Optimization Of Stochastic Models
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Optimization of Stochastic Models
Author: Georg Ch. Pflug
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.
Stochastic Simulation Optimization: An Optimal Computing Budget Allocation
With the advance of new computing technology, simulation is becoming very popular for designing large, complex and stochastic engineering systems, since closed-form analytical solutions generally do not exist for such problems. However, the added flexibility of simulation often creates models that are computationally intractable. Moreover, to obtain a sound statistical estimate at a specified level of confidence, a large number of simulation runs (or replications) is usually required for each design alternative. If the number of design alternatives is large, the total simulation cost can be very expensive.Stochastic Simulation Optimization addresses the pertinent efficiency issue via smart allocation of computing resource in the simulation experiments for optimization, and aims to provide academic researchers and industrial practitioners with a comprehensive coverage of OCBA approach for stochastic simulation optimization. Starting with an intuitive explanation of computing budget allocation and a discussion of its impact on optimization performance, a series of OCBA approaches developed for various problems are then presented, from the selection of the best design to optimization with multiple objectives. Finally, this book discusses the potential extension of OCBA notion to different applications such as data envelopment analysis, experiments of design and rare-event simulation.
Stochastic Global Optimization
Author: Anatoly Zhigljavsky
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-11-20
This book aims to cover major methodological and theoretical developments in the ?eld of stochastic global optimization. This ?eld includes global random search and methods based on probabilistic assumptions about the objective function. We discuss the basic ideas lying behind the main algorithmic schemes, formulate the most essential algorithms and outline the ways of their theor- ical investigation. We try to be mathematically precise and sound but at the same time we do not often delve deep into the mathematical detail, referring instead to the corresponding literature. We often do not consider the most g- eral assumptions, preferring instead simplicity of arguments. For example, we only consider continuous ?nite dimensional optimization despite the fact that some of the methods can easily be modi?ed for discrete or in?nite-dimensional optimization problems. The authors’ interests and the availability of good surveys on particular topics have in uenced the choice of material in the book. For example, there are excellent surveys on simulated annealing (both on theoretical and - plementation aspects of this method) and evolutionary algorithms (including genetic algorithms). We thus devote much less attention to these topics than they merit, concentrating instead on the issues which are not that well d- umented in literature. We also spend more time discussing the most recent ideas which have been proposed in the last few years.