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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


Papers
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Journal ArticleDOI
TL;DR: This paper considers a stochastic integer programming model for the airline crew scheduling problem and develops a branching algorithm to identify expensive flight connections and find alternative solutions that better withstand disruptions.
Abstract: Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modeling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution methodology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects are minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and develop a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the problem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm.

195 citations

Book
01 Jan 2003
TL;DR: An attempt is made to describe the theoretical prop- erties of several stochastic adaptive search methods, which may allow us to better predict algorithm performance and ultimately design new and improved algorithms.
Abstract: The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these other publications with a focus on stochastic methods for global optimization. Stochastic methods, such as simulated annealing and genetic algo- rithms, are gaining in popularity among practitioners and engineers be- they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems. However, the theoretical performance of these stochastic methods is not well under- stood. In this book, an attempt is made to describe the theoretical prop- erties of several stochastic adaptive search methods. Such a theoretical understanding may allow us to better predict algorithm performance and ultimately design new and improved algorithms. This book consolidates a collection of papers on the analysis and de- velopment of stochastic adaptive search. The first chapter introduces random search algorithms. Chapters 2-5 describe the theoretical anal- ysis of a progression of algorithms. A main result is that the expected number of iterations for pure adaptive search is linear in dimension for a class of Lipschitz global optimization problems. Chapter 6 discusses algorithms, based on the Hit-and-Run sampling method, that have been developed to approximate the ideal performance of pure random search. The final chapter discusses several applications in engineering that use stochastic adaptive search methods.

195 citations

Journal ArticleDOI
TL;DR: A Historical Sketch on Sensitivity Analysis and Parametric Programming T.J. Greenberg and the Optimal Set and Optimal Partition Approach.
Abstract: Foreword. Preface. 1. A Historical Sketch on Sensitivity Analysis and Parametric Programming T. Gal. 2. A Systems Perspective: Entity Set Graphs H. Muller-Merbach. 3. Linear Programming 1: Basic Principles H.J. Greenberg. 4. Linear Programming 2: Degeneracy Graphs T. Gal. 5. Linear Programming 3: The Tolerance Approach R.E. Wendell. 6. The Optimal Set and Optimal Partition Approach A.B. Berkelaar, et al. 7. Network Models G.L. Thompson. 8. Qualitative Sensitivity Analysis A. Gautier, et al. 9. Integer and Mixed-Integer Programming C. Blair. 10. Nonlinear Programming A.S. Drud, L. Lasdon. 11. Multi-Criteria and Goal Programming J. Dauer, Yi-Hsin Liu. 12. Stochastic Programming and Robust Optimization H. Vladimirou, S.A. Zenios. 13. Redundancy R.J. Caron, et al. 14. Feasibility and Viability J.W. Chinneck. 15. Fuzzy Mathematical Programming H.-J. Zimmermann. Subject Index.

195 citations

Journal ArticleDOI
TL;DR: This work provides an overview of Enterprise-wide Optimization in terms of a mathematical programming framework, and describes several applications to show the potential of this area.

194 citations

Proceedings ArticleDOI
26 Jul 2009
TL;DR: This paper proposes a methodology to determine the required level of spinning and nonspinning reserves in a power system with a high penetration of wind power through a stochastic programming market-clearing model spanning a daily time horizon.
Abstract: This paper proposes a methodology to determine the required level of spinning and non-spinning reserves in a power system with a high penetration of wind power. The computation of the required reserve levels and their costs is achieved through a stochastic programming market-clearing model spanning a daily time horizon. This model considers the network constraints and takes into account the cost of both the load shedding and the wind spillage. The methodology proposed is illustrated using an example and a realistic case study. Some conclusions are finally drawn.

194 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532