href="#ulink_3c584c75-ce99-5991-9312-dc83478a0e57">11 Optimization under Uncertainty11.1 Stochastic Programming (SP)11.1.1 Two-stage Stochastic Linear Programs with Fixed Recourse11.1.2 Multi-stage Stochastic Programs with Recourse11.2 Chance-Constrained Programming11.2.1 Model and Properties11.2.2 Example11.3 Robust Optimization (RO)11.3.1 Uncertain Linear Optimization (LO) and its Robust Counterparts11.3.2 Tractability of Robust Counterparts11.3.3 Robust Optimization (RO) with Cardinality Constrained Uncertainty Set11.3.4 Example11.4 ExercisesReferences12 Applications12.1 Multi-objective Optimization (MOO) Framework for the Integration of Distributed Renewable Generation and Storage12.1.1 Description of Distributed Generation (DG) System12.1.2 Optimal Power Flow (OPF)12.1.3 Performance Indicators12.1.4 MOO Problem Formulation12.1.5 Solution Approach and Case Study Results12.2 Redundancy Allocation for Binary-State Series-Parallel Systems (BSSPSs) under Epistemic Uncertainty12.2.1 Problem Description12.2.2 Robust Model12.2.3 ExperimentReferences14 Index
List of Illustrations
1 Chapter 1Figure 1.1 The pmf of the binomial...Figure 1.2 The pmf of the Poisson...Figure 1.3 The pdf of the exponential...Figure 1.4 The pdf of the Weibull...Figure 1.5 The pdf of the gamma...Figure 1.6 The pdf of the lognormal...Figure 1.7 Illustration of Paris...Figure 1.8 Reliability block diagram...Figure 1.9 Reliability block diagram...Figure 1.10 Reliability block diagram...Figure 1.11 Bridge system.Figure 1.12 Block decision diagram...Figure 1.13 Electrical generating system.Figure 1.14 Reliability block diagram...Figure 1.15 Diagram of the power grid...Figure 1.16 Reliability block diagram...
2 Chapter 2Figure 2.1 Example for the search tree...Figure 2.2 Shortest...
3 Chapter 4Figure 4.1 The Markov Diagram of the...Figure 4.2 The Markov Diagram of the...Figure 4.3 Degradation Process of...Figure 4.4 Sample Path of...Figure 4.5 A Three-state semi-Markov...Figure 4.6 An illustrative example of a system...Figure 4.7 The Evolution of Degradation Processes...Figure 4.8 The Diagram of the Series-parallel...Figure 4.9 State Transition Diagram for...
4 Chapter 5Figure 5.1 comparison between inverse sampling...Figure 5.2 Distribution obtained by...Figure 5.3 State distribution...Figure 5.4 Markov jump process...Figure 5.5 M-H samplingFigure 5.6 Sampling with Gibbs...Figure 5.7 Sampling with Multiple-try...
5 Chapter 6Figure 6.1 (a). A non-normal convex fuzzy...Figure 6.2 Possibility distribution...Figure 6.3 Three-dimensional and two-dimensional...
6 Chapter 7Figure 7.1 Conceptual diagram of the representative...Figure 7.2 Comparison of joint propagation...Figure 7.4 Comparison of joint propagation...Figure 7.3 Comparison of joint propagation...Figure 7.5 Transition diagram of the multi-state...Figure 7.6 Convergence plots of state...
7 Chapter 8Figure 8.1 Graphical solution to the...Figure 8.2 Search tree.Figure 8.3 The search tree...Figure 8.4 The search tree...
8 Chapter 9Figure 9.1 Example of binary...Figure 9.2 Example of tree-based...Figure 9.3 Swap operator for...Figure 9.4 One example of tree-based...Figure 9.5 Single-point crossoverFigure 9.6 Two-point crossover....Figure 9.7 Uniform crossover.Figure 9.8 Example of Order 1 crossover.Figure 9.9 Example of crossover for...
9 Chapter 10Figure 10.1 Pareto dominance and...Figure 10.2 Fast non-dominance sorting...Figure 10.3 An example of crowding distance.Figure 10.4 An example of generational...Figure 10.5 An example of computing spacing.Figure 10.6 An example of illustration...Figure 10.7 Best-compromise solution...Figure 10.8 Illustration of the compromise Min-Max...
10 Chapter 12Figure 12.1 Example of distribution generation...Figure 12.2 Graphical representation...Figure 12.3 Flow chart of NSGA-II...Figure 12.4 Pareto fronts for different...Figure 12.5 EENS v/s ECg [4].Figure 12.6 Violation probabilities...Figure 12.7 Change percentage in...
List of Tables
1 Chapter 4Table 4.1 Results for the degradation mode...
2 Chapter 7Table 7.1 Different uncertainties of the energy...Table 7.2 Case study parameter definitions and...Table 7.3 Comparison of the simulation results...
3 Chapter 10Table 10.1 Payoff Table of the MOO problem...Table 10.2 Steps of fast non-dominance sorting...Table 10.3 Example of removal iterations.
4 Chapter 11Table 11.1 The cost ($) of different maintenance...Table 11.2 Tractable RC representations
Guide
1 Cover
6 Table of Contents
8 Preface
11 Notations
13 Index
Pages
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2 ii
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4 iv
5 v
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