๐ Local Search & Metaheuristics Overview
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# ๐ Local Search & Metaheuristics Overview ## 1. ๐ฏ Learning Objectives - Compare iterated, stochastic, and random-restart hill climbing - Explain how VND uses multiple neighborhood structures - Choose appropriate metaheuristic for problem type ## 2.
๐ Local Search & Metaheuristics Overview
1. ๐ฏ Learning Objectives
- Compare iterated, stochastic, and random-restart hill climbing
- Explain how VND uses multiple neighborhood structures
- Choose appropriate metaheuristic for problem type
2. ๐ Core Content
3.1 Iterated Hill Climbing
Run HC multiple times from random starts, keep best result.
3.2 Stochastic Hill Climbing
Randomly select among improving neighbors (not just the best). Adds randomness to escape local optima.
3.3 Variable Neighborhood Descent (VND)
Switch neighborhoods systematically: Nโ, Nโ, ..., Nโ. If no improvement in Nแตข, try Nแตขโโ. Example for TSP: Nโ=2-opt, Nโ=3-opt, Nโ=Or-opt.
3.4 Metaheuristic Comparison
| Method | Escapes Local Optima? | Memory | Complexity |
|---|---|---|---|
| Hill Climbing | No | O(1) | Fast |
| Random Restart | Partially | O(1) | Moderate |
| Simulated Annealing | Yes | O(1) | Slow |
| Tabu Search | Yes | O(k) | Moderate |
| VND | Partially | O(1) | Moderate |