A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems

There is a need for a methodology to fairly compare and present evaluation study results of stochastic global optimization algorithms. This need raises two important questions of (i) an appropriate set of benchmark test problems that the algorithms may be tested upon and (ii) a methodology to compactly and completely present the results. To address the first question, we compiled a collection of test problems, some are better known than others. Although the compilation is not exhaustive, it provides an easily accessible collection of standard test problems for continuous global optimization. Five different stochastic global optimization algorithms have been tested on these problems and a performance profile plot based on the improvement of objective function values is constructed to investigate the macroscopic behavior of the algorithms. The paper also investigates the microscopic behavior of the algorithms through quartile sequential plots, and contrasts the information gained from these two kinds of plots. The effect of the length of run is explored by using three maximum numbers of function evaluations and it is shown to significantly impact the behavior of the algorithms.     

Modeling Anisotropic Single Crystal Growth Kinetics in Liquid Phase Sintered α-Al2O3

Single crystals of -alumina with {0001}, {11 and {01 2} orientations were embedded in a matrix of liquid phase sintered alumina to study -alumina single crystal growth in the presence of a calcium aluminosilicate liquid. Growth on the {11 0} and {01 2} surfaces was observed to occur by a diffusion-controlled mechanism while growth on the basal surface was controlled by two-dimensional nucleation. Growth models, which incorporate the change in matrix grain size, were derived and shown to fit the growth kinetics.     

The roots of vacuum microbalance techniques and the international conferences on this subject

Journal of Thermal Analysis and Calorimetry -     

Explicit algebraic stress modelling of homogeneous and inhomogeneous flows

Capability of the explicit algebraic stress models to predict homogeneous and inhomogeneous shear flows are examined. The importance of the explicit solution of the production to dissipation ratio is first highlighted by examining the algebraic stress models performance at purely irrotational strain conditions. Turbulent recirculating flows within sudden expanding pipes are further simulated with explicit algebraic stress model and anisotropic eddy viscosity model. Both models predict better stress–strain interactions, showing reasonable shear layer developments. The anisotropic stress field are also accurately predicted by the models, though the anisotropic eddy viscosity model of Craft et al. returns marginally better results. Copyright © 2005 John Wiley & Sons, Ltd.     

A physical basis for Krein's prediction formula

A prediction problem of the following variety is considered. A stationary random process w(·) of known spectrum is observed over |t|?a. Using these observed values, w(b) is to be predicted for some b with |b|>a. We present a physical interpretation of a solution to this problem due to Krein, which used the theory of inverse Sturm-Liouville problems. Our physical model involves a nonuniform lossless transmission line excited at one end by white noise. The signal at the other end is the process w(t), and the prediction is found by calculating as intermediate quantities the voltage and current stored on the line at t=0. These quantities are spatially uncorrelated and provide a spatial representation at t=0 of the innovations of w(t) over |t|?a.     

Computer-oriented, n-body modelling of minimal surfaces

In this paper a new approach to the modelling of minimal surfaces is described and applied. Rather than use a continuous model, we develop a discrete, _n-body model with basic tensile interactions derived from classical molecular force formulae. Computer results are described and discussed.     

Fission fragment track etching modelling for the cellular localisation of Neptunium-237 nuclei in rat tissues

Heavy ion recording in dielectric isotropic detectors has a wide range of applications in uranium cartography or dating. In this study, solid state nuclear tracks detectors (SSNTDs) have been applied to localise neptunium-237, in vivo, by means of the neutron-induced fission cartography of neptunium-237 nuclei in organ sections. At the cellular level, a precise localisation can only be achieved with a good understanding of the etch pit evolution during the chemical etching process.

A tailor-made software for modelling the etching process has been developed to simulate the profile of an etched track produced by a neutron-induced fission fragment. This software is based on a model that considers the evolution of the track etching velocity along the damage trail in order to perfectly model the shape of the track.     

Probabilistic kinetics of macroprocesses in broken microscopic reversibility

Probabilistic kinetics following the Pauli master equation without microscopic reversibility determines an asymptotic structure of macroprocesses in a coarse-grained phase space of many degrees of freedom. The structure, which is asymptotically realized, minimizes its irreversible decay rate among various candidates. This least irreversible decay rate is consistent with the assertion for the minimum K-entropy which has been argued to apply to the nonequilibrium asymptotic state. The irreversible decay rate is a state function characteristic of macrostructure on a coarse-grained time scale. Macrofluctuations, which always appear around the asymptote as fluctuations of the state function, do not obey the central limit theorem, implying that fluctuations whose characteristic times are not less than some finite value are never excluded.     

Simulated annealing and quantum detailed balance

The analogue of simulated annealing is considered for time-inhomogeneous evolutions of a von Neumann algebra of operators, whose instantaneous generator at each timet satisfies the quantum detailed balance condition with respect to a faithful normal state which depends on time through a suitable cooling schedule. Convergence to the (nonfaithful) limiting state is proved under the usual kinds of assumptions. The approach is interesting in view of possible applications to stochastic Ising models and to Boltzmann machines.