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Systems Science
Optimization Theory
1. Foundations of Optimization
2. Mathematical Foundations
3. Unconstrained Optimization
4. Constrained Optimization Theory
5. Linear Programming
6. Nonlinear Programming
7. Integer and Combinatorial Optimization
8. Dynamic Programming
9. Stochastic Optimization
10. Heuristic and Metaheuristic Methods
11. Multi-Objective Optimization
12. Specialized Optimization Topics
13. Applications and Case Studies
14. Computational Aspects and Software
11.
Multi-Objective Optimization
11.1.
Fundamental Concepts
11.1.1.
Pareto Dominance
11.1.2.
Pareto Optimality
11.1.3.
Pareto Set and Pareto Front
11.1.4.
Ideal and Nadir Points
11.1.5.
Utopia Point
11.2.
Scalarization Approaches
11.2.1.
Weighted Sum Method
11.2.2.
ε-Constraint Method
11.2.3.
Goal Programming
11.2.4.
Achievement Scalarizing Functions
11.2.5.
Reference Point Methods
11.3.
Interactive Methods
11.3.1.
Progressive Articulation of Preferences
11.3.2.
NIMBUS Method
11.3.3.
Reference Direction Approach
11.3.4.
Satisficing Trade-Off Method
11.4.
Evolutionary Multi-Objective Optimization
11.4.1.
NSGA-II (Non-Dominated Sorting Genetic Algorithm)
11.4.2.
SPEA2 (Strength Pareto Evolutionary Algorithm)
11.4.3.
MOEA/D (Multi-Objective Evolutionary Algorithm based on Decomposition)
11.4.4.
Performance Metrics
11.4.4.1.
Hypervolume
11.4.4.2.
Inverted Generational Distance
11.4.4.3.
Spread Metrics
11.5.
Many-Objective Optimization
11.5.1.
Challenges with High-Dimensional Objectives
11.5.2.
Dimensionality Reduction Techniques
11.5.3.
Preference-Based Approaches
11.6.
Decision Making
11.6.1.
Multi-Criteria Decision Analysis
11.6.2.
Preference Elicitation
11.6.3.
Trade-Off Analysis
11.6.4.
Robust Decision Making
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12. Specialized Optimization Topics