffraction (SPA-LEED), varying extensively the growth temperature (200–500 K) and the film thickness (0.5–14 ML). The incommensurate growth of NaCl on Ag(1 0 0) yields (1 0 0)-terminated epitaxial NaCl domains, which are preferentially oriented with their [0 1 0] axis parallel to that of the substrate. At 300 K, the NaCl domains exhibit an azimuthal mosaicity by 14° around this orientation and the NaCl unit cell is laterally contracted in the first layers by 0.9% with respect to the bulk. At higher growth temperatures, the azimuthal mosaic distribution sharpens and additional distinct orientations appear, presumably due to a higher-order commensurability. The evolution of the azimuthal mosaic distribution with increasing temperature can be ascribed to both the NaCl thermal expansion and higher diffusion rates of NaCl on Ag(1 0 0). The best epitaxy, i.e. that with the highest selectivity of a specific azimuthal domain orientation, is achieved by growing NaCl films at low deposition rate (0.1 ML min⁻¹) on the Ag(1 0 0) substrate at constant high temperature (450–500 K). The observations made here can probably be applied more generally to other heterogeneous interfaces and, in particular, be used to improve the quality of thin insulating films.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

Near-field-enhanced,off-resonant laser sintering of semiconductor particles for additive manufacturing of dispersed Au–ZnO-micro/nano hybrid structures

Off-resonant near-field enhancement by gold nanoparticles adsorbed on crystalline zinc oxide significantly increases the energy efficiency of infrared laser sintering. In detail, ten different gold mass loads on zinc oxide were exposed to 1,064 nm cw-laser radiation. Variation of scan speed, laser power, and spot size showed that the energy threshold required for sintering decreases and sintering process window widens compared to laser sintering of pure zinc oxide powder. Transmission electron microscope analysis after focused ion beam cross sectioning of the sintered particles reveals that supported gold nanoparticles homogenously resolidify in the sintered semiconductor matrix. The enhanced sintering process with ligand-free gold nanoparticles gives access to metal–semiconductor hybrid materials with potential application in light harvesting or energy conversion.