Stochastic global optimization as a filtering problem

We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access to noisy measurements of the functions or statistical estimates provided through Monte Carlo sampling. This makes iterative optimization algorithms behave like stochastic maps. Naive global optimization amounts to evolving a collection of realizations of this stochastic map and picking the realization with the best properties. This motivates the use of filtering techniques to allow focusing on realizations that are more promising than others. In particular, we present a filtering reformulation of global optimization in terms of a special case of sequential importance sampling methods called particle filters. The increasing popularity of particle filters is based on the simplicity of their implementation and their flexibility. We utilize the flexibility of particle filters to construct a stochastic global optimization algorithm which can converge to the optimal solution appreciably faster than naive global optimization. Several examples of parametric exponential density estimation are provided to demonstrate the efficiency of the approach.     

Heterocyclic reactive mesogens: synthesis, characterisation and mesomorphic behaviour

Novel heterocyclic and photopolymerizable liquid crystalline materials (reactive mesogens) with smectic phases have been synthesized and characterized. A selection of heterocyclic rings, such as benzothiazole, benzothiadiazole and pyrimidine, has been incorporated into the aromatic core to control the electrochemical/luminescence properties and the structural geometry. Particular emphasis is focused on structure-property relationships, in which the variation of molecular structure and its subsequent effect on the liquid crystalline transition temperatures have been investigated.     

Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity

In this paper, we consider nondifferentiable multiobjective fractional programming problems. A concept of generalized convexity, which is called (C,α,ρ,d)-convexity, is first discussed. Based on this generalized convexity, we obtain efficiency conditions for multiobjective fractional programming (MFP). Furthermore, we establish duality results for three types of dual problems of (MFP) and present the corresponding duality theorems.     

Synthesis of Segmented Silica Rods by Regulation of the Growth Temperature

The control of the diameter of colloidal structures is of fundamental interest and practical importance. We synthesized segmented silica rods by regulating the reaction temperature while the rods were growing. With higher growth temperatures, the segment diameter became smaller. Longer incubation times gave longer segments at the same temperature. Similarly, high temperature for the same incubation time gave longer segments. It appears that the correlation between temperature and diameter results from the relation between temperature and the size of the emulsion droplet, that is, the higher the temperature, the smaller the emulsion droplet.     

Fractal Dimension of Microbead Assemblies Used for Protein Detection

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest–Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles.     

Linearly Constrained Global Optimization and Stochastic Differential Equations

A stochastic algorithm is proposed for the global optimization of nonconvex functions subject to linear constraints. Our method follows the trajectory of an appropriately defined Stochastic Differential Equation (SDE). The feasible set is assumed to be comprised of linear equality constraints, and possibly box constraints. Feasibility of the trajectory is achieved by projecting its dynamics onto the set defined by the linear equality constraints. A barrier term is used for the purpose of forcing the trajectory to stay within the box constraints. Using Laplace’s method we give a characterization of a probability measure (Π) that is defined on the set of global minima of the problem. We then study the transition density associated with the projected diffusion process and show that its weak limit is given by Π. Numerical experiments using standard test problems from the literature are reported. Our results suggest that the method is robust and applicable to large-scale problems.     

Lower Bound Improvement and Forcing Rule for Quadratic Binary Programming

In this paper several equivalent formulations for the quadratic binary programming problem are presented. Based on these formulations we describe four different kinds of strategies for estimating lower bounds of the objective function, which can be integrated into a branch and bound algorithm for solving the quadratic binary programming problem. We also give a theoretical explanation for forcing rules used to branch the variables efficiently, and explore several properties related to obtained subproblems. From the viewpoint of the number of subproblems solved, new strategies for estimating lower bounds are better than those used before. A variant of a depth-first branch and bound algorithm is described and its numerical performance is presented.     

Kinetic isotope effect for hydrogen/deuterium abstraction by chlorine atoms from (CH3)2NNO2 and (CD3)2NNO2

The kinetic isotope effect for the abstraction of hydrogen/deuterium from dimethylnitramine and dimethylnitramine-d₆ by chlorine atoms has been studied in the temperature range 273–353 K. The rate constant ratio k_H0/k_D is given by the Arrhenius expression, k_H/k_D=(0.92 ± 0.07)exp(286 ± 250/RT), where R is expressed in cal mol^?1 K^?1. The absolute rate constant for the deuterium abstraction reaction is extrapolated as k_D=(1.50 ± 0.90) × 10^?10 exp(?1,486 ± 370/RT) cm³ molecule^?1 s^?1. The temperature dependence of the kinetic isotope effect was calculated using the conventional transition-state theory, and the obtained values for k_H/k_D and ΔE_{H, D} are in good agreement with the experimental value for a bent transition state geometry, with two new vibrational frequencies of 340 cm^?1 (272 cm^?1) corresponding to the in-plane and out-of-plane motions of hydrogen (deuterium) atoms in the Cl…H…C arrangement. © 1993 John Wiley & Sons, Inc.     

Evaluation of various high-order-accuracy schemes with and without flux limiters

Conventional high-order schemes with reduced levels of numerical diffusion produce results with spurious oscillations in areas where steep velocity gradients exist. To prevent the development of non-physical oscillations in the solution, several monotonic schemes have been proposed. In this work, three monotonic schemes, namely Van Leer's scheme, Roe's flux limiter and the third-order SHARP scheme, are compared and evaluated against schemes without flux limiters. The latter schemes include the standard first-order upwind scheme, the second-order upwind scheme and the QUICK scheme. All the above schemes are applied to four two-dimensional problems: (i) rotation of a scalar ‘cone’ field, (ii) transport of a scalar ‘square’ field, (iii) mixing of a cold with a hot front and (iv) deformation of a scalar ‘cone’ field. These problems test the ability of the selected schemes to produce oscillation-free and accurate results in critical convective situations. The evaluation of the schemes is based on several aspects, such as accuracy, economy and complexity. The tests performed in this work reveal the merits and demerits of each scheme. It is concluded that high-order schemes with flux limiters can significantly improve the accuracy of the results.