An Improvement Study of the Decomposition-based Algorithm Global WASF-GA for Evolutionary Multiobjective Optimization

The convergence and the diversity of the decompositionbased evolutionary algorithm Global WASF-GA (GWASF-GA) relies on a set of weight vectors that determine the search directions for new non-dominated solutions in the objective space. Although using weight vectors whose search directions are widely distributed may lead to a well-diversified approximation of the Pareto front (PF), this may not be enough to obtain a good approximation for complicated PFs (discontinuous, non-convex, etc.). Thus, we propose to dynamically adjust the weight vectors once GWASF-GA has been run for a certain number of generations. This adjustment is aimed at re-calculating some of the weight vectors, so that search directions pointing to overcrowded regions of the PF are redirected toward parts with a lack of solutions that may be hard to be approximated. We test different parameters settings of the dynamic adjustment in optimization problems with three, five, and six objectives, concluding that GWASF-GA performs better when adjusting the weight vectors dynamically than without applying the adjustment.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Event-B model decomposition

Two methods have been identified in the DEPLOY project for Event-B model decomposition: the shared variable decomposition (called A-style decomposition), and the shared event decomposition (or B-style decomposition). Both allow the decomposition of a (concrete) model into several independent sub-models which may then be refined separately. The purpose of this paper is to introduce the Event-B model decomposition, from theory (A-style vs. B-style, differences and similarities) to practice (decomposition plug-in of the Rodin [1] platform)

Thermal Decomposition of Hydrazines from Reactive Dynamics Using the ReaxFF Reactive Force Field

We report reactive dynamics (RD) studies on: the decomposition of bulk hydrazine (N_2H_4); the decomposition of bulk monomethyl-hydrazine (CH_3N_2H_3), hereafter referred to simply as methyl-hydrazine; the decomposition of hydrazine in the presence of hydrogen peroxide (H_2O_2); and decomposition hydrazine on catalytic surfaces Pt[100] and Pt[111] under various conditions. These studies use the ReaxFF reactive force field to describe the multitude of chemical reactions in these systems for a variety of reaction conditions in order to show that this approach leads to realistic decomposition mechanisms and rates. In particular, we determined how the decomposition of hydrazine is affected by temperature, pressure, and heating rate. We analyzed chemical reaction mechanism of the decomposition of hydrazine at the studied conditions and found that at lower temperatures the initial product from hydrazine decomposition is NH_3, whereas at higher temperatures H_2 and N_2 are the dominant early products. Prominent intermediates observed during these decompositions include N_2H_3, N_2H_2, and NH_2, in agreement with quantum mechanical studies (7.3 ps at 3000 K). As the heating rate is decreased, the onset for hydrazine decomposition shifts to lower temperatures. Using a constant heating rate, we found that higher pressure (increased density) favors formation of NH_3 over N_2 and H_2. In studies of the catalytic decomposition of hydrazine on surfaces Pt[100] and Pt[111], we found that the presence of a Pt-catalyst reduces the initial decomposition temperature of hydrazine by about 50%. We found that the Pt[100]-surface is 20 times more active for hydrazine decomposition than the Pt[111]-surface, in qualitative agreement with experiments. These studies indicate how ReaxFF RD can be useful in understanding the chemical processes involved in bulk and catalytic decomposition and in oxidation of reactive species under various reaction conditions

Variable Hardy Spaces

We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including a "finite" decomposition; this decomposition is more like the decomposition for weighted Hardy spaces due to Stromberg and Torchinsky than the classical atomic decomposition. As an application of the atomic decomposition we show that singular integral operators are bounded on variable Hardy spaces with minimal regularity assumptions on the exponent function

Decomposition of Optical Flow on the Sphere

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are motivated by recent trends in image analysis. In particular we treat $u+v$ decomposition as well as hierarchical decomposition. Helmholtz decomposition of motion fields is obtained as a natural by-product of the chosen numerical method based on vector spherical harmonics. All models are tested on time-lapse microscopy data depicting fluorescently labelled endodermal cells of a zebrafish embryo.Comment: The final publication is available at link.springer.co