Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy

We present an approach to interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy.The approach relies on formulae for lower and upper bounds on coordinates of the outcome of an arbitrary efficient variant corresponding to preference information expressed by the Decision Maker. In contrast to earlier works on that subject, here lower and upper bounds can be calculated and their accuracy controlled entirely within evolutionary computation framework. This is made possible by exploration of not only the region of feasible variants - a standard within evolutionary optimization, but also the region of infeasible variants, the latter to our best knowledge being a novel approach within Evolutionary Multiobjective Optimization.To illustrate how this concept can be applied to interactive Multiple Criteria Decision Making, two algorithms employing evolutionary computations are proposed and their usefulness demonstrated by a numerical example.     

Effect of boron additive on the formation of the carbon fiber structure

Effect of boron on the process of directed recrystallyzation of a nanostructured fibrous carbon material in a high-temperature thermomechanical treatment was studied by means of X-ray diffraction analysis.     

On the quasistability of trajectory problems of vector optimization

We consider quasistable multicriteria problems of discrete optimization on systems of subsets (trajectory problems). We single out the class of problems for which new Pareto optima can appear, while other optima for the problems do not disappear when the coefficients of the objective functions are slightly perturbed (in the Chebyshev metric). For the case of linear criteria (MINSUM), we obtain a formula for calculating the quasistability radius of the problem. Translated fromMatemalicheskie Zametki, Vol. 63, No. 1, pp. 21–27, January, 1998. This research was supported by the Belarus Foundation for Basic Research under grant No. F95-70.     

On the quasistability of trajectory problems of vector optimization

We consider quasistable multicriteria problems of discrete optimization on systems of subsets (trajectory problems). We single out the class of problems for which new Pareto optima can appear, while other optima for the problems do not disappear when the coefficients of the objective functions are slightly perturbed (in the Chebyshev metric). For the case of linear criteria (MINSUM), we obtain a formula for calculating the quasistability radius of the problem.     

Multiphysical simulation analysis of the dislocation structure in germanium single crystals

To grow high-quality germanium crystals is one of the most important problems of growth industry. The dislocation density is an important parameter of the quality of single crystals. The dislocation densities in germanium crystals 100 mm in diameter, which have various shapes of the side surface and are grown by the Czochralski technique, are experimentally measured. The crystal growth is numerically simulated using heat-transfer and hydrodynamics models and the Alexander–Haasen dislocation model in terms of the CGSim software package. A comparison of the experimental and calculated dislocation densities shows that the dislocation model can be applied to study lattice defects in germanium crystals and to improve their quality.     

On the Grothendieck group of simply connected semisimple algebraic groups

The K₀ groups of simply connected semisimple algebraic groups are calculated. The triviality of the Chow groups CH¹ and CH² of such groups is obtained as a consequence. Bibliography: 14 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 223–235.     

Effect of Temperature of Thermomechanical Processing on the Heterogeneous Structure of Carbon Fiber

Technical Physics - X-ray diffraction is used to study changes of fine structure of carbon fibers caused by an increase in the heat-treatment temperature. It is shown that the fiber material is...     

Effect of Crystallization Front Shape on the Dislocation Density in Germanium Single Crystals

Crystallography Reports - The effect of crystallization front shape on the dislocation density in Ge single crystals with a diameter of 100 mm, grown by the Czochralski method, has been studied....