A branch and bound method for stochastic global optimization

A stochastic branch and bound method for solving stochastic global optimization problems is proposed. As in the deterministic case, the feasible set is partitioned into compact subsets. To guide the partitioning process the method uses stochastic upper and lower estimates of the optimal value of the objective function in each subset. Convergence of the method is proved and random accuracy estimates derived. Methods for constructing stochastic upper and lower bounds are discussed. The theoretical considerations are illustrated with an example of a facility location problem.     

Temperature variation of the Debye-Waller factors of metal and halide ions in CsCl and CsBr powders by X-ray diffraction. II. Debye-Waller factors of Cs+ and Br− ions in CsBr from room temperature to 78.2°K

The temperature variation of the Debye-Waller factors of Cs⁺ and Br⁻ ions in CsBr powder has been studied using powder X-ray diffraction. The integrated intensities of the Bragg peaks at different temperatures have been obtained. These results have been verified by structure factor least squares refinement program. Theoretical shell model lattice dynamical calculations have been done using a 7-parameter model in the harmonic approximation and the values compared with the present X-ray measurements. The observed intensities have been corrected for first order thermal diffuse scattering.     

Traffic jams and ordering far from thermal equilibrium

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.     

Linearized perturbation method for stochastic analysis of a rill erosion model

The linearization and correction method (LCM) proposed by He is a simple and effective perturbation technique to solve nonlinear equations. To analyze the random properties of rill erosion model, a new stochastic perturbation technique called linearized perturbation method is developed by combining the traditional stochastic perturbation method with the LCM. Comparisons between the numerical results obtained by the linearized perturbation method and those obtained by Monte Carlo method indicated an excellent agreement. However, the calculation efficiency of the linearized perturbation method is higher.     

On stochastic lot-sizing problems with random lead times

We give multi-stage stochastic programming formulations for lot-sizing problems where costs, demands and order lead times follow a general discrete-time stochastic process with finite support. We characterize the properties of an optimal solution and give a dynamic programming algorithm, polynomial in the scenario tree size, when orders do not cross in time.     

Risk aversion and optimal forest replanting: A stochastic efficiency study

A new stochastic efficiency analysis approach, called stochastic efficiency with respect to a function (SERF), is applied to analyse optimal tree replanting on an area of recently harvested forest land. SERF partitions a set of risky alternative tree replanting strategies in terms of certainty equivalents (CEs) for a specified range of attitudes to risk. Both the entailed risk and the forest owner’s risk aversion are taken into account. The forest owner’s degree of risk aversion affects both the optimal tree replacement strategy and the reinvestment decision. The degree of risk aversion also needs to be taken into account when designing policy measures to affect forest investment.     

The determination of quasistationary distributions directly from the transition rates of an absorbing Markov chain

There are many stochastic systems arising in areas as diverse as wildlife management, chemical kinetics and reliability theory, which eventually “die out,” yet appear to be stationary over any reasonable time scale. The notion of a quasistationary distribution has proved to be a potent tool in modelling this behaviour. In finite-state systems the existence of a quasistationary distribution is guaranteed. However, in the infinite-state case this may not always be so and the question of whether or not quasistationary distributions exist requires delicate mathematical analysis. The purpose of this paper is to present simple conditions for the existence of quasistationary distributions for continuous-time Markov chains and to demonstrate how these can be applied in practice.     

A stochastic theory of chemical reaction rates. I. Formalism

A class of stochastic processes is studied that can be used to model elementary and complex chemical reactions composed of a series of several distinct steps. Formal correlation function expressions are directly computed for the stochastic model to yield the overall rate constant for the reaction. One of the main results is a formula connecting the overall rate constant to the rate constants characterizing the elementary steps of the reaction.     

Stochastic viability of convex sets

We investigate necessary and sufficient conditions for viability of a closed convex set K under weak solutions of a stochastic differential equation. These conditions are expressed in terms of the distance function to K. When in addition the boundary of K is smooth, then our necessary and sufficient conditions reduce to two relations that have to be verified just on the boundary of K.     

Microcomputer simulation of the countercurrent liquid-liquid distribution

The simulation of the countercurrent liquid-liquid distribution by using a microcomputer is described. The computer program that is proposed for this simulation has been made in BASIC language and its characteristics are discussed. According to the wide possibility of calculation that this program presents, several simulations of different solute mixtures have been performed.