Optimization Under Stochastic Uncertainty
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Optimization Under Stochastic Uncertainty
This book examines application and methods to incorporating stochastic parameter variations into the optimization process to decrease expense in corrective measures. Basic types of deterministic substitute problems occurring mostly in practice involve i) minimization of the expected primary costs subject to expected recourse cost constraints (reliability constraints) and remaining deterministic constraints, e.g. box constraints, as well as ii) minimization of the expected total costs (costs of construction, design, recourse costs, etc.) subject to the remaining deterministic constraints. After an introduction into the theory of dynamic control systems with random parameters, the major control laws are described, as open-loop control, closed-loop, feedback control and open-loop feedback control, used for iterative construction of feedback controls. For approximate solution of optimization and control problems with random parameters and involving expected cost/loss-type objective, constraint functions, Taylor expansion procedures, and Homotopy methods are considered, Examples and applications to stochastic optimization of regulators are given. Moreover, for reliability-based analysis and optimal design problems, corresponding optimization-based limit state functions are constructed. Because of the complexity of concrete optimization/control problems and their lack of the mathematical regularity as required of Mathematical Programming (MP) techniques, other optimization techniques, like random search methods (RSM) became increasingly important. Basic results on the convergence and convergence rates of random search methods are presented. Moreover, for the improvement of the – sometimes very low – convergence rate of RSM, search methods based on optimal stochastic decision processes are presented. In order to improve the convergence behavior of RSM, the random search procedure is embedded into a stochastic decision process for an optimal control of the probability distributions of the search variates (mutation random variables).
Supply Chain Optimization under Uncertainty
Drawing on cutting-edge research, this book proposes a new 'Supply Chain Optimization under Uncertainty’, technology. Its application can bring many proven benefits to supply chain entities, any associated service providers, and, of course, the customers. The technology can provide the best design and operating solution for a Supply Chain Network (SCN) that is subject to any prevailing conditions of Operational Uncertainty (OU). A SCN is defined as a network of production facilities, distribution centers and retail sales outlets. OU is defined as any relevant combination of i) multiple process objectives e.g. a business needs to maximize operating profits and to minimize inventory levels, ii) fuzziness (<, <=, >, or >=) e.g. sales <= 1500 t/mth and iii) probability e.g. sale of fertilizer is dependent on probabilistic rainfall. Following this method always enables the determination of realistic optimum supply chain solutions, since the effects of any operational uncertainties are always provided for. The book is arranged in two parts. The first part covers the theory and recent research into supply chain optimization under uncertainty. The second part documents the application of the newly proposed technology to an agricultural fertilizer’s (NPK, South Africa) supply chain.
Constrained Optimization and Optimal Control for Partial Differential Equations
Author: Günter Leugering
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-01-03
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.