Operations Research and Optimization

  1. Heuristics and Metaheuristics
    1. Introduction to Heuristics
      1. Heuristic Definition
        1. Motivation for Heuristics
          1. Computational Complexity
            1. Time Constraints
              1. Solution Quality Trade-offs
              2. Types of Heuristics
                1. Construction Heuristics
                  1. Improvement Heuristics
                    1. Hybrid Approaches
                    2. Performance Evaluation
                      1. Solution Quality
                        1. Computational Time
                          1. Approximation Ratios
                        2. Classical Heuristics
                          1. Greedy Algorithms
                            1. Greedy Strategy
                              1. Local Optimization
                                1. Limitations
                                2. Local Search Methods
                                  1. Neighborhood Structures
                                    1. Local Optima
                                      1. Hill Climbing
                                        1. Steepest Descent
                                          1. First Improvement
                                            1. Best Improvement
                                            2. Construction Heuristics
                                              1. Nearest Neighbor
                                                1. Savings Algorithm
                                                  1. Insertion Methods
                                                2. Metaheuristic Frameworks
                                                  1. Trajectory-Based Methods
                                                    1. Single Solution Evolution
                                                      1. Neighborhood Exploration
                                                        1. Escape Mechanisms
                                                        2. Population-Based Methods
                                                          1. Multiple Solution Management
                                                            1. Information Exchange
                                                              1. Diversity Maintenance
                                                              2. Hybrid Metaheuristics
                                                                1. Method Combination
                                                                  1. Complementary Strengths
                                                                2. Simulated Annealing
                                                                  1. Algorithm Framework
                                                                    1. Temperature Parameter
                                                                      1. Cooling Schedule
                                                                        1. Acceptance Probability
                                                                        2. Implementation Details
                                                                          1. Initial Temperature
                                                                            1. Cooling Rate
                                                                              1. Stopping Criteria
                                                                              2. Parameter Tuning
                                                                                1. Temperature Schedule Design
                                                                                  1. Neighborhood Design
                                                                                  2. Applications
                                                                                    1. Combinatorial Optimization
                                                                                      1. Continuous Optimization
                                                                                    2. Tabu Search
                                                                                      1. Basic Concepts
                                                                                        1. Tabu List
                                                                                          1. Forbidden Moves
                                                                                            1. Memory Structures
                                                                                            2. Advanced Features
                                                                                              1. Aspiration Criteria
                                                                                                1. Intensification
                                                                                                  1. Diversification
                                                                                                    1. Long-term Memory
                                                                                                    2. Implementation Issues
                                                                                                      1. Tabu Tenure
                                                                                                        1. Candidate List Strategies
                                                                                                          1. Stopping Criteria
                                                                                                        2. Genetic Algorithms
                                                                                                          1. Evolutionary Concepts
                                                                                                            1. Population
                                                                                                              1. Chromosomes
                                                                                                                1. Genes
                                                                                                                  1. Fitness
                                                                                                                  2. Genetic Operators
                                                                                                                    1. Selection Methods
                                                                                                                      1. Roulette Wheel Selection
                                                                                                                        1. Tournament Selection
                                                                                                                          1. Rank-Based Selection
                                                                                                                          2. Crossover Operators
                                                                                                                            1. Single-Point Crossover
                                                                                                                              1. Multi-Point Crossover
                                                                                                                                1. Uniform Crossover
                                                                                                                                2. Mutation Operators
                                                                                                                                  1. Bit Flip Mutation
                                                                                                                                    1. Swap Mutation
                                                                                                                                      1. Inversion Mutation
                                                                                                                                    2. Algorithm Parameters
                                                                                                                                      1. Population Size
                                                                                                                                        1. Crossover Rate
                                                                                                                                          1. Mutation Rate
                                                                                                                                            1. Selection Pressure
                                                                                                                                            2. Representation Issues
                                                                                                                                              1. Binary Encoding
                                                                                                                                                1. Real-Valued Encoding
                                                                                                                                                  1. Permutation Encoding
                                                                                                                                                2. Swarm Intelligence
                                                                                                                                                  1. Ant Colony Optimization
                                                                                                                                                    1. Ant Behavior Model
                                                                                                                                                      1. Pheromone Trails
                                                                                                                                                        1. Probabilistic Solution Construction
                                                                                                                                                          1. Pheromone Update Rules
                                                                                                                                                            1. Evaporation Mechanism
                                                                                                                                                            2. Particle Swarm Optimization
                                                                                                                                                              1. Particle Representation
                                                                                                                                                                1. Velocity Updates
                                                                                                                                                                  1. Position Updates
                                                                                                                                                                    1. Social and Cognitive Components
                                                                                                                                                                      1. Inertia Weight
                                                                                                                                                                        1. Neighborhood Topologies
                                                                                                                                                                        2. Other Swarm Methods
                                                                                                                                                                          1. Bee Colony Optimization
                                                                                                                                                                            1. Firefly Algorithm
                                                                                                                                                                          2. Multi-Objective Metaheuristics
                                                                                                                                                                            1. Pareto Optimality
                                                                                                                                                                              1. Dominance Relations
                                                                                                                                                                                1. Pareto Front
                                                                                                                                                                                  1. Non-Dominated Solutions
                                                                                                                                                                                  2. Multi-Objective Genetic Algorithms
                                                                                                                                                                                    1. NSGA-II
                                                                                                                                                                                      1. SPEA2
                                                                                                                                                                                        1. MOEA/D
                                                                                                                                                                                        2. Performance Metrics
                                                                                                                                                                                          1. Convergence Metrics
                                                                                                                                                                                            1. Diversity Metrics
                                                                                                                                                                                              1. Hypervolume Indicator

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                                                                                                                                                                                          10. Decision Analysis

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                                                                                                                                                                                          12. Advanced Optimization Topics