Optimization Theory

  1. Multi-Objective Optimization
    1. Fundamental Concepts
      1. Pareto Dominance
        1. Pareto Optimality
          1. Pareto Set and Pareto Front
            1. Ideal and Nadir Points
              1. Utopia Point
              2. Scalarization Approaches
                1. Weighted Sum Method
                  1. ε-Constraint Method
                    1. Goal Programming
                      1. Achievement Scalarizing Functions
                        1. Reference Point Methods
                        2. Interactive Methods
                          1. Progressive Articulation of Preferences
                            1. NIMBUS Method
                              1. Reference Direction Approach
                                1. Satisficing Trade-Off Method
                                2. Evolutionary Multi-Objective Optimization
                                  1. NSGA-II (Non-Dominated Sorting Genetic Algorithm)
                                    1. SPEA2 (Strength Pareto Evolutionary Algorithm)
                                      1. MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition)
                                        1. Performance Metrics
                                          1. Hypervolume
                                            1. Inverted Generational Distance
                                              1. Spread Metrics
                                            2. Many-Objective Optimization
                                              1. Challenges with High-Dimensional Objectives
                                                1. Dimensionality Reduction Techniques
                                                  1. Preference-Based Approaches
                                                  2. Decision Making
                                                    1. Multi-Criteria Decision Analysis
                                                      1. Preference Elicitation
                                                        1. Trade-Off Analysis
                                                          1. Robust Decision Making

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                                                        10. Heuristic and Metaheuristic Methods

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                                                        12. Specialized Optimization Topics