This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these methods assume that there are a small number of scenarios to be evaluated for calculation of the probabilistic objective function and constraints. This book begins to tackle these issues by describing a generalized method for stochastic nonlinear programming problems. This title is best suited for practitioners, researchers and students in engineering, operations research, and management science who desire a complete understanding of the BONUS algorithm and its applications to the real world.
Author(s): Urmila Diwekar, Amy David
Series: SpringerBriefs in Optimization
Publisher: Springer
Year: 2015
Language: English
Pages: C, XVIII, 146
Cover
SpringerBriefs in Optimization
BONUS Algorithm for Large Scale Stochastic Nonlinear Programming Problems
Copyright
© Urmila Diwekar; Amy David 2015
ISSN 2190-8354
ISSN 2191-575X (electronic)
ISBN 978-1-4939-2281-9
ISBN 978-1-4939-2282-6 (eBook)
DOI 10.1007/978-1-4939-2282-6
Library of Congress Control Number: 2014955715
Preface
Contents
List of Figures
List of Tables
Chapter 1 Introduction
1.1 Stochastic Optimization Problems
1.2 Stochastic Nonlinear Programming
1.3 Summary
Notations
Chapter 2 Uncertainty Analysis and Sampling Techniques
2.1 Specifying Uncertainty Using Probability Distributions
2.2 Sampling Techniques
2.2.1 Monte Carlo Sampling
2.3 Variance Reduction Techniques
2.3.1 Importance Sampling
2.3.2 Stratified Sampling
2.3.3 Quasi-Monte Carlo Methods
2.4 Summary
Notations
Chapter 3 Probability Density Functions and Kernel Density Estimation
3.1 The Histogram
3.2 Kernel Density Estimator
3.3 Summary
Notations
Chapter 4 The BONUS Algorithm
4.1 Reweighting Schemes
4.2 Effect of Sampling on Reweighting
4.3 BONUS: The Novel SNLP Algorithm
4.4 Summary
Notations
Chapter 5 Water Management Under Weather Uncertainty
5.1 Introduction
5.2 The Pulverized Coal Power Plant
5.3 Parameter Uncertainty
5.4 Problem Formulation
5.5 Selection of Decision Variables
5.6 Implementation of BONUS Algorithm
5.7 Results
5.8 Summary
Notations
Chapter 6 Real-Time Optimization for Water Management
6.1 Introduction
6.2 Power Plant Operations
6.3 Formulation of the Stochastic Problem
6.4 Solution Approach
6.5 Weather Forecasting and Uncertainty Quantification
6.5.1 Ensemble Initialization
6.5.2 Ensemble Propagation
6.5.3 Validation of Weather Forecast
6.6 Application to Pulverized Coal Power Plant
6.7 Summary
Notations
Chapter 7 Sensor Placement Under Uncertainty for Power Plants
7.1 Introduction
7.1.1 The Integrated Gasification Combined Cycle Power Plant
7.1.2 Measurement Uncertainty
7.2 Fisher Information and Its Use in the Sensor-Placement Problem
7.3 Computation of Fisher Information
7.3.1 Reweighting Using the BONUS Method
7.3.2 Calculating the Fisher Information from Kernel Density Estimation
7.4 The Optimization Problem
7.4.1 Defining the Objective Function
7.4.2 The IGCC Power Plant
7.4.3 Problem Approach
7.4.4 Results
7.5 Summary
Notations
Chapter 8 The L-Shaped BONUS Algorithm
8.1 The L-Shaped BONUS Algorithm
8.2 Illustrative Example 1: The Farmer's Problem
8.2.1 Problem Formulation
8.2.2 Problem Solution
8.2.3 Results of the Farmer's Problem
8.3 Illustrative Example 2: The Blending Problem
8.3.1 Problem Formulation
8.3.2 Simulations and Results
8.4 Summary
Notations
Chapter 9 The Environmental Trading Problem
9.1 Introduction
9.2 Basics of Pollutant Trading
9.3 Christina Watershed Nutrient Management
9.4 Trading Problem Formulation
9.5 Results
9.6 Summary
Notations
Chapter 10 Water Security Networks
10.1 Introduction
10.2 Motivation and Prior Work
10.3 Solution Methodology
10.3.1 Use of BONUS Reweighting for Pattern Estimation
10.3.2 Back Estimation of Flow Patterns
10.4 Results
10.5 Summary
Notations
References
Index
