Optimization Theory

10.

Heuristic and Metaheuristic Methods

10.1.

Local Search Algorithms

10.1.1.

10.1.1.1.

Steepest Ascent

10.1.1.2.

First Improvement

10.1.1.3.

10.1.2.

Simulated Annealing

10.1.2.1.

Cooling Schedules

10.1.2.2.

Acceptance Probability

10.1.2.3.

Parameter Tuning

10.1.3.

10.1.3.1.

Tabu List Management

10.1.3.2.

Aspiration Criteria

10.1.3.3.

Intensification and Diversification

10.1.4.

Variable Neighborhood Search

10.2.

Population-Based Metaheuristics

10.2.1.

Genetic Algorithms

10.2.1.1.

Representation and Encoding

10.2.1.2.

Selection Mechanisms

10.2.1.2.1.

Tournament Selection

10.2.1.2.2.

Roulette Wheel Selection

10.2.1.2.3.

Rank-Based Selection

10.2.1.3.

Crossover Operators

10.2.1.3.1.

Single-Point Crossover

10.2.1.3.2.

Multi-Point Crossover

10.2.1.3.3.

Uniform Crossover

10.2.1.4.

Mutation Operators

10.2.1.5.

Replacement Strategies

10.2.2.

Evolution Strategies

10.2.2.1.

(μ + λ) and (μ, λ) Strategies

10.2.2.2.

Self-Adaptation

10.2.2.3.

Covariance Matrix Adaptation

10.2.3.

Particle Swarm Optimization

10.2.3.1.

Velocity and Position Updates

10.2.3.2.

10.2.3.3.

Acceleration Coefficients

10.2.3.4.

Topology and Neighborhoods

10.2.4.

Ant Colony Optimization

10.2.4.1.

Pheromone Trail Updates

10.2.4.2.

Heuristic Information

10.2.4.3.

Ant System Variants

10.2.5.

Differential Evolution

10.2.5.1.

Mutation and Crossover

10.2.5.2.

Parameter Control

10.3.

Hybrid Approaches

10.3.1.

Memetic Algorithms

10.3.2.

10.3.3.

Large Neighborhood Search

10.3.4.

Variable Neighborhood Descent

10.4.

Performance Analysis

10.4.1.

Convergence Properties

10.4.2.

Parameter Sensitivity

10.4.3.

Benchmarking and Comparison

10.4.4.

No Free Lunch Theorems

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11. Multi-Objective Optimization