Determining initial bound by "Ray-method" in branch and bound procedure

In this paper we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of this algorithm is based on the use of "ray" as introduced in the "ray-method" developed for solving integer linear programming problems [11], [12]. Instead of solving an integer programming problem we use the main idea of the ray-method to find an integer feasible solution of an integer linear programming problem along the ray as close to an optimal solution of the relaxation problem as possible. The objective value obtained in this manner may be used as an initial bound for the B&B method. It is well known that getting a "good bound" as soon as possible can often significantly increase the performance of the B&B method

THE RAY-METHOD: THEORETICAL BACKGROUND AND COMPUTATIONAL RESULTS

In our talk we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of the algorithm is based on the use of the "ray" introduced in the "ray-method" developed for solving integer programming problems [13], [14]. Instead of solving a common integer programming problem we use the main idea of the ray-method to find an integer feasible solution of integer linear programming (ILP) problem along the ray as close to optimal solution of relaxation problem, as possible. Objective value obtained in this way may be used as an initial bound for B&B method. The algorithm has been implemented in the frame of educational package WinGULF [3] for linear and linear-fractional programming and has been tested on various ILP problems. Then inspired by the results obtained we implemented the method using the so-called callable library of CPLEX package by IBM. omputational experiments with the algorithm proposed show that such preprocessing procedure in many cases results an integer feasible solution very close to the solution of relaxation problem. Initial bound for branch and bound method determined in this way often can significantly decrease the size of the binary tree to be searched and in this manner can improve performance of the B&B method

On the nature of supernovae Ib and Ic

Utilizing non-local thermodynamic equilibrium time-dependent radiative-transfer calculations, we investigate the impact of mixing and non-thermal processes associated with radioactive decay on Type IIb/Ib/Ic supernova (SN IIb/Ib/Ic) light curves and spectra. Starting with short-period binary models of ≾5M_⊙ helium-rich stars, originally 18 and 25M_⊙ on the main sequence, we produce 1.2B ejecta which we artificially mix to alter the chemical stratification. While the total ^(56)Ni mass influences the light-curve peak, the spatial distribution of ^(56)Ni, controlled by mixing processes, impacts both the multiband light curves and spectra. With enhanced γ-ray escape. Non-thermal electrons, crucial for the production of He_I lines, deposit a large fraction of their energy as heat, and this fraction approaches 100 per cent under fully ionized conditions. Because energy deposition is generally local well after the light-curve peak, the broad He_I line characteristics of maximum-light SN IIb/Ib spectra require mixing that places ^(56)Ni and helium nuclei to within a γ-ray mean free path. This requirement indicates that SNe IIb and Ib most likely arise from the explosions of stripped-envelope massive stars (main-sequence masses ≾25M_⊙) that have evolved through mass transfer in a binary system, rather than from more massive single Wolf-Rayet stars. In contrast, the lack of He_I lines in SNe Ic may result from a variety of causes: a genuine helium deficiency; strongly asymmetric mixing; weak mixing; or a more massive, perhaps single, progenitor characterized by a larger oxygen-rich core. Helium deficiency is not a prerequisite for SNe Ic. Our models, subject to different mixing magnitudes, can produce a variety of SN types, including IIb, IIc, Ib and Ic. As it is poorly constrained by explosion models, mixing challenges our ability to infer the progenitor and explosion properties of SNe IIb/Ib/Ic

Ground state determination, ground state preserving fit for cluster expansion and their integration for robust CE construction

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, February 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 106-111).In this thesis, we propose strategies to solve the general ground state problem for arbitrary effective cluster interactions and construct ground state preserving cluster expansions. A full mathematical definition of our problem has been formalized to illustrate its generality and clarify our discussion. We review previous methods in material science community: Monte Carlo based method, configurational polytope method, and basic ray method. Further, we investigate the connection of the ground state problem with deeper mathematical results about computational complexity and NP-hard combinatorial optimization (MAX-SAT). We have proposed a general scheme, upper bound and lower bound calculation to approach this problem. Firstly, based on the traditional configurational polytope method, we have proposed a method called cluster tree optimization method, which eliminates the necessity of introducing an exponential number of variables to counter frustration, and thus significantly improves tractability. Secondly, based on convex optimization and finite optimization without periodicity, we have introduced a beautiful MAX-MIN method to refine lower bound calculation. Finally, we present a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of the reference data.by Wenxuan Huang.Ph. D