BONUS Algorithm for Large Scale Stochastic Nonlinear Programming Problems

1. Front Matter

   Pages i-xviii

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2. Introduction

   • Urmila Diwekar, Amy David

   Pages 1-7

3. Uncertainty Analysis and Sampling Techniques

   • Urmila Diwekar, Amy David

   Pages 9-25

4. Probability Density Functions and Kernel Density Estimation

   • Urmila Diwekar, Amy David

   Pages 27-34

5. The BONUS Algorithm

   • Urmila Diwekar, Amy David

   Pages 35-56

6. Water Management Under Weather Uncertainty

   • Urmila Diwekar, Amy David

   Pages 57-66

7. Real-Time Optimization forWater Management

   • Urmila Diwekar, Amy David

   Pages 67-79

8. Sensor Placement Under Uncertainty for Power Plants

   • Urmila Diwekar, Amy David

   Pages 81-94

9. The L-Shaped BONUS Algorithm

   • Urmila Diwekar, Amy David

   Pages 95-115

10. The Environmental Trading Problem

    • Urmila Diwekar, Amy David

    Pages 117-126

11. Water Security Networks

    • Urmila Diwekar, Amy David

    Pages 127-137

12. Back Matter

    Pages 139-146

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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.

• BONUS algorithm
• SNLP
• Stochastic Programming
• power systems
• sensor placement
• water management

“The authors try to introduce and give a survey of two types of solution algorithms: the BONUS (Better Optimization of Nonlinear Uncertain System) algorithm and the L-shaped BONUS algorithm. … the text is written in an understandable way and it should prove useful to specialists from different fields of investigation.” (Vlasta Kaňková, Mathematical Reviews, May, 2016)

• Clarendon Hills, USA

  Urmila Diwekar

• Krennert School of Business, Purdue University, West Lafayette, USA

  Amy David

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