Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Quality Estimation of e-Learning Systems

Existing approaches to quality estimation of e-learning systems are analyzed. The “layered” approach for quality estimation of e-learning systems enhanced with learning process modeling and simulation is presented. The method of quality estimation using learning process modeling and quality criteria are suggested. The learning process model based on extended colored stochastic Petri net is described. The method has been implemented in the automated system of quality estimation of e-learning systems named “QuAdS”. Results of approbation of the developed method and quality criteria are shown. We argue that using learning process modeling for quality estimation simplifies identifying lacks of an e-learning system for an expert.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

Comparison between conventional and stochastic pinning control

Theoretical developments on pinning control of complex dynamical networks have mainly focused on the deterministic versions of the model dynamics. However, the dynamical behavior of most real networks is often affected by stochastic noise components. In this paper the pinning control of a stochastic version of the coupled map lattice network with spatiotemporal characteristics is studied. The control of these complex dynamical networks have functional uncertainty which should be considered when calculating stabilizing control signals. Two feedback control methods are considered: the conventional feedback control and modified stochastic feedback control. It is shown that the typically-used conventional control method suffers from the ignorance of model uncertainty leading to a reduction and potentially a collapse in the control efficiency. Numerical verification of the main result is provided for a chaotic coupled map lattice network. © 2011 IEEE.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

A simulation analysis of spoke-terminals operating in LTL Hub-and-Spoke freight distribution systems

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT The research presented in this thesis is concerned with Discrete-Event Simulation (DES) modelling as a method to facilitate logistical policy development within the UK Less-than-Truckload (LTL) freight distribution sector which has been typified by “Pallet Networks” operating on a hub-and-spoke philosophy. Current literature relating to LTL hub-and-spoke and cross-dock freight distribution systems traditionally examines a variety of network and hub design configurations. Each is consistent with classical notions of creating process efficiency, improving productivity, reducing costs and generally creating economies of scale through notions of bulk optimisation. Whilst there is a growing abundance of papers discussing both the network design and hub operational components mentioned above, there is a shortcoming in the overall analysis when it comes to discussing the “spoke-terminal” of hub-and-spoke freight distribution systems and their capabilities for handling the diverse and discrete customer profiles of freight that multi-user LTL hub-and-spoke networks typically handle over the “last-mile” of the delivery, in particular, a mix of retail and non-retail customers. A simulation study is undertaken to investigate the impact on operational performance when the current combined spoke-terminal delivery tours are separated by ‘profile-type’ (i.e. retail or nonretail). The results indicate that a potential improvement in delivery performance can be made by separating retail and non-retail delivery runs at the spoke-terminal and that dedicated retail and non-retail delivery tours could be adopted in order to improve customer delivery requirements and adapt hub-deployed policies. The study also leverages key operator experiences to highlight the main practical implementation challenges when integrating the observed simulation results into the real-world. The study concludes that DES be harnessed as an enabling device to develop a ‘guide policy’. This policy needs to be flexible and should be applied in stages, taking into account the growing retail-exposure.

Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

Numerical Analysis of Chemical Reactions by Monte Carlo Simulation

Добри Данков, Владимир Русинов, Мария Велинова, Жасмина Петрова - Изследвана е химическа реакция чрез два начина за моделиране на вероятността за химическа реакция използвайки Direct Simulation Monte Carlo метод. Изследван е порядъка на разликите при температурите и концентрациите чрез тези начини. Когато активността на химическата реакция намалява, намаляват и разликите между концентрациите и температурите получени по двата начина. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Learning with a strategic management simulation game:a case study

The use of simulation games as a pedagogic method is well established though its effective use is context-driven. This study adds to the increasing growing body of empirical evidence of the effectiveness of simulation games but more importantly emphasises why by explaining the instructional design implemented reflecting best practices. This multi-method study finds evidence that student learning was enhanced through the use of simulation games, reflected in the two key themes; simulation games as a catalyst for learning and simulation games as a vehicle for learning. In so doing the research provides one of the few empirically based studies that support simulation games in enhancing learning and, more importantly, contextualizes the enhancement in terms of the instructional design of the curriculum. This research should prove valuable for those with an academic interest in the use of simulation games and management educators who use, or are considering its use. Further, the findings contribute to the academic debate concerning the effective implementation of simulation game-based training in business and management education.

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

Short-term wind power forecasting using Gaussian processes

Since wind has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safety and economics of wind energy utilization. In this paper, we investigate a combination of numeric and probabilistic models: one-day-ahead wind power forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical Weather Prediction (NWP) model. Firstly the wind speed data from NWP was corrected by a GP. Then, as there is always a defined limit on power generated in a wind turbine due the turbine controlling strategy, a Censored GP was used to model the relationship between the corrected wind speed and power output. To validate the proposed approach, two real world datasets were used for model construction and testing. The simulation results were compared with the persistence method and Artificial Neural Networks (ANNs); the proposed model achieves about 11% improvement in forecasting accuracy (Mean Absolute Error) compared to the ANN model on one dataset, and nearly 5% improvement on another.