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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
7.
Integer and Combinatorial Optimization
7.1.
Problem Formulations
7.1.1.
Pure Integer Programming
7.1.2.
Mixed-Integer Linear Programming (MILP)
7.1.3.
Mixed-Integer Nonlinear Programming (MINLP)
7.1.4.
Binary Integer Programming
7.1.5.
Combinatorial Optimization Problems
7.2.
Solution Methodologies
7.2.1.
Enumeration Methods
7.2.1.1.
Complete Enumeration
7.2.1.2.
Branch and Bound
7.2.1.2.1.
Branching Strategies
7.2.1.2.2.
Bounding Techniques
7.2.1.2.3.
Node Selection Rules
7.2.1.2.4.
Pruning Conditions
7.2.2.
Cutting Plane Methods
7.2.2.1.
Gomory Cuts
7.2.2.2.
Chvátal-Gomory Cuts
7.2.2.3.
Lift-and-Project Cuts
7.2.2.4.
Disjunctive Cuts
7.2.3.
Branch and Cut
7.2.3.1.
Integration of Branching and Cutting
7.2.3.2.
Cut Generation Strategies
7.2.3.3.
Preprocessing Techniques
7.3.
Specialized Integer Programming Topics
7.3.1.
Knapsack Problems
7.3.1.1.
0-1 Knapsack Problem
7.3.1.2.
Unbounded Knapsack Problem
7.3.1.3.
Multiple Knapsack Problems
7.3.2.
Set Covering and Packing Problems
7.3.3.
Traveling Salesman Problem
7.3.4.
Network Flow Problems with Integer Variables
7.4.
Approximation Algorithms
7.4.1.
Performance Guarantees
7.4.2.
Greedy Algorithms
7.4.3.
Local Search Approximations
7.4.4.
Randomized Algorithms
7.5.
Computational Complexity
7.5.1.
NP-Completeness
7.5.2.
Polynomial-Time Approximation Schemes
7.5.3.
Fixed-Parameter Tractability
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8. Dynamic Programming