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Preface; Contents; 1 Foundations of Random-Like Bi-Level Decision Making; 1.1 Random Sets Theory; 1.1.1 General Concepts; Measure Space; Outer Measures; Probability Space; Product Probability Space; Conditional Probability and Independence; Probability Distribution; 1.1.2 Random Variable; Discrete Random Variable; Continuous Random Variable; Random Vector; 1.1.3 Fuzzy Variable; 1.1.4 Ra-Ra Variable; Discrete Ra-Ra Variable; Continuous Ra-Ra Variable; 1.1.5 Ra-Fu Variable; Discrete Ra-Fu Variable; Continuous Ra-Fu Variable; 1.2 Bi-Level Programming; 1.2.1 Linear Bi-Level Programming
1.2.2 Nonlinear Bi-Level Programming1.2.3 Complexity and Optimality Conditions; 1.2.4 Traditional Methods; KKT Approach; Brand-and-Bound; Penalty Function; Interactive Programming Method; 1.2.5 Developments of Algorithms; 1.3 Synthetical Analysis of Literature; References; 2 Bi-Level Decision Making in Random Phenomenon; 2.1 Regional Water Resources Allocation Problem; 2.1.1 Random Phenomenon; 2.1.2 Bi-Level Description; 2.2 Bi-Level Decision Making Models with Random Coefficients; 2.3 Random EEEE Model; 2.3.1 General Form of Random EEEE Model; 2.3.2 Reference Point Method for Linear Models
2.3.3 Genetic Approach for Nonlinear ModelsRandom Simulation 1 for Expected Value; Goal Programming Method; RWGA; Numerical Example; 2.4 Random CECC Model; 2.4.1 General Form of Random CECC Model; 2.4.2 KKT Method for Linear Model; KKT Method; Numerical Example; 2.4.3 Genetic Algorithm for Nonlinear Model; E-Constraint Method; Random Simulation for Critical Values; EBS-Based GA; Numerical Example; 2.5 Random DEDC Model; 2.5.1 General Form of Random DEDC Model; 2.5.2 Interactive Fuzzy Goal Programming for Linear Model; Interactive Fuzzy Goal Programming Approach; Numerical Example
2.5.3 Random Simulation-Based BPMOGA for Nonlinear ModelRandom Simulation for Probability; Two-Stage Method; BPMOGA; Numerical Example; 2.6 Regional Water Resources Allocation Problem in the Gan-Fu Plain; 2.6.1 Modelling; Assumptions; Lower Level Model for Water Allocation Problems in Sub-areas; Upper Level Model for Water Allocation Problem in the Overall Region; Global Model; 2.6.2 Presentation of the Case Problem; 2.6.3 Parameter Selection for EBS-Based GA; 2.6.4 Results and Discussion; References; 3 Bi-Level Decision Making in Ra-Ra Phenomenon ; 3.1 Transport Flow Distribution Problem
3.1.1 Ra-Ra Phenomenon3.1.2 Bi-Level Description; 3.2 Bi-Level Decision Making Model with Ra-Ra Coefficients; 3.3 Ra-Ra EEDE Model; 3.3.1 General Form of Ra-Ra EEDE Model; 3.3.2 The Steepest Descent Direction Method for Linear Model; Crisp Equivalent Model; The Steepest Descent Direction Method; Numerical Example; 3.3.3 Ra-Ra Simulation-Based PSO for Nonlinear Models; Ra-Ra Simulation for Expected Value and Chance; Lexicographic Method; C-PSO; Numerical Example; 3.4 Ra-Ra ECEC Model; 3.4.1 General Form of Ra-Ra ECEC Model; 3.4.2 A Homotopy Method for Linear Model; Homotopy Method
1.2.2 Nonlinear Bi-Level Programming1.2.3 Complexity and Optimality Conditions; 1.2.4 Traditional Methods; KKT Approach; Brand-and-Bound; Penalty Function; Interactive Programming Method; 1.2.5 Developments of Algorithms; 1.3 Synthetical Analysis of Literature; References; 2 Bi-Level Decision Making in Random Phenomenon; 2.1 Regional Water Resources Allocation Problem; 2.1.1 Random Phenomenon; 2.1.2 Bi-Level Description; 2.2 Bi-Level Decision Making Models with Random Coefficients; 2.3 Random EEEE Model; 2.3.1 General Form of Random EEEE Model; 2.3.2 Reference Point Method for Linear Models
2.3.3 Genetic Approach for Nonlinear ModelsRandom Simulation 1 for Expected Value; Goal Programming Method; RWGA; Numerical Example; 2.4 Random CECC Model; 2.4.1 General Form of Random CECC Model; 2.4.2 KKT Method for Linear Model; KKT Method; Numerical Example; 2.4.3 Genetic Algorithm for Nonlinear Model; E-Constraint Method; Random Simulation for Critical Values; EBS-Based GA; Numerical Example; 2.5 Random DEDC Model; 2.5.1 General Form of Random DEDC Model; 2.5.2 Interactive Fuzzy Goal Programming for Linear Model; Interactive Fuzzy Goal Programming Approach; Numerical Example
2.5.3 Random Simulation-Based BPMOGA for Nonlinear ModelRandom Simulation for Probability; Two-Stage Method; BPMOGA; Numerical Example; 2.6 Regional Water Resources Allocation Problem in the Gan-Fu Plain; 2.6.1 Modelling; Assumptions; Lower Level Model for Water Allocation Problems in Sub-areas; Upper Level Model for Water Allocation Problem in the Overall Region; Global Model; 2.6.2 Presentation of the Case Problem; 2.6.3 Parameter Selection for EBS-Based GA; 2.6.4 Results and Discussion; References; 3 Bi-Level Decision Making in Ra-Ra Phenomenon ; 3.1 Transport Flow Distribution Problem
3.1.1 Ra-Ra Phenomenon3.1.2 Bi-Level Description; 3.2 Bi-Level Decision Making Model with Ra-Ra Coefficients; 3.3 Ra-Ra EEDE Model; 3.3.1 General Form of Ra-Ra EEDE Model; 3.3.2 The Steepest Descent Direction Method for Linear Model; Crisp Equivalent Model; The Steepest Descent Direction Method; Numerical Example; 3.3.3 Ra-Ra Simulation-Based PSO for Nonlinear Models; Ra-Ra Simulation for Expected Value and Chance; Lexicographic Method; C-PSO; Numerical Example; 3.4 Ra-Ra ECEC Model; 3.4.1 General Form of Ra-Ra ECEC Model; 3.4.2 A Homotopy Method for Linear Model; Homotopy Method