A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs [electronic resource] : With Application in Energy Production /
Mahlke, Debora.author.
Optimization problems involving uncertain data arise in many areas of industrial and economic applications. Stochastic programming provides a useful framework for modeling and solving optimization problems for which a probability distribution of the unknown parameters is available. Motivated by practical optimization problems occurring in energy systems with regenerative energy supply, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer models. For their solution, the author proposes a novel decomposition approach which relies on the concept of splitting the underlying scenario tree into subtrees. Based on the formulated models from energy production, the algorithm is computationally investigated and the numerical results are discussed.
Description based upon print version of record.
Acknowledgments; Abstract; Contents; List of Figures; List of Tables; Chapter 1 Overview; Chapter 2 An Energy Production Problem; 2.1 Introduction; 2.2 Problem Description; 2.3 Technical Background; 2.3.1 Fossil-Fuel Power Plants; 2.3.2 Energy Storages; 2.4 Related Literature; Chapter 3 Mathematical Modeling; 3.1 Deterministic Model; 3.1.1 Sets and Parameters; 3.1.2 Variables and E ciency Functions; 3.1.3 Constraints; 3.1.4 Objective Function; 3.1.5 Linearization of the Nonlinear Functions; 3.1.6 The D-OPGen Model; 3.2 Stochastic Model; 3.2.1 Basic Concepts in Stochastic Programming
3.2.2 The S-OPGen ModelChapter 4 Polyhedral Study of Stochastic Switching Polytopes; 4.1 Mathematical Formulation; 4.2 Literature Overview; 4.3 Polyhedral Investigations; 4.4 Separation; Chapter 5 Primal Heuristics; 5.1 Relax-and-Fix; 5.2 A Rolling Horizon Approach to the D-OP Gen Problem; 5.2.1 Approximation Strategies; 5.2.2 Feasibility; 5.3 An Approximate-and-Fix Approach to the S-OPGen Problem; Chapter 6 A Scenario Tree-Based Decomposition of Multistage Stochastic Mixed-Integer Problems; 6.1 Motivation and Idea; 6.2 Reformulation and Decomposition of the Stochastic Problem
6.3 A Scenario Tree-Based Decomposition Combined with Branch-and-Bound6.4 Improving SD-BB by Applying Lagrangian Relaxation; 6.4.1 Lagrangian Relaxation of Coupling Constraints; 6.4.2 Integration of Lagrangian Relaxation into the SD-BB Algorithm; Chapter 7 Algorithmic Implementation; 7.1 Decomposing a Scenario Tree; 7.1.1 Finding an Optimal K-Subdivision; 7.1.2 Rearranging an Optimal K-Subdivision; 7.2 Branching; 7.2.1 Variable Selection; 7.2.2 Branching on Continuous Variables; 7.3 Computing Lower Bounds; 7.3.1 Generation of a First Lower Bound
7.3.2 Caching of Subproblems for the Computation of Lower Bounds7.4 Computing Feasible Solutions; 7.4.1 Primal Start Solution; 7.4.2 Primal Solutions Based on Local Information; Chapter 8 Computational Results; 8.1 Test Instances; 8.1.1 Facilities in the Power Generation System; 8.1.2 Stochastic Data; 8.1.3 Test Instances for Parameter Tuning; 8.2 Separation; 8.3 Heuristics; 8.3.1 Rolling Horizon Algorithm; 8.3.2 Approximate-and-Fix Heuristic; 8.4 SD-BB Algorithm; 8.4.1 Decomposing the Scenario Tree; 8.4.2 Computing a First Lower Bound; 8.4.3 Heuristics; 8.4.4 Branching; 8.4.5 Accuracy
8.4.6 Solving Large InstancesChapter 9 Conclusions; Bibliography; Akademischer Werdegang
Includes bibliographical references (p. [175]-182).
Optimization problems involving uncertain data arise in many areas of industrial and economic applications. Stochastic programming provides a useful framework for modeling and solving optimization problems for which a probability distribution of the unknown parameters is available. Motivated by practical optimization problems occurring in energy systems with regenerative energy supply, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer models. For their solution, the author proposes a novel decomposition approach which relies on the concept of splitting the underlying scenario tree into subtrees. Based on the formulated models from energy production, the algorithm is computationally investigated and the numerical results are discussed.
Probabilities.
Mathematics.
Probability Theory and Stochastic Processes.
Mathematics, general.